# Applied Physics and Applied Mathematics

200 S. W. Mudd, MC 4701

212-854-4457

Applied Physics and Applied Mathematics: apam.columbia.edu

Materials Science and Engineering: matsci.apam.columbia.edu

The Department of Applied Physics and Applied Mathematics includes undergraduate and graduate studies in the fields of applied physics, applied mathematics, and materials science and engineering. The graduate program in applied physics includes plasma physics and controlled fusion; solid-state physics; optical and laser physics and medical physics. The graduate program in applied mathematics includes research in applied analysis, data science, and atmospheric, oceanic, and earth physics. The graduate programs in materials science and engineering are described here.

## Current Research Activities in Applied Physics and Applied Mathematics

**Applied Physics.
Plasma physics and fusion energy.**

In experimental plasma physics, research is being conducted on:

- equilibrium, stability, and transport in fusion plasmas: high-beta tokamaks, spherical tokamaks, and levitated dipoles;
- magnetospheric physics: trapped particle instabilities and stochastic particle motion;
- confinement of toroidal nonneutral plasmas;
- plasma source operation and heating techniques; and
- the development of new plasma measurement techniques.

The results from our fusion science experiments are used as a basis for collaboration with large national and international experiments. For example, methods of active feedback control of plasma instability developed at Columbia University are guiding research on NSTX at the Princeton Plasma Physics Laboratory, on the DIII-D tokamak at General Atomics, and for the design of the next-generation burning plasma experiment, ITER. In theoretical plasma physics, research is conducted in the theory of plasma equilibrium and stability, active control of MHD instabilities, the kinetic theory of turbulence and transport, and the development of techniques based on the theory of general coordinates and dynamical systems. The work is applied to magnetic fusion, nonneutral and space plasmas.

**Optical and laser physics. **Active areas of research include inelastic light scattering in nanomaterials, optical diagnostics of film processing, flat optics, metasurfaces, nonlinear optics, ultrafast optoelectronics, photonic switching, optical physics of surfaces, laser-induced crystallization, and photon integrated circuits.

**Solid-state physics**. Research in solid-state physics covers nanoscience and nanoparticles, electronic transport and inelastic light scattering in low-dimensional correlated electron systems, heterostructure physics and applications, grain boundaries and interfaces, nucleation in thin films, molecular electronics, nanostructure analysis, and electronic structure calculations.

Applied physics is part of the Columbia Quantum Initiative. Research opportunities also exist within the Columbia Nano Initiative (CNI), including the NSF Materials Research Science and Engineering Center, which focuses on low dimensional materials.

**Applied mathematics.** Current research encompasses analytical and numerical analysis of deterministic and stochastic partial differential equations, large-scale scientific computation, fluid dynamics, dynamical systems and chaos, inverse problems, algorithms for data and learning, as well as applications to various fields of physical and biological sciences. The applications to physical science include quantum and condensed-matter physics, materials science, electromagnetics, optics, photonics, plasma physics, medical imaging, and the earth sciences, notably atmospheric, oceanic, and climate science, and solid earth geophysics (see below). Other applications include machine learning and biophysical modeling, e.g., collaborations with Columbia’s Data Science Institute (DSI), the Department of Systems Biology, and the Department of Statistics. Extensive collaborations exist with national climate research centers (the Geophysical Fluid Dynamics Laboratory and the National Center for Atmospheric Research) and with national laboratories of the U.S. Department of Energy, custodians of the nation’s most powerful supercomputers.

**Atmospheric, oceanic, and earth physics. **Current research focuses on the dynamics of the atmosphere and the ocean, climate modeling, cloud physics, radiation transfer, remote sensing, geophysical/geological fluid dynamics, and geochemistry. The department engages in ongoing research with the NASA Goddard Institute for Space Studies and the Lamont-Doherty Earth Observatory. Seven faculty members share appointments with the Department of Earth and Environmental Sciences.

In addition to the faculty and graduate students, many others participate in these projects, including full-time research faculty, faculty and students from other departments, and visiting scientists.

## Laboratory and Computational Facilities in Applied Physics and Applied Mathematics

The Plasma Physics Laboratory, founded in 1961, is one of the leading university laboratories for the study of plasma physics in the United States. There are four experimental facilities. The Columbia High-Beta Tokamak (HBT-EP) supports the national program to develop controlled fusion energy. It utilizes high voltage, pulsed power systems, and laser and magnetic diagnostics to study the properties of high-beta plasmas and the use of feedback stabilization to increase the achievable beta. A collaborative program with the Princeton Plasma Physics Laboratory and the DIII-D tokamak group at General Atomics is studying the properties of high-beta plasmas in order to maximize fusion power production in these large, neutral beam-heated tokamaks and spherical tori. The stellarator known as Columbia Nonneutral Torus (CNT) conducts research on the magnetohydrodynamic stability, microwave heating, and microwave diagnostics of neutral stellarator plasmas. Two smaller devices investigate, respectively, an innovative tokamak-stellarator hybrid plasma confinement concept and the use of toroidal electron-heated plasmas as sources of ions for accelerators.

Experimental research in solid-state physics and laser physics is conducted within the department and also in association with the Columbia Nano Initiative. Facilities include laser processing and spectroscopic apparatus, ultrahigh vacuum chambers for surface analysis, picosecond and femtosecond lasers, and a clean room that includes photo-lithography and thin film fabrication systems. Within this field, the Laser Diagnostics and Solid State Physics Laboratory conducts studies in laser spectroscopy of nanomaterials and semiconductor thin films, and laser diagnostics of thin film processing. The Laser Lab focuses on the study of laser surface chemical processing and new semiconductor structures. Research is also conducted in the shared characterization laboratories and clean room operated by CNI.

The department has a leadership role in development and support of Columbia Shared Computing resources and has access to multiple HPC clusters. In addition, the research of the Plasma Lab is supported by a dedicated data acquisition/data analysis system. Researchers in the department are additionally using supercomputing facilities at the National Center for Atmospheric Research; the San Diego Supercomputing Center; the National Energy Research Supercomputer Center in Berkeley, California; the National Leadership Class Facility at Oak Ridge, Tennessee; various allocations via ACCESS; and others. The Amazon Elastic Compute Cloud (EC2) is also utilized to supplement computing resources in times of high demand.

## Current Research Activities and Laboratory Facilities in Materials Science and Engineering

See Current Research Activities and Laboratory Facilities in Materials Science and Engineering.

## Chair

Marc W. Spiegelman

208 S. W. Mudd

## Department Administrator

Marri Davis

## Professors

Katayun Barmak

Daniel Bienstock, Industrial Engineering and Operations Research

Simon J. L. Billinge

Allen H. Boozer

Liliana Borcea

Mark A. Cane, Professor Emeritus, Earth and Environmental Sciences

Siu-Wai Chan

Qiang Du

Alexander Gaeta

Oleg Gang, Chemical Engineering

Irving P. Herman, Professor Emeritus

James S. Im

Michal Lipson, Electrical Engineering

Michael E. Mauel

Gerald A. Navratil

Ismail C. Noyan

Lorenzo M. Polvani, Earth and Environmental Sciences

Kui Ren

Christopher H. Scholz, Professor Emeritus, Earth and Environmental Sciences

Adam Sobel, Earth and Environmental Sciences

Marc W. Spiegelman, Earth and Environmental Sciences

Latha Venkataraman

Wen I. Wang, Electrical Engineering

Michael I. Weinstein

Renata M. Wentzcovitch

Cheng-Shie Wuu, Radiation Oncology

## Associate Professors

William E. Bailey

Chris A. Marianetti

Carlos Paz-Soldan

Michael K. Tippett

Chris H. Wiggins, Systems Biology

Yuan Yang

Nanfang Yu

## Assistant Professors

Aravind Devarakonda

Xuenan Li

Elizabeth Paul

Shanyin Tong

Xueyue (Sherry) Zhang

## Lecturer in Discipline

Drew Youngren

## Adjunct Professors

Zohaib Ahmad

Sean L. Berry

Peter F. Caracappa

C. Julian Chen

Stephen L. Ostrow

Boyu Peng

Marco Zaider

Pat Zanzonico

## Adjunct Associate Professors

Brian Cairns

Perry S. Gerard

Yuan He

Anastasia Romanou

Anna Rozenshtein

## Adjunct Assistant Professors

Sachin R. Jambawalikar

## Senior Research Scientists

Steven A. Sabbagh

## Adjunct Senior Research Scientists

John Marshall

Patricia Mooney

## Research Scientists

Jacek Chowdhary

Gregory Elsaesser

Igor Geogdzhayev

Christopher J. Hansen

Jeffrey Levesque

Nikolas C. Logan

Catherine Naud

## Associate Research Scientists

Mikhail Alexandrov

Alexander F. Battey

Robert Field

Jeremy Hanson

Paul Lerner

Nils Leuthold

A. Oak Nelson

Ian G. Stewart

Francesca Turco

Veronika Zamkovska

## Adjunct Associate Research Scientists

Gabriel Chiodo

## Postdoctoral Research Scientists

Kossi Pierre Amenoagbadji

Zhengqian Cheng

Sai Kanth Dacha

Bithi De

Vladimir Kobzar

Simon H. Lee

Kelsey Malloy

Zachary S. McGraw

James M. Scott

Yun Zhao

## Postdoctoral Research Fellows

Miriam Blau

Johan Wärnegård

## Special Lecturers

Monique C. Katz

## Course Descriptions

**AMCS E4302 PARALLEL SCI COMPUTING.** *3.00 points*.

**APAM E1601 Introduction to computational mathematics and physics.** *3 points*.

Lect: 3.**Not offered during 2023-2024 academic year.**

Introduction to computational methods in applied mathematics and physics. Students develop solutions in a small number of subject areas to acquire experience in the practical use of computers to solve mathematics and physics problems. Topics change from year to year. Examples include elementary interpolation of functions, solution of nonlinear algebraic equations, curve-fitting and hypothesis testing, wave propagation, fluid motion, gravitational and celestial mechanics, and chaotic dynamics. The basic requirement for this course is one year of college-level calculus and physics; programming experience is not required.

**APAM E3899 Research Training.** *0.00 points*.

Research training course. Recommended in preparation for laboratory related research

**APAM E3999 UNDERGRADUATE FIELDWORK.** *1.00-2.00 points*.

1-2 pts.

Prerequisites: Obtained internship and approval from faculty advisor.

May be repeated for credit, but no more than 3 total points may be used toward the 128credit degree requirement. Only for APAM undergraduate students who include relevant off-campus work experience as part of their approved program of study. Final report and letter of evaluation required. Fieldwork credits may not count toward any major core, technical, elective, and nontechnical requirements. May not be taken for pass/fail credit or audited

Spring 2024: APAM E3999 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APAM 3999 | 001/20720 | |
Adam Sobel | 1.00-2.00 | 1/5 |

Summer 2024: APAM E3999 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

APAM 3999 | 001/12898 | |
Qiang Du | 1.00-2.00 | 2/5 |

Fall 2024: APAM E3999 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

APAM 3999 | 001/21338 | |
Lorenzo Polvani | 1.00-2.00 | 2/5 |

**APAM E4114 Quantum and Nonlinear Photonics.** *3.00 points*.

Quantum and Nonlinear Photonics is an advanced senior-level/MS/PhD course that describes the interaction of laser light with matter in both the classical and quantum domains. The first half of the course introduces the microscopic origin of optical nonlinearities through formal derivation of the nonlinear susceptibilities, with emphasis on second- and third-order optical processes. These susceptibilities are incorporated into Maxwell's wave equation, and nonlinear optical processes such as second-harmonic, difference-frequency generation, four-wave mixing and self-phase modulation are described. Various applications of these processes are discussed including frequency conversion, and optical parametric amplifiers and oscillators. The second half of the course describes two-level atomic systems and quantization of the electromagnetic field. Descriptions of coherent, Fock, and squeezed states of light are discussed and techniques to generate such states are outlined

**APAM E4899 Research Training.** *0.00 points*.

Research training course. Recommended in preparation for laboratory related research

**APAM E4901 Seminar: Problems in Applied Mathematics.** *0 points*.

0 pts. Lect: 1.

This course is required for, and can be taken only by, all applied mathematics majors in the junior year. Prerequisites or corequisites: APMA E4200 and E4204 or their equivalents. Introductory seminars on problems and techniques in applied mathematics. Typical topics are nonlinear dynamics, scientific computation, economics, operations research, etc.

**APAM E4999 SUPERVISED INTERNSHIP.** *1.00-3.00 points*.

1-3 pts.

Only for masters students in the Department of Applied Physics and Applied Mathematics who may need relevant work experience a part of their program of study. Final report required. May not be taken for pass/fail or audited

Summer 2024: APAM E4999 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APAM 4999 | 001/12838 | |
Kui Ren | 1.00-3.00 | 2/7 |

Fall 2024: APAM E4999 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

APAM 4999 | 007/18874 | |
Klaus Hamacher | 1.00-3.00 | 2/3 |

**APAM E6650 RESEARCH PROJECT.** *1.00-6.00 points*.

May be repeated for credit. A special investigation of a problem in nuclear engineering, medical physics, applied mathematics, applied physics, and/or plasma physics consisting of independent work on the part of the student and embodied in a formal report

Spring 2024: APAM E6650 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APAM 6650 | 001/20722 | |
Dmitri Basov | 1.00-6.00 | 1/5 |

APAM 6650 | 002/20994 | |
Simon Billinge | 1.00-6.00 | 1/5 |

APAM 6650 | 006/20898 | |
Alexander Gaeta | 1.00-6.00 | 3/5 |

APAM 6650 | 012/20581 | |
Elizabeth Paul | 1.00-6.00 | 3/5 |

APAM 6650 | 013/17669 | |
Carlos Paz Soldan | 1.00-6.00 | 4/5 |

APAM 6650 | 014/17598 | |
Lorenzo Polvani | 1.00-6.00 | 1/5 |

APAM 6650 | 015/17765 | |
Kui Ren | 1.00-6.00 | 10/8 |

APAM 6650 | 022/20800 | |
Nanfang Yu | 1.00-6.00 | 3/5 |

APAM 6650 | 023/17679 | |
Steven Sabbagh | 1.00-6.00 | 1/5 |

Summer 2024: APAM E6650 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

APAM 6650 | 001/12837 | |
Nanfang Yu | 1.00-6.00 | 1/10 |

Fall 2024: APAM E6650 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

APAM 6650 | 001/21010 | |
Lorenzo Polvani | 1.00-6.00 | 1/5 |

APAM 6650 | 002/21011 | |
Adam Sobel | 1.00-6.00 | 1/5 |

APAM 6650 | 004/17548 | |
Aravind Devarakonda | 1.00-6.00 | 1/15 |

APAM 6650 | 007/19114 | |
Carlos Paz Soldan | 1.00-6.00 | 3/10 |

APAM 6650 | 008/21262 | |
Nanfang Yu | 1.00-6.00 | 1/5 |

APAM 6650 | 009/21102 | |
Michael Tippett | 1.00-6.00 | 1/10 |

APAM 6650 | 010/21170 | |
Alexander Gaeta | 1.00-6.00 | 1/10 |

**APAM E9301 DOCTORAL RESEARCH.** *0.00-15.00 points*.

0-15 pts.

Required of doctoral candidates

Spring 2024: APAM E9301 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APAM 9301 | 001/17565 | |
Dmitri Basov | 0.00-15.00 | 1/5 |

APAM 9301 | 002/17567 | |
Daniel Bienstock | 0.00-15.00 | 1/5 |

APAM 9301 | 007/17568 | |
Qiang Du | 0.00-15.00 | 5/5 |

APAM 9301 | 008/17569 | |
Alexander Gaeta | 0.00-15.00 | 6/8 |

APAM 9301 | 009/17570 | |
Oleg Gang | 0.00-15.00 | 0/5 |

APAM 9301 | 011/17571 | |
Michal Lipson | 0.00-15.00 | 4/5 |

APAM 9301 | 013/17572 | |
Michael Mauel | 0.00-15.00 | 3/5 |

APAM 9301 | 014/17573 | |
Gerald Navratil | 0.00-15.00 | 2/5 |

APAM 9301 | 015/17574 | |
Elizabeth Paul | 0.00-15.00 | 2/5 |

APAM 9301 | 016/17575 | |
Carlos Paz Soldan | 0.00-15.00 | 7/7 |

APAM 9301 | 017/17576 | |
Robert Pincus | 0.00-15.00 | 2/5 |

APAM 9301 | 018/17577 | |
Lorenzo Polvani | 0.00-15.00 | 0/5 |

APAM 9301 | 019/17578 | |
Kui Ren | 0.00-15.00 | 4/5 |

APAM 9301 | 020/17579 | |
Steven Sabbagh | 0.00-15.00 | 2/5 |

APAM 9301 | 021/17580 | |
Adam Sobel | 0.00-15.00 | 2/5 |

APAM 9301 | 022/17581 | |
Marc Spiegelman | 0.00-15.00 | 1/5 |

APAM 9301 | 025/17582 | |
Michael Weinstein | 0.00-15.00 | 4/5 |

APAM 9301 | 027/17584 | |
Cheng Wuu | 0.00-15.00 | 0/5 |

APAM 9301 | 028/17585 | |
Nanfang Yu | 0.00-15.00 | 5/5 |

Fall 2024: APAM E9301 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

APAM 9301 | 001/17448 | |
Daniel Bienstock | 0.00-15.00 | 1/10 |

APAM 9301 | 004/17449 | |
Qiang Du | 0.00-15.00 | 5/10 |

APAM 9301 | 005/17450 | |
Alexander Gaeta | 0.00-15.00 | 5/10 |

APAM 9301 | 008/17451 | |
Michal Lipson | 0.00-15.00 | 4/10 |

APAM 9301 | 010/17452 | |
Michael Mauel | 0.00-15.00 | 4/10 |

APAM 9301 | 011/17453 | |
Gerald Navratil | 0.00-15.00 | 0/10 |

APAM 9301 | 012/17454 | |
Elizabeth Paul | 0.00-15.00 | 4/10 |

APAM 9301 | 013/17455 | |
Carlos Paz Soldan | 0.00-15.00 | 10/10 |

APAM 9301 | 014/17456 | |
Lorenzo Polvani | 0.00-15.00 | 2/10 |

APAM 9301 | 015/17457 | |
Kui Ren | 0.00-15.00 | 6/10 |

APAM 9301 | 016/17458 | |
Steven Sabbagh | 0.00-15.00 | 4/10 |

APAM 9301 | 017/17459 | |
Adam Sobel | 0.00-15.00 | 1/10 |

APAM 9301 | 018/17460 | |
Marc Spiegelman | 0.00-15.00 | 4/10 |

APAM 9301 | 019/17461 | |
Michael Weinstein | 0.00-15.00 | 4/10 |

APAM 9301 | 020/17462 | |
Nanfang Yu | 0.00-15.00 | 5/10 |

**APAM E9800 DOCTORAL RESEARCH INSTRUCTION.** *3.00-12.00 points*.

3, 6, 9, or 12 pts.

A candidate for the Eng.Sc.D. degree must register for 12 points of doctoral research instruction. Registration for APAM E9800 may not be used to satisfy the minimum residence requirement for the degree

**APAM E9900 DOCTORAL DISSERTATION.** *0.00 points*.

0 pts.

A candidate for the doctorate may be required to register for this course every term after the coursework has been completed, and until the dissertation has been accepted

**APBM E4650 ANATOMY FOR PHYSICISTS ＆ ENGR.** *3.00 points*.

Lect: 3.

Prerequisites: Engineering or physics background

Systemic approach to the study of the human body from a medical imaging point of view: skeletal, respiratory, cardiovascular, digestive, and urinary systems, breast and womens issues, head and neck, and central nervous system. Lectures are reinforced by examples from clinical two- and three-dimensional and functional imaging (CT, MRI, PET, SPECT, U/S, etc.)

Fall 2024: APBM E4650 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APBM 4650 | 001/13876 | T Th 4:00pm - 5:20pm 601b Fairchild Life Sciences Bldg |
Zohaib Ahmad, Perry Gerard, Anna Rozenshtein, Monique Katz | 3.00 | 11/24 |

**APMA E Multivariable Calculus for Engineers and Applied Scientists.** *0 points*.

**APMA E2000 MULTV. CALC. FOR ENGI ＆ APP SCI.** *4.00 points*.

Lect: 3.

Differential and integral calculus of multiple variables. Topics include partial differentiation; optimization of functions of several variables; line, area, volume, and surface integrals; vector functions and vector calculus; theorems of Green, Gauss, and Stokes; applications to selected problems in engineering and applied science

Spring 2024: APMA E2000 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 2000 | 001/13177 | T Th 8:40am - 9:55am 227 Seeley W. Mudd Building |
Drew Youngren | 4.00 | 31/48 |

APMA 2000 | 002/13180 | T Th 1:10pm - 2:25pm 501 Northwest Corner |
Drew Youngren | 4.00 | 102/110 |

Fall 2024: APMA E2000 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

APMA 2000 | 001/10001 | T Th 8:40am - 9:55am 227 Seeley W. Mudd Building |
Shanyin Tong | 4.00 | 57/86 |

APMA 2000 | 002/13896 | T Th 1:10pm - 2:25pm 402 Chandler |
Drew Youngren | 4.00 | 124/123 |

APMA 2000 | 003/13897 | T Th 5:40pm - 6:55pm 702 Hamilton Hall |
Drew Youngren | 4.00 | 99/96 |

**APMA E2001 MULTV. CALC. FOR ENGI ＆ APP SCI.** *0.00 points*.

Required recitation session for students enrolled in APMA E2000

Spring 2024: APMA E2001 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 2001 | R01/13198 | F 2:40pm - 3:30pm 327 Seeley W. Mudd Building |
Nathan Soedjak | 0.00 | 30/30 |

APMA 2001 | R02/13204 | Th 4:10pm - 5:00pm 301m Fayerweather |
Zirui Xu | 0.00 | 25/30 |

APMA 2001 | R03/13207 | F 10:10am - 11:00am 227 Seeley W. Mudd Building |
Nathan Soedjak | 0.00 | 28/30 |

APMA 2001 | R04/13210 | Th 4:10pm - 5:00pm 520 Mathematics Building |
Yinxi Pan | 0.00 | 29/30 |

APMA 2001 | R05/13213 | Th 5:10pm - 6:00pm 333 Uris Hall |
Zirui Xu | 0.00 | 16/30 |

APMA 2001 | R06/13323 | Th 5:10pm - 6:00pm 224 Pupin Laboratories |
Yinxi Pan | 0.00 | 7/30 |

Fall 2024: APMA E2001 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

APMA 2001 | R01/13900 | Th 2:40pm - 3:30pm 141 Uris Hall |
Yinxi Pan | 0.00 | 38/40 |

APMA 2001 | R02/13901 | Th 4:10pm - 5:00pm 602 Northwest Corner |
Yin Zhou | 0.00 | 29/32 |

APMA 2001 | R03/13903 | F 10:10am - 11:00am 414 Pupin Laboratories |
Ling Lan | 0.00 | 28/36 |

APMA 2001 | R04/13904 | Th 11:40am - 12:30pm 407 Mathematics Building |
Yinxi Pan | 0.00 | 31/30 |

APMA 2001 | R05/13905 | Th 4:10pm - 5:00pm 337 Seeley W. Mudd Building |
Yinxi Pan | 0.00 | 33/34 |

APMA 2001 | R06/13906 | F 2:40pm - 3:30pm 414 Pupin Laboratories |
Ling Lan | 0.00 | 28/36 |

APMA 2001 | R07/13907 | Th 2:40pm - 3:30pm 633 Seeley W. Mudd Building |
Yin Zhou | 0.00 | 38/40 |

APMA 2001 | R08/17562 | Th 11:40am - 12:30pm 337 Seeley W. Mudd Building |
Yin Zhou | 0.00 | 37/34 |

APMA 2001 | R09/13909 | F 1:10pm - 2:00pm 307 Pupin Laboratories |
Ling Lan | 0.00 | 29/30 |

**APMA E2101 INTRO TO APPLIED MATHEMATICS.** *3.00 points*.

Lect: 3.

Prerequisites: Calculus III.

A unified, single-semester introduction to differential equations and linear algebra with emphases on (1) elementary analytical and numerical technique and (2) discovering the analogs on the continuous and discrete sides of the mathematics of linear operators: superposition, diagonalization, fundamental solutions. Concepts are illustrated with applications using the language of engineering, the natural sciences, and the social sciences. Students execute scripts in Mathematica and MATLAB (or the like) to illustrate and visualize course concepts (programming not required)

Spring 2024: APMA E2101 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 2101 | 001/13331 | T Th 1:10pm - 2:25pm 614 Schermerhorn Hall |
Yuan He | 3.00 | 85/123 |

Fall 2024: APMA E2101 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

APMA 2101 | 001/13914 | T Th 1:10pm - 2:25pm 303 Uris Hall |
Yuan He | 3.00 | 64/125 |

**APMA E3101 APPLIED MATH I: LINEAR ALGEBRA.** *3.00 points*.

Lect: 3.

Matrix algebra, elementary matrices, inverses, rank, determinants. Computational aspects of solving systems of linear equations: existence-uniqueness of solutions, Gaussian elimination, scaling, ill-conditioned systems, iterative techniques. Vector spaces, bases, dimension. Eigenvalue problems, diagonalization, inner products, unitary matrices

Fall 2024: APMA E3101 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 3101 | 001/13915 | T Th 10:10am - 11:25am 415 Schapiro Cepser |
Yuan He | 3.00 | 28/52 |

**APMA E3102 APPLIED MATHEMATICS II: PDE'S.** *3.00 points*.

Lect: 3.

Prerequisites: (MATH UN2030) or the equivalent

Introduction to partial differential equations; integral theorems of vector calculus. Partial differential equations of engineering in rectangular, cylindrical, and spherical coordinates. Separation of the variables. Characteristic-value problems. Bessel functions, Legendre polynomials, other orthogonal functions; their use in boundary value problems. Illustrative examples from the fields of electromagnetic theory, vibrations, heat flow, and fluid mechanics

Spring 2024: APMA E3102 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 3102 | 001/13336 | T Th 1:10pm - 2:25pm 644 Seeley W. Mudd Building |
Michael Tippett | 3.00 | 37/44 |

**APMA E3900 UNDERGRAD RES IN APPLIED MATH.** *0.00-4.00 points*.

0-4 pts.

Prerequisites: Written permission from instructor and approval from adviser.

This course may be repeated for credit, but no more than 6 points of this course may be counted toward the satisfaction of the B.S. degree requirements. Candidates for the B.S. degree may conduct an investigation in applied mathematics or carry out a special project under the supervision of the staff. Credit for the course is contingent upon the submission of an acceptable thesis or final report

Spring 2024: APMA E3900 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 3900 | 001/20897 | |
Qiang Du | 0.00-4.00 | 1/5 |

APMA 3900 | 002/20997 | |
Kui Ren | 0.00-4.00 | 1/5 |

APMA 3900 | 003/21123 | |
Michael Weinstein | 0.00-4.00 | 1/5 |

APMA 3900 | 009/21079 | |
Shanyin Tong | 0.00-4.00 | 1/5 |

Summer 2024: APMA E3900 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

APMA 3900 | 001/12914 | |
Lorenzo Polvani | 0.00-4.00 | 2/5 |

Fall 2024: APMA E3900 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

APMA 3900 | 001/21355 | |
Marc Spiegelman | 0.00-4.00 | 2/5 |

APMA 3900 | 005/18974 | |
Lorenzo Polvani | 0.00-4.00 | 2/10 |

**APMA E4001 PRINCIPLES OF APPLIED MATH.** *3.00 points*.

Prerequisites: Introductory Linear Algebra required. Ordinary Differential Equations recommended. Review of finite-dimensional vector spaces and elementary matrix theory. Linear transformations, change of basis, eigenspaces. Matrix representation of linear operators and diagonalization. Applications to difference equations, Markov processes, ordinary differential equations, and stability of nonlinear dynamical systems. Inner product spaces, projection operators, orthogonal bases, Gram-Schmidt orthogonalization. Least squares method, pseudo-inverses, singular value decomposition. Adjoint operators, Hermitian and unitary operators, Fredholm Alternative Theorem. Fourier series and eigenfunction expansions. Introduction to the theory of distributions and the Fourier Integral Transform. Greens functions. Application to Partial Differential Equations

**APMA E4007 APPLIED LINEAR ALGEBRA.** *3.00 points*.

Fundamentals of Linear Algebra including vector and Matrix algebra, solution of linear systems, existence and uniqueness, gaussian elimination, gauss-jordan elimination, the matrix inverse, elementary matrices and the LU factorization, computational cost of solutions. Vector spaces and subspaces, linear independence, basis and dimension. The 4 fundamental subspaces of a matrix. Orthogonal projection onto a subspace and solution of Linear Least Squares problems, unitary matrices, inner products, orthogonalization algorithms and the QR factorization, applications. Determinants and applications. Eigen problems including diagonalization, symmetric matrices, positive-definite systems, eigen factorization and applications to dynamical systems and iterative maps. Introduction to the singular value decomposition and its applications

Fall 2024: APMA E4007 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 4007 | 001/13917 | T Th 1:10pm - 2:25pm 517 Hamilton Hall |
Michael Tippett | 3.00 | 86/85 |

**APMA E4008 Advanced and Applied Linear Algebra.** *3.00 points*.

Advanced topics in linear algebra with applications to data analysis, algorithms, dynamics and differential equations, and more. (1) General vector spaces, linear transformations, spaces isomorphisms; (2) spectral theory - normal matrices and their spectral properties, Rayleigh quotient, Courant-Fischer Theorem, Jordan forms, eigenvalue perturbations; (3) least squares problem and the Gauss-Markov Theorem; (4) singular value decomposition, its approximation properties, matrix norms, PCA and CCA

Spring 2024: APMA E4008 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 4008 | 001/13340 | T Th 8:40am - 9:55am 633 Seeley W. Mudd Building |
Yuan He | 3.00 | 58/70 |

**APMA E4100 Applied Analysis.** *3.00 points*.

Elementary introduction to fundamental concepts and techniques in classical analysis; applications of such techniques in different topics in applied mathematics. Brief review of essential concepts and techniques in elementary analysis; elementary properties of metric and normed spaces; completeness, compactness, and their consequences; continuous functions and their properties; Contracting Mapping Theorem and its applications; elementary properties of Hilbert and Banach spaces; bounded linear operators in Hilbert spaces; Fourier series and their applications

Fall 2024: APMA E4100 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 4100 | 001/18707 | M W 2:40pm - 3:55pm 1024 Seeley W. Mudd Building |
Kui Ren | 3.00 | 34/50 |

APMA 4100 | V01/18937 | |
Kui Ren | 3.00 | 4/99 |

**APMA E4101 APPL MATH III:DYNAMICAL SYSTMS.** *3.00 points*.

Lect: 3.

Prerequisites: (APMA E2101) and (APMA E3101)

An introduction to the analytic and geometric theory of dynamical systems; basic existence, uniqueness and parameter dependence of solutions to ordinary differential equations; constant coefficient and parametrically forced systems; Fundamental solutions; resonance; limit points, limit cycles and classification of flows in the plane (Poincare-Bendixson Therem); conservative and dissipative systems; linear and nonlinear stability analysis of equilibria and periodic solutions; stable and unstable manifolds; bifurcations, e.g. Andronov-Hopf; sensitive dependence and chaotic dynamics; selected applications

Spring 2024: APMA E4101 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 4101 | 001/13369 | M W 8:40am - 9:55am 209 Havemeyer Hall |
Xuenan Li | 3.00 | 51/86 |

**APMA E4150 APPLIED FUNCTIONAL ANALYSIS.** *3.00 points*.

Prerequisites: Advanced calculus and course in basic analysis, or instructor's permission.

Introduction to modern tools in functional analysis that are used in the analysis of deterministic and stochastic partial differential equations and in the analysis of numerical methods: metric and normed spaces. Banach space of continuous functions, measurable spaces, the contraction mapping theorem, Banach and Hilbert spaces bounded linear operators on Hilbert spaces and their spectral decomposition, and time permitting distributions and Fourier transforms

Spring 2024: APMA E4150 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 4150 | 001/13387 | M W 2:40pm - 3:55pm 327 Seeley W. Mudd Building |
Kui Ren | 3.00 | 24/39 |

**APMA E4200 PARTIAL DIFFERENTIAL EQUATIONS.** *3.00 points*.

Prerequisites: Course in ordinary differential equations.

Techniques of solution of partial differential equations. Separation of the variables. Orthogonality and characteristic functions, nonhomogeneous boundary value problems. Solutions in orthogonal curvilinear coordinate systems. Applications of Fourier integrals, Fourier and Laplace transforms. Problems from the fields of vibrations, heat conduction, electricity, fluid dynamics, and wave propagation are considered

Spring 2024: APMA E4200 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 4200 | 001/13404 | T Th 1:10pm - 2:25pm 633 Seeley W. Mudd Building |
James Scott | 3.00 | 25/70 |

Fall 2024: APMA E4200 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

APMA 4200 | 001/12479 | M W 11:40am - 12:55pm 313 Fayerweather |
James Scott | 3.00 | 62/70 |

APMA 4200 | V01/20996 | |
James Scott | 3.00 | 3/99 |

**APMA E4204 FUNCTNS OF A COMPLEX VARIABLE.** *3.00 points*.

Prerequisites: (MATH UN1202) or the equivalent.

Complex numbers, functions of a complex variable, differentiation and integration in the complex plane. Analytic functions, Cauchy integral theorem and formula, Taylor and Laurent series, poles and residues, branch points, evaluation of contour integrals. Conformal mapping, Schwarz-Christoffel transformation. Applications to physical problems

Fall 2024: APMA E4204 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 4204 | 001/13919 | M W 1:10pm - 2:25pm 1024 Seeley W. Mudd Building |
Xuenan Li | 3.00 | 48/55 |

APMA 4204 | V01/20997 | |
Xuenan Li | 3.00 | 3/99 |

**APMA E4300 COMPUT MATH:INTRO-NUMERCL METH.** *3.00 points*.

Lect: 3.

Prerequisites: (MATH UN1201) and (MATH UN2030) and (APMA E3101) and (ENGI E1006) or their equivalents. Programming experience in Python extremely useful.

Programming experience in Python extremely useful. Introduction to fundamental algorithms and analysis of numerical methods commonly used by scientists, mathematicians and engineers. Designed to give a fundamental understanding of the building blocks of scientific computing that will be used in more advanced courses in scientific computing and numerical methods for PDEs (e.g. APMA E4301, E4302). Topics include numerical solutions of algebraic systems, linear least-squares, eigenvalue problems, solution of non-linear systems, optimization, interpolation, numerical integration and differentiation, initial value problems and boundary value problems for systems of ODEs. All programming exercises will be in Python

Spring 2024: APMA E4300 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 4300 | 001/13408 | T Th 10:10am - 11:25am 833 Seeley W. Mudd Building |
Marc Spiegelman | 3.00 | 80/120 |

Fall 2024: APMA E4300 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

APMA 4300 | 001/13921 | T Th 10:10am - 11:25am 614 Schermerhorn Hall |
Marc Spiegelman | 3.00 | 126/120 |

APMA 4300 | V01/18691 | |
Marc Spiegelman | 3.00 | 11/99 |

**APMA E4301 NUMERICAL METHODS/PDE'S.** *3.00 points*.

Lect: 3.

Prerequisites: (APMA E4300) and (APMA E3102) or (APMA E4200) or or equivalents.

Numerical solution of differential equations, in particular partial differential equations arising in various fields of application. Presentation emphasizes finite difference approaches to present theory on stability, accuracy, and convergence with minimal coverage of alternate approaches (left for other courses). Method coverage includes explicit and implicit time-stepping methods, direct and iterative solvers for boundary-value problems

Spring 2024: APMA E4301 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 4301 | 001/13414 | T Th 11:40am - 12:55pm 524 Seeley W. Mudd Building |
Qiang Du | 3.00 | 15/40 |

**APMA E4302 METHODS IN COMPUTATIONAL SCI.** *3.00 points*.

Lect: 3.

Prerequisites: (APMA E4300) and application and knowledge in C, Fortran or similar complied language.

Introduction to the key concepts and issues in computational science aimed at getting students to a basic level of understanding where they can run simulations on machines aimed at a range of applications and sizes from a single workstation to modern super-computer hardware. Topics include but are not limited to basic knowledge of UNIX shells, version control systems, reproducibility, Open MP, MPI, and many-core technologies. Applications will be used throughout to demonstrate the various use cases and pitfalls of using the latest computing hardware

**APMA E4306 Applied Stochastic Analysis.** *3.00 points*.

Provides elementary introduction to fundamental ideas in stochastic analysis for applied mathematics. Core material includes: (i) review of probability theory (including limit theorems), and introduction to discrete Markov chains and Monte Carlo methods; (ii) elementary theory of stochastic process, Ito's stochastic calculus and stochastic differential equations; (iii) introductions to probabilistic representation of elliptic partial differential equations (the Fokker-Planck equation theory); (iv) stochastic approximation algorithms; and (v) asymptotic analysis of SDEs

Spring 2024: APMA E4306 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 4306 | 001/13419 | M W 10:10am - 11:25am 1127 Seeley W. Mudd Building |
Shanyin Tong | 3.00 | 23/39 |

**APMA E4400 INTRO TO BIOPHYSICAL MODELING.** *3.00 points*.

Lect: 3.

Prerequisites: (PHYS UN1401) and (APMA E2101) or (MATH UN2030) or or equivalent.

Introduction to physical and mathematical models of cellular and molecular biology. Physics at the cellular scale (viscosity, heat, diffusion, statistical mechanics). RNA transcription and regulation of genetic expression. Genetic and biochemical networks. Bioinformatics as applied to reverse-engineering of naturally-occurring networks and to forward-engineering of synthetic biological networks. Mathematical and physical aspects of functional genomics

**APMA E4901 SEM-PROBLEMS IN APPLIED MATH.** *0.00-1.00 points*.

Lect: 1.

Required for, and can be taken only by, all applied mathematics majors in the junior year. Introductory seminars on problems and techniques in applied mathematics. Typical topics are nonlinear dynamics, scientific computation, economics, operation research, etc

Fall 2024: APMA E4901 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 4901 | 001/13923 | M W 11:40am - 12:55pm 501 Northwest Corner |
Chris Wiggins | 0.00-1.00 | 67/70 |

**APMA E4903 SEM-PROBLEMS IN APPLIED MATH.** *3.00-4.00 points*.

3-4 pts. Lect: 1

Required for all applied mathematics majors in the senior year. Term paper required. Examples of problem areas are nonlinear dynamics, asymptotics, approximation theory, numerical methods, etc. Approximately three problem areas are studied per term

Fall 2024: APMA E4903 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 4903 | 001/13924 | M W 11:40am - 12:55pm 501 Northwest Corner |
Chris Wiggins | 3.00-4.00 | 52/70 |

**APMA E4904 SEM-PROBLEMS IN APPLIED MATH.** *3.00-4.00 points*.

**APMA E4990 SPEC TOPICS IN APPLIED MATH.** *3.00 points*.

1-3 pts. Lect: 3.

Prerequisites: Advanced calculus and junior year applied mathematics, or their equivalents.

May be repeated for credit. Topics and instructors from the Applied Mathematics Committee and the staff change from year to year. For advanced undergraduate students and graduate students in engineering, physical sciences, biological sciences, and other fields. Examples of topics include multi-scale analysis and Applied Harmonic Analysis

Spring 2024: APMA E4990 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 4990 | 001/13424 | M W 11:40am - 12:55pm 1127 Seeley W. Mudd Building |
Vladimir Kobzar | 3.00 | 14/39 |

Fall 2024: APMA E4990 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

APMA 4990 | 001/13940 | M W 10:10am - 11:25am 608 Martin Luther King Building |
Madison Ihrig | 3.00 | 12/20 |

**APMA E6100 RESEARCH SEMINAR.** *0.00 points*.

Lect: 3. **Not offered during 2023-2024 academic year.**

Prerequisites: (MATH UN3027) or (APMA E4101) or (MATH UN3028) or (APMA E4200) or (MATH UN2010) or (APMA E3101) or their equivalents.

Corequisites: MATH UN3027

APMA E4101

MATH UN3028

APMA E4200

MATH UN2010

APMA E3101

An M.S. degree requirement. Students attend at least three Applied Mathematics research seminars within the Department of Applied Physics and Applied Mathematics and submit reports on each

Fall 2024: APMA E6100 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 6100 | 001/13942 | T 4:10pm - 5:00pm 627 Seeley W. Mudd Building |
Kui Ren | 0.00 | 53/50 |

APMA 6100 | V01/18729 | |
Kui Ren | 0.00 | 9/99 |

**APMA E6301 ANALYTIC METHODS FOR PDE'S.** *3.00 points*.

Lect: 2.

Prerequisites: (APMA E3101) and (APMA E4200) or their equivalents, Advanced calculus, basic concepts in analysis, or instructor's permission.

Introduction to analytic theory of PDEs of fundamental and applied science; wave (hyperbolic), Laplace and Poisson equations (elliptic), heat (parabolic) and Schroedinger (dispersive) equations; fundamental solutions, Greens functions, weak/distribution solutions, maximum principle, energy estimates, variational methods, method of characteristics; elementary functional analysis and applications to PDEs; introduction to nonlinear PDEs, shocks; selected applications

Fall 2024: APMA E6301 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 6301 | 001/13949 | T Th 1:10pm - 2:25pm 327 Seeley W. Mudd Building |
Michael Weinstein | 3.00 | 22/35 |

**APMA E6302 NUMERICAL ANALYSIS OF PDE'S.** *3.00 points*.

Lect: 2.

Prerequisites: (APMA E3102) or (APMA E4200)

Numerical analysis of initial and boundary value problems for partial differential equations. Convergence and stability of the finite difference method, the spectral method, the finite element method and applications to elliptic, parabolic, and hyperbolic equations

Fall 2024: APMA E6302 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 6302 | 001/13953 | T Th 10:10am - 11:25am 327 Seeley W. Mudd Building |
Qiang Du | 3.00 | 21/35 |

**APMA E6901 SPECIAL TOPICS IN APPLIED MATH.** *3.00 points*.

Lect: 3.

Prerequisites: Advanced calculus and junior year applied mathematics, or their equivalents.

May be repeated for credit. Topics and instructors from the Applied Mathematics Committee and the staff change from year to year. For students in engineering, physical sciences, biological sciences, and other fields

**APMA E9101 RESEARCH I.** *1.00-4.00 points*.

1-4 pts.

Prerequisites: Prerequisite: the permission of the supervising faculty member.

May be repeated. Advanced study in a special area

**APMA E9102 RESEARCH II.** *1.00-4.00 points*.

1-4 pts.

Prerequisites: Prerequisite: the permission of the supervising faculty member.

May be repeated. Advanced study in a special area

**APMA E9810 MATHEMATICAL EARTH SCIENCE SEM.** *0.00 points*.

0 pts. Lect: 1.

Prerequisites: Instructor's permission.

Current research in problems at the interface between applied mathematics and earth and environmental sciences

**APPH E1300 PHYSICS OF THE HUMAN BODY.** *3.00 points*.

**APPH E3100 INTRO TO QUANTUM MECHANICS.** *3.00 points*.

Lect: 3.

Prerequisites: (PHYS UN1403) or the equivalent, and differential and integral calculus.

Corequisites: APMA E3101

Basic concepts and assumptions of quantum mechanics, Schrodinger's equation, solutions for one-dimensional problems including square wells, barriers and the harmonic oscillator, introduction to the hydrogen atom, atomic physics and X-rays, electron spin

Spring 2024: APPH E3100 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 3100 | 001/13429 | M W 1:10pm - 2:25pm 327 Seeley W. Mudd Building |
Aravind Devarakonda | 3.00 | 21/35 |

**APPH E3200 MECHANICS:FUND ＆ APPLICATIONS.** *3.00 points*.

Lect: 3

Prerequisites: (PHYS UN1402) and (MATH UN2030) or or equivalent.

Basic non-Euclidean coordinate systems, Newtonian Mechanics, oscillations, Greens functions, Newtonian graviation, Lagrangian mechanics, central force motion, two-body collisions, noninertial reference frames, rigid body dynamics. Applications, including GPS and feedback control systems, are emphasized throughout

Fall 2024: APPH E3200 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 3200 | 001/13968 | M W 10:10am - 11:25am 140 Uris Hall |
Elizabeth Paul | 3.00 | 19/35 |

**APPH E3300 APPLIED ELECTROMAGNETISM.** *3.00 points*.

Lect: 3.

Corequisites: APMA E3102

Vector analysis, electrostatic fields, Laplaces equation, multipole expansions, electric fields in matter: dielectrics, magnetostatic fields, magnetic materials, and superconductors. Applications of electromagnetism to devices and research areas in applied physics

Spring 2024: APPH E3300 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 3300 | 001/13430 | T Th 2:40pm - 3:55pm 601b Fairchild Life Sciences Bldg |
Gerald Navratil | 3.00 | 19/25 |

**APPH E3400 PHYSICS OF THE HUMAN BODY.** *3.00 points*.

Lect: 3.

Prerequisites: (PHYS UN1201) or (PHYS UN1401) and (MATH UN1101)

Corequisites: PHYS UN1202,PHYS UN1402,MATH UN1102

This introductory course analyzes the human body from the basic principles of physics. Topics covered include the energy balance in the body, the mechanics of motion, fluid dynamics of the heart and circulation, vibrations in speaking and hearing, muscle mechanics, gas exchange and transport in the lungs, vision, structural properties and limits, electrical properties and the development and sensing of magnetic fields, and basics of equilibrium and regulatory control. In each case, a simple model of the body organ, property, or function will be derived and then applied

**APPH E3900 UNDERGRAD RESRCH-APPLD PHYSICS.** *0.00-4.00 points*.

0-4 pts.

Prerequisites: Written permission from instructor and approval from adviser.

This course may be repeated for credit, but no more than 6 points of this course may be counted toward the satisfaction of the B.S. degree requirements. Candidates for the B.S. degree may conduct an investigation in applied physics or carry out a special project under the supervision of the staff. Credit for the course is contingent upon the submission of an acceptable thesis or final report

Spring 2024: APPH E3900 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 3900 | 010/21114 | |
Elizabeth Paul | 0.00-4.00 | 1/5 |

APPH 3900 | 011/20730 | |
Carlos Paz Soldan | 0.00-4.00 | 6/5 |

Summer 2024: APPH E3900 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

APPH 3900 | 001/13737 | |
Simon Billinge | 0.00-4.00 | 1/5 |

Fall 2024: APPH E3900 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

APPH 3900 | 001/21274 | |
Nanfang Yu | 0.00-4.00 | 1/10 |

APPH 3900 | 003/18681 | |
Latha Venkataraman | 0.00-4.00 | 1/5 |

APPH 3900 | 004/19113 | |
Carlos Paz Soldan | 0.00-4.00 | 8/10 |

**APPH E4010 INTRODUCTN TO NUCLEAR SCIENCE.** *3.00 points*.

Introductory course is for individuals with an interest in medical physics and other branches of radiation science. Topics include basic concepts, nuclear models, semi-empirical mass formula, interaction of radiation with matter, nuclear detectors, nuclear structure and instability, radioactive decay process and radiation, particle accelerators, and fission and fusion processes and technologies

Fall 2024: APPH E4010 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 4010 | 001/13869 | T 6:30pm - 9:00pm 610 Martin Luther King Building |
Stephen Ostrow | 3.00 | 20/25 |

**APPH E4018 APPLIED PHYSICS LABORATORY.** *2.00 points*.

Lab: 4.

Prerequisites: (ELEN E3401) or or equivalent.

Typical experiments are in the areas of plasma physics, microwaves, laser applications, optical spectroscopy physics, and superconductivity

Spring 2024: APPH E4018 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 4018 | 001/13431 | |
Michael Mauel | 2.00 | 29/30 |

**APPH E4100 QUANTUM PHYSICS OF MATTER.** *3.00 points*.

Lect: 3.

Prerequisites: (APPH E3100)

Corequisites: APMA E3102

Basic theory of quantum mechanics, well and barrier problems, the harmonic oscillator, angular momentum identical particles, quantum statistics, perturbation theory and applications to the quantum physics of atoms, molecules, and solids

Fall 2024: APPH E4100 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 4100 | 001/13969 | T Th 10:10am - 11:25am 545 Seeley W. Mudd Building |
Latha Venkataraman | 3.00 | 19/45 |

APPH 4100 | V01/20998 | |
Latha Venkataraman | 3.00 | 3/99 |

**APPH E4110 MODERN OPTICS.** *3.00 points*.

Lect: 3.

Prerequisites: (APPH E3300)

Ray optics, matrix formulation, wave effects, interference, Gaussian beams, Fourier optics, diffraction, image formation, electromagnetic theory of light, polarization and crystal optics, coherence, guided wave and fiber optics, optical elements, photons, selected topics in nonlinear optics

Spring 2024: APPH E4110 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 4110 | 001/13435 | T Th 11:40am - 12:55pm 233 Seeley W. Mudd Building |
Nanfang Yu | 3.00 | 20/35 |

**APPH E4112 LASER PHYSICS.** *3.00 points*.

Lect: 3.

Prerequisites: Recommended but not required: APPH E3100 and APPH E3300 or their equivalents.

Optical resonators, interaction of radiation and atomic systems, theory of laser oscillation, specific laser systems, rate processes, modulation, detection, harmonic generation, and applications

Fall 2024: APPH E4112 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 4112 | 001/13971 | T Th 11:40am - 12:55pm 545 Seeley W. Mudd Building |
Nanfang Yu | 3.00 | 22/35 |

APPH 4112 | V01/17549 | |
Nanfang Yu | 3.00 | 6/99 |

**APPH E4114 Quantum and Nonlinear Photonics.** *3.00 points*.

Advanced senior-level/MS/PhD course covering interaction of laser light with matter in both classical and quantum domains. First half introduces microscopic origin of optical nonlinearities through formal derivation of nonlinear susceptibilities, emphasis on second- and third-order optical processes. Topics include Maxwell's wave equation, and nonlinear optical processes such as second-harmonic, difference frequency generation, four-wave mixing, and self-phase modulation, including various applications of processes such as frequency conversion, and optical parametric amplifiers and oscillators. Second half describes two-level atomic systems and quantization of electromagnetic field. Descriptions of coherent, Fock, and squeezed states of light discussed and techniques to generate such states outlined

Spring 2024: APPH E4114 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 4114 | 001/13442 | W 1:10pm - 3:40pm 411 Kent Hall |
Alexander Gaeta | 3.00 | 19/25 |

**APPH E4130 PHYSICS/SOLAR ENERGY.** *3.00 points*.

Lect: 3.

Prerequisites: (PHYS UN1403) or (PHYS UN1602) and (MATH UN1202) or (MATH UN2030) or instructor's permission.

The physics of solar energy including solar radiation, the analemma, atmospheric efforts, thermodynamics of solar energy, physics of solar cells, energy storage and transmission, and physics and economics in the solar era

Fall 2024: APPH E4130 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 4130 | 001/13973 | M W 1:10pm - 2:25pm 545 Seeley W. Mudd Building |
Julian Chen | 3.00 | 29/35 |

APPH 4130 | V01/17517 | |
Julian Chen | 3.00 | 2/99 |

**APPH E4164 Electric Field Effects in Catalysis.** *1.50 point*.

Real-time exposition of an emerging area of study at the interface between chemistry, physics, engineering, and biology to understand and control how electric fields can be used to catalyze chemical transformations. Taught by a cross-disciplinary group of faculty. Topics covered: (1) theoretical underpinnings for catalysis in nanoscale electrical environments, (2) experimental tools used to study these chemical transformations, (3) experimental demonstrations of catalysis in electric fields. Each topic will draw on elements of organometallic/organic catalysis, quantum mechanics, enzymatic catalysis, and nano electronics to form the basis for understanding this new branch of catalytic science

**APPH E4200 PHYSICS OF FLUIDS.** *3.00 points*.

Lect: 3.

Prerequisites: (APMA E3102) or (PHYS UN1401) or (PHYS UN1601) or or equivalent.

An introduction to the physical behavior of fluids for science and engineering students. Derivation of basic equations of fluid dynamics: conservation of mass, momentum, and energy. Dimensional analysis. Vorticity. Laminar boundary layers. Potential flow. Effects of compressibility, stratification, and rotation. Waves on a free surface; shallow water equations. Turbulence

Fall 2024: APPH E4200 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 4200 | 001/13984 | Th 4:10pm - 6:40pm 401 Chandler |
Lorenzo Polvani | 3.00 | 8/35 |

**APPH E4210 GEOPHYSICAL FLUID DYNAMICS.** *3.00 points*.

Lect: 3.

Prerequisites: (APMA E3101) and (APMA E3102) and (APPH E4200) or equivalents or permission from instructor.

Fundamental concepts in the dynamics of rotating, stratified flows. Geostrophic and hydrostatic balances, potential vorticity, f and beta plane approximations, gravity and Rossby waves, geostrophic adjustment and quasigeostrophy, baroclinic and barotropic instabilities, Sverdrup balance, boundary currents, Ekman layers

**APPH E4300 APPLIED ELECTRODYNAMICS.** *3.00 points*.

Overview of properties and interactions of static electric and magnetic fields. Study of phenomena of time dependent electric and magnetic fields including induction, waves, and radiation as well as special relativity. Applications are emphasized

Fall 2024: APPH E4300 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 4300 | 001/13976 | W 4:10pm - 6:40pm 337 Seeley W. Mudd Building |
Alexander Gaeta | 3.00 | 32/35 |

**APPH E4301 INTRO TO PLASMA PHYSICS.** *3.00 points*.

Lect: 3.

Prerequisites: (PHYS UN3008) or (APPH E3300)

Definition of a plasma. Plasmas in laboratories and nature, plasma production. Motion of charged particles in electric and magnetic fields, adiabatic invariants. Heuristic treatment of collisions, diffusion, transport, and resistivity. Plasma as a conducting fluid. Electrostatic and magnetostatic equilibria of plasmas. Waves in cold plasmas. Demonstration of laboratory plasma behavior, measurement of plasma properties. Illustrative problems in fusion, space, and nonneutral or beam plasmas

**APPH E4330 RADIOBIOLOGY FOR MED PHYS.** *3.00 points*.

Lect: 3.

Prerequisites: (APPH E4010) or equivalent or

Corequisites: APPH E4010

Interface between clinical practice and quantitative radiation biology. Microdosimetry, dose-rate effects and biological effectiveness thereof; radiation biology data, radiation action at the cellular and tissue level; radiation effects on human populations, carcinogenesis, genetic effects; radiation protection; tumor control, normal-tissue complication probabilities; treatment plan optimization

Fall 2024: APPH E4330 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
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APPH 4330 | 001/13877 | Th 6:00pm - 8:00pm 1106b Seeley W. Mudd Building |
Marco Zaider | 3.00 | 5/15 |

**APPH E4500 HEALTH PHYSICS.** *3.00 points*.

Lect: 3.

Prerequisites: (APPH E4600) or

Corequisites: APPH E4600

Fundamental principles and objectives of health physics (radiation protection), the quantities of radiation dosimetry (the absorbed dose, equivalent dose, and effective dose) used to evaluate human radiation risks, elementary shielding calculations and protection measures for clinical environments, characterization and proper use of health physics instrumentation, and regulatory and administrative requirements of health physics programs in general and as applied to clinical activities

**APPH E4501 MEDICAL HLTH PHYS TUTORIAL.** *0.00 points*.

**APPH E4550 MEDICAL PHYSICS SEMINAR.** *0.00 points*.

0 pts. Lect: 1.

Required for all graduate students in the Medical Physics Program. Practicing professionals and faculty in the field present selected topics in medical physics

**APPH E4600 FUNDAMENTALS OF DOSIMETRY.** *3.00 points*.

Lect: 3.

Prerequisites: (APPH E4010) or or equivalent

Corequisites: APPH E4010

Basic radiation physics: radioactive decay, radiation producing devices, characteristics of the different types of radiation (photons, charged and uncharged particles) and mechanisms of their interactions with materials. Essentials of the determination, by measurement and calculation, of absorbed doses from ionizing radiation sources used in medical physics (clinical) situations and for health physics purposes

Fall 2024: APPH E4600 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 4600 | 001/13870 | W 4:00pm - 6:50pm 606 Lewisohn Hall |
Sean Berry | 3.00 | 8/20 |

**APPH E4710 RAD INSTRUMENT/MEASUREMENT LAB.** *3.00 points*.

Lect: 1. Lab: 4.

Prerequisites: (APPH E4010) or

Corequisites: APPH E4010

Lab fee: $50. Theory and use of alpha, beta, gamma, and X-ray detectors and associated electronics for counting, energy spectroscopy, and dosimetry; radiation safety; counting statistics and error propagation; mechanisms of radiation emission and interaction. (Topic coverage may be revised.)

Fall 2024: APPH E4710 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 4710 | 001/13874 | M 5:00pm - 9:00pm 214 Seeley W. Mudd Building |
Stephen Ostrow, Marco Zaider | 3.00 | 8/15 |

**APPH E4711 RAD INSTRUMENT/MEASUREMENT LAB.** *3.00 points*.

Lect: 1. Lab: 4.

Prerequisites: (APPH E4010) or

Corequisites: APPH E4010

Lab fee: $50. Additional detector types; applications and systems including coincidence, low-level, and liquid scintillation counting; neutron activation; TLD dosimetry, gamma camera imaging. (Topic coverage may be revised.)

**APPH E4901 SEM-PROBLMS IN APPLIED PHYSICS.** *1.00 point*.

Lect: 1.

Required for, and can be taken only by, all applied physics majors and minors in the junior year. Discussion of specific and self-contained problems in areas such as applied electrodynamics, physics of solids, and plasma physics. Topics change yearly

Fall 2024: APPH E4901 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 4901 | 001/13985 | M W 11:40am - 12:55pm 829 Seeley W. Mudd Building |
Michael Mauel | 1.00 | 13/35 |

**APPH E4903 SEM-PROBLMS IN APPLIED PHYSICS.** *2.00 points*.

Lect: 1. Tutorial:1.

Required for, and can be taken only by, all applied physics majors in the senior year. Discussion of specific and self-contained problems in areas such as applied electrodynamics, physics of solids, and plasma physics. Formal presentation of a term paper required. Topics change yearly

Fall 2024: APPH E4903 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 4903 | 001/13986 | M W 11:40am - 12:55pm 829 Seeley W. Mudd Building |
Michael Mauel | 2.00 | 14/35 |

**APPH E4990 SPEC TOPICS IN APPLIED PHYSICS.** *3.00 points*.

May be repeated for credit. Topics and instructors change from year to year. For advanced undergraduate students and graduate students in engineering, physical sciences, and other fields

**APPH E6081 SOLID STATE PHYSICS I.** *3.00 points*.

Lect: 3.

Prerequisites: (APPH E3100) or the equivalent. Knowledge of statistical physics on the level of MSAE E3111 or PHYS GU4023 strongly recommended.

Crystal structure, reciprocal lattices, classification of solids, lattice dynamics, anharmonic effects in crystals, classical electron models of metals, electron band structure, and low-dimensional electron structures

**APPH E6091 Magnetism and magnetic materials.** *3 points*.

Lect. 3. **Not offered during 2023-2024 academic year.**

Prerequisites: (MSAE E4206) or (APPH E6081) or equivalent.

Types of magnetism. Band theory of ferromagnetism. Magnetic metals, insulators, and semiconductors. Magnetic nanostructures: ultrathin films, superlattices, and particles. Surface magnetism and spectroscopies. High speed magnetization dynamics. Spin electronics.

**APPH E6101 PLASMA PHYSICS I.** *3.00 points*.

Lect: 3.

Prerequisites: (APPH E4300)

Debye screening. Motion of charged particles in space- and time-varying electromagnetic fields. Two-fluid description of plasmas. Linear electrostatic and electromagnetic waves in unmagnetized and magnetized plasmas. The magnetohydrodynamic (MHD) model, including MHD equilibrium, stability, and MHD waves in simple geometries

Fall 2024: APPH E6101 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 6101 | 001/13988 | M W 1:10pm - 2:25pm 233 Seeley W. Mudd Building |
Gerald Navratil | 3.00 | 14/35 |

**APPH E6102 PLASMA PHYSICS II.** *3.00 points*.

Lect: 3.

Prerequisites: (APPH E6101)

Magnetic coordinates. Equilibrium, stability, and transport of torodial plasmas. Ballooning and tearing instabilities. Kinetic theory, including Vlasov equation, Fokker-Planck equation, Landau damping, kinetic transport theory. Drift instabilities

Spring 2024: APPH E6102 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 6102 | 001/13451 | M W 1:10pm - 2:25pm 825 Seeley W. Mudd Building |
Carlos Paz Soldan | 3.00 | 13/35 |

**APPH E6319 CLIN NUCLEAR MEDICINE PHYSICS.** *3.00 points*.

Lect: 3.

Prerequisites: (APPH E4010) or equivalent.

Introduction to the instrumentation and physics used in clinical nuclear medicine and PET with an emphasis on detector systems, tomography and quality control. Problem sets, papers and term project

**APPH E6330 DIAGNOSTIC RADIOLOGY PHYSICS.** *3.00 points*.

Lect: 3.

Prerequisites: (APPH E4600)

Physics of medical imaging. Imaging techniques: radiography, fluoroscopy, computed tomography, mammography, ultrasound, magnetic resonance. Includes conceptual, mathematical/theoretical, and practical clinical physics aspects

**APPH E6333 RADIATION THERAPY PHYS PRACT.** *3.00 points*.

Prerequisites: Grade of B+ or better in APPH E6335 and instructor's permission.

Students spend two to four days per week studying the clinical aspects of radiation therapy physics. Projects on the application of medical physics in cancer therapy within a hospital environment are assigned; each entails one or two weeks of work and requires a laboratory report. Two areas are emphasized: 1. computer-assisted treatment planning (design of typical treatment plans for various treatment sites including prostate, breast, head and neck, lung, brain, esophagus, and cervix) and 2. clinical dosimetry and calibrations (radiation measurements for both photon and electron beams, as well as daily, monthly, and part of annual QA)

Fall 2024: APPH E6333 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 6333 | 001/13878 | |
Cheng Wuu | 3.00 | 2/8 |

**APPH E6335 RADIATION THERAPY PHYSICS.** *3.00 points*.

Lect: 3.

Prerequisites: (APPH E4600) APPH E4330 recommended.

Review of X-ray production and fundamentals of nuclear physics and radioactivity. Detailed analysis of radiation absorption and interactions in biological materials as specifically related to radiation therapy and radiation therapy dosimetry. Surveys of use of teletherapy isotopes and X-ray generators in radiation therapy plus the clinical use of interstitial and intracavitary isotopes. Principles of radiation therapy treatment planning and isodose calculations. Problem sets taken from actual clinical examples are assigned

**APPH E6336 ADV TPCS IN RADIATION THERAPY.** *3.00 points*.

Lect: 3.

Prerequisites: (APPH E6335)

Advanced technology applications in radiation therapy physics, including intensity modulated, image guided, stereotactic, and hypofractionated radiation therapy. Emphasis on advanced technological, engineering, clinical, and quality assurance issues associated with high technology radiation therapy and the special role of the medical physicist in the safe clinical application of these tools

Fall 2024: APPH E6336 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 6336 | 001/13886 | W 2:00pm - 5:00pm 414 Schapiro Cepser |
Cheng Wuu | 3.00 | 1/10 |

**APPH E6340 DIAGNOSTIC RADIOL PRACTICUM.** *3.00 points*.

Lab: 6.

Prerequisites: Grade of B+ or better in APPH E6330 and instructor's permission.

Practical applications of diagnostic radiology for various measurements and equipment assessments. Instruction and supervised practice in radiation safety procedures, image quality assessments, regulatory compliance, radiation dose evaluations and calibration of equipment. Students participate in clinical QC of the following imaging equipment: radiologic units (mobile and fixed), fluoroscopy units (mobile and fixed), angiography units, mammography units, CT scanners, MRI units and ultrasound units. The objective is familiarization in routine operation of test instrumentation and QC measurements utilized in diagnostic medical physics. Students are required to submit QC forms with data on three different types of radiology imaging equipment

Fall 2024: APPH E6340 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 6340 | 001/13880 | |
Boyu Peng | 3.00 | 1/10 |

**APPH E6365 NUCLEAR MEDICINE PRACTICUM.** *3.00 points*.

Lab: 6.

Prerequisites: Grade of B+ or better in APPH E6319 and instructor's permission.

Practical applications of nuclear medicine theory and application for processing and analysis of clinical images and radiation safety and quality assurance programs. Topics may include tomography, instrumentation, and functional imaging. Reports

Fall 2024: APPH E6365 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 6365 | 001/13881 | |
Klaus Hamacher | 3.00 | 1/3 |

**APPH E6380 HEALTH PHYSICS PRACTICUM.** *3.00 points*.

Lab: 6.

Prerequisites: Grade of B+ or better in APPH E4500 and permission of the instructor, or

Corequisites: APPH E4500

Radiation protection practices and procedures for clinical and biomedical research environments. Includes design, radiation safety surveys of diagnostic and therapeutic machine source facilities, the design and radiation protection protocols for facilities using unsealed sources of radioactivity – nuclear medicine suites and sealed sources – brachytherapy suites. Also includes radiation protection procedures for biomedical research facilities and the administration of programs for compliance to professional health physics standards and federal and state regulatory requirements for the possession and use of radioactive materials and machine sources of ionizing and non ionizing radiations in clinical situations. Individual topics are decided by the student and the collaborating Clinical Radiation Safety Officer

Fall 2024: APPH E6380 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 6380 | 001/13883 | |
Peter Caracappa | 3.00 | 0/10 |

**APPH E9143 APPLIED PHYSICS SEMINAR.** *3.00 points*.

Sem: 3.**Not offered during 2023-2024 academic year.**

May be repeated for credit. Selected topics in applied physics. Topics and instructors change from year to year

Spring 2024: APPH E9143 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 9143 | 001/13461 | T Th 2:40pm - 3:55pm 307 Uris Hall |
Elizabeth Paul | 3.00 | 8/35 |

**APCH E4080 SOFT CONDENSED MATTER.** *3.00 points*.

Course is aimed at senior undergraduate and graduate students. Introduces fundamental ideas, concepts, and approaches in soft condensed matter with emphasis on biomolecular systems. Covers the broad range of molecular, nanoscale, and colloidal phenomena with revealing their mechanisms and physical foundations. The relationship between molecular architecture and interactions and macroscopic behavior are discussed for the broad range of soft and biological matter systems, from surfactants and liquid crystals to polymers, nanoparticles, and biomolecules. Modern characterization methods for soft materials, including X-ray scattering, molecular force probing, and electron microcopy are reviewed. Example problems, drawn from the recent scientific literature, link the studied materials to the actively developed research areas. Course grade based on midterm and final exams, weekly homework assignments, and final individual/team project

**CHAP E4120 STATISTICAL MECHANICS AND COMP METHODS.** *3.00 points*.

Lect: 3.

Prerequisites: (CHEN E3210) or equivalent thermodynamics course, or instructor's permission.

Boltzmann’s entropy hypothesis and its restatement to calculate the Helmholtz and Gibbs free energies and the grand potential. Applications to interfaces, liquid crystal displays, polymeric materials, crystalline solids, heat capacity and electrical conductivity of crystalline materials, fuel cell solid electrolytes, rubbers, surfactants, molecular self assembly, ferroelectricity. Computational methods for molecular systems. Monte Carlo (MC) and molecular dynamics (MD) simulation methods. MC method applied to liquid-gas and ferromagnetic phase transitions. Deterministic MD simulations of isolated gases and liquids. Stochastic MD simulation methods