Mechanical Engineering (BS)
Mechanical Engineering
The Mechanical Engineering Undergraduate Program at Columbia University has the following Program Educational Objectives (PEOs) for its graduates:
- Practice mechanical engineering in a broad range of industries.
- Pursue advanced education, research and development, and other creative and innovative efforts in science, engineering, and technology, as well as other professional careers.
- Conduct themselves in a responsible, professional, and ethical manner.
- Participate in activities that support humanity and economic development nationally and globally, developing as leaders in their fields of expertise.
As stated on the Mechanical Engineering department website, graduates of the Mechanical Engineering program at Columbia University will attain:
- an ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics
- an ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors
- an ability to communicate effectively with a range of audiences
- an ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts
- an ability to function effectively on teams whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives
- an ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions
- an ability to acquire and apply new knowledge as needed, using appropriate learning strategies.
Highly qualified students are permitted to pursue an honors course consisting of independent study under the guidance of a member of the faculty.
Upon graduation, the student may wish to enter employment in industry or government, or continue with graduate study. Alternatively, training in mechanical engineering may be viewed as a basis for a career in business, patent law, medicine, or management. Thus, the department’s undergraduate program provides a sound foundation for a variety of professional endeavors.
The program in mechanical engineering leading to the B.S. degree is accredited by the Engineering Accreditation Commission of ABET, http://www.abet.org.
Undergraduates who wish to declare mechanical engineering as their major should do so prior to the start of their junior year. Students who declare in their first year should follow the Early Decision Track. Students who declare in their second year should follow the Standard Track. Students who wish to declare during or after the fall semester of their junior year must first obtain approval from the Mechanical Engineering Department.
Of the 18 points of elective content in the third and fourth years, at least 9 points of technical elective courses, including at least 6 points from the Department of Mechanical Engineering, must be taken. A technical elective can be any engineering course offered in the SEAS bulletin that is 3000 level or above. Those prior remaining points of electives are intended primarily as an opportunity to complete the four-year, 27-point nontechnical requirement. Consistent with professional accreditation standards, courses in engineering science and courses in design must have a combined credit of 45 points. Students should see their advisers for details.
Undergraduate students who intend to pursue graduate studies in engineering are strongly encouraged to take the combination of a stand-alone course in linear algebra (either APMA E3101 APPLIED MATH I: LINEAR ALGEBRA or MATH UN2010 LINEAR ALGEBRA) and a stand-alone course in ordinary differential equations (either MATH UN2030 ORDINARY DIFFERENTIAL EQUATIONS or MATH UN3027 Ordinary Differential Equations), instead of the combined topics course APMA E2101 INTRO TO APPLIED MATHEMATICS. In addition, such students are encouraged to take a course in partial differential equations (APMA E3102 APPLIED MATHEMATICS II: PDE'S or APMA E4200 PARTIAL DIFFERENTIAL EQUATIONS) as well as a course in numerical methods (APAM E3105 or APMA E4300 COMPUT MATH:INTRO-NUMERCL METH) as technical electives. Ideally, planning for these courses should start at the beginning of the sophomore year.
Fundamentals of Engineering (FE) Exam
The FE exam is a state licensing exam and the first step toward becoming a Professional Engineer (P.E.). P.E. licensure is important for engineers to obtain—it shows a demonstrated commitment to professionalism and an established record of abilities that will help a job candidate stand out in the field. Ideally, the FE exam should be taken in the senior year while the technical material learned while pursuing the undergraduate degree is still fresh in the student’s mind. In addition to the FE exam, achieving P.E. licensure requires some years of experience and a second examination, which tests knowledge gained in engineering practice. For more information, please see http://ncees.org/exams/fe-exam.
The Mechanical Engineering Department strongly encourages all seniors to take this exam and offers a review course covering material relevant to the exam, including a practice exam to simulate the testing experience. The FE exam is given in the fall and spring of each year. The review course is offered in the spring semester, concluding before the spring exam.
Integrated B.S./M.S. Program
The Integrated B.S./M.S. degree program is open to a qualified group of Columbia juniors and makes possible the earning of both the B.S. and M.S. degree in an integrated fashion. Benefits of this program include optimal matching of graduate courses with corresponding undergraduate prerequisites, greater ability to plan ahead for most advantageous course planning, opportunities to do research for credit during the summer after senior year, and up to 6 points of 4000-level technical electives from the B.S. requirement may count toward the fulfillment of the point requirement of the M.S. degree. Additional benefits include simplified application process, no GRE is required, and no reference letters are required. To qualify for this program, students must have a cumulative GPA of at least 3.4 and strong recommendations from within the Department. Students should apply for the program by April 30 in their junior year. For more information on requirements and access to an application form, please visit me.columbia.edu/integrated-bsms-program.
Express M.S. Application
The Express M.S. Application is offered to current seniors, including 3-2 students, who are enrolled in the BS program. In the Express M.S. Application, a master’s degree can be earned seamlessly. Graduate classes are available for seniors to apply toward their M.S. degree and the advanced courses that will be taken have been designed to have the exact prerequisites completed as an undergraduate. Other advantages include the opportunity for better course planning and creating a streamlined set of courses more possible. Additional benefits include simplified application process, no GRE is required and no reference letters are required. To qualify for this program, your cumulative GPA should be at least 3.5. For more information on requirements and access to an application, please visit me.columbia.edu/ms-express-application-1.
Barnard 4+1 Mechanical Engineering Pathways - Physics
The Barnard 4+1 Pathway in Physics is offered to current Barnard College juniors with a GPA of 3.5 or higher to apply to Master's programs in Civil Engineering, Electrical Engineering, and Mechanical Engineering. Students should inquire with Beyond Barnard and plan on attending an introductory information sessions for the unique 4+1 Pathway they may be interested in pursuing.
Faculty contact at Barnard: Professor Reshmi Mukherjee, rmukherj@barnard.edu; at SEAS: Professor Gerard Ateshian, gaa3@columbia.edu
Degree Track
An overview of the degree track in PDF format can be found here.
Mechanical Engineering Program Standard Track
| First Year | ||
|---|---|---|
| Semester I | ||
| MATH UN1101 | CALCULUS I | |
| Choose one of the following Physics courses depending on track: | ||
| INTRO TO MECHANICS ＆ THERMO | ||
| PHYSICS I:MECHANICS/RELATIVITY | ||
| ACCELERATED PHYSICS I | ||
| Choose a one-semester Chemistry lecture: | ||
| GENERAL CHEMISTRY I-LECTURES | ||
| GENERAL CHEMISTRY II-LECTURES | ||
| INTENSVE ORGANIC CHEMISTRY | ||
| 2ND TERM GEN CHEM (INTENSIVE) | ||
| ENGL CC1010 (taken Semester l or ll) | UNIVERSITY WRITING | |
| Choose one of the following Computer Science courses (taken Semester l or lll): | ||
| Introduction to Computer Science and Programming in Java | ||
| Introduction to Computer Science and Programming in MATLAB | ||
| INTRO TO COMP FOR ENG/APP SCI | ||
| PHED UN1001 | PHYSICAL EDUCATION ACTIVITIES | |
| ENGI E1102 (taken Semester l or ll) | THE ART OF ENGINEERING | |
| Semester II | ||
| MATH UN1102 | CALCULUS II | |
| Choose one of the following Physics courses depending on track: | ||
| INTRO ELEC/MAGNETSM ＆ OPTCS | ||
| PHYSICS II: THERMO, ELEC ＆ MAG | ||
| ACCELERATED PHYSICS II | ||
| CHEM UN15001 | GENERAL CHEMISTRY LABORATORY | |
| ENGL CC1010 (taken Semester l or ll) | UNIVERSITY WRITING | |
| PHED UN1002 | PHYSICAL EDUCATION ACTIVITIES | |
| ENGI E1102 (taken Semester l or ll) | THE ART OF ENGINEERING | |
| Second Year | ||
| Semester III | ||
| APMA E2000 - APMA E2001 (taken Semester lll or lV) | MULTV. CALC. FOR ENGI ＆ APP SCI | |
| ORCA E2500 (taken Semester lll or lV)2 | FOUNDATIONS OF DATA SCIENCE | |
| Choose one of the following Physics courses depending on track: | ||
| PHYS UN14033 | INTRO-CLASSCL ＆ QUANTUM WAVES | |
| PHYS UN26013 | PHYSICS III:CLASS/QUANTUM WAVE | |
| Choose one of the following Required Nontechnical Electives: | ||
| EURPN LIT-PHILOS MASTERPIECS I | ||
| CONTEMP WESTERN CIVILIZATION I | ||
Global Core (3–4) | ||
| HUMA UN1121 or UN1123 | MASTERPIECES OF WESTERN ART | |
| Choose one of the following Computer Science courses (taken Semester l or lll): | ||
| Introduction to Computer Science and Programming in Java | ||
| Introduction to Computer Science and Programming in MATLAB | ||
| INTRO TO COMP FOR ENG/APP SCI | ||
| Semester IV | ||
| APMA E2000 - APMA E2001 (taken Semester lll or lV) | MULTV. CALC. FOR ENGI ＆ APP SCI | |
| ORCA E2500 (taken Semester lll or lV)2 | FOUNDATIONS OF DATA SCIENCE | |
| Choose one of the following Mathematics: | ||
| INTRO TO APPLIED MATHEMATICS | ||
Linear Alebra and ODE5, 6 | ||
| Choose one of the following Required Nontechnical Electives: | ||
| EURPN LIT-PHILOS MASTRPIECS II | ||
| CONTEMP WESTRN CIVILIZATION II | ||
Global Core (3–4) | ||
| ECON UN1105 - ECON UN1155 | PRINCIPLES OF ECONOMICS | |
| ENME E3105 | MECHANICS | |
| Third Year | ||
| Semester V | ||
| MECE E3018 | MECHANICAL ENGINEERING LAB I | |
| MECE E3100 | INTRO TO MECHANCIS OF FLUIDS | |
| MECE E3301 | THERMODYNAMICS | |
| MECE E3408 | COMPUTER GRAPHICS ＆ DESIGN | |
| MECE E34147 | Mechanics of Solids for Mechanical Engineers | |
| MECE E1008 (taken Semester V or Vl) | INTRO TO MACHINING | |
| Nontech Electives (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll)8, 9 | ||
| Semester VI | ||
| MECE E3028 | MECHANICAL ENGINEERING LAB II | |
| ENME E3106 | DYNAMICS AND VIBRATIONS | |
| MECE E3311 | HEAT TRANSFER | |
| MECE E3610 | MATERIALS/PROCESSES IN MANUFAC | |
| ELEN E120110 | INTRO-ELECTRICAL ENGINEERING | |
| MECE E1008 (taken Semester V or Vl) | INTRO TO MACHINING | |
| Technical Electives (taken Semester Vl, Vll, or Vlll)11, 12 | ||
| Nontech Electives (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll)8, 9 | ||
| Fourth Year | ||
| Semester VII | ||
| MECE E3409 | MACHINE DESIGN | |
| MECE E3420 | ENG DES-CONCPT/DESIGN GENERATN | |
| Technical Electives (taken Semester Vl, Vll, or Vlll)11, 12 | ||
| Nontech Electives (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll)8, 9 | ||
| Semester VIII | ||
| MECE E3430 | ENGINEERING DESIGN | |
| EEME E3601 | CLASSICAL CONTROL SYSTEMS | |
| Technical Electives (taken Semester Vl, Vll, or Vlll)11, 12 | ||
| Nontech Electives (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll)8, 9 | ||
- 1
May substitute Physics Lab PHYS UN1494 INTRO TO EXPERIMENTAL PHYS-LAB (3) or PHYS UN3081 INTERMEDIATE LABORATORY WORK (2).
- 2
Offered in spring semester.
- 3
May substitute EEEB UN2001 ENVIRONMENTAL BIOLOGY I, BIOL UN2005 INTRO BIO I: BIOCHEM,GEN,MOLEC, or higher.
- 4
Students who take APMA E2101 INTRO TO APPLIED MATHEMATICS must complete an additional 3 point course in math or basic science with one of the following course designators: MATH, PHYS, CHEM, BIOL, STAT, APMA, or EEEB. One technical elective 3000-level or higher), with the approval of your ME faculty adviser, may be substituted for this purpose.
- 5
Linear algebra may be fulfilled by either APMA E3101 APPLIED MATH I: LINEAR ALGEBRA orMATH UN2010 LINEAR ALGEBRA.
- 6
Ordinary differential equations may be fulfilled by either MATH UN2030 ORDINARY DIFFERENTIAL EQUATIONS or MATH UN3027 Ordinary Differential Equations.
- 7
Required for class of 2025 and beyond.
- 8
Not required for Combined Plan students.
- 9
Not required for Combined Plan students.
- 10
Strongly recommended to be taken in Semester III or IV.
- 11
If APMA E2101 INTRO TO APPLIED MATHEMATICS is taken instead of Linear algebra and ODE, students must complete an additional 3-point course in math or basic science with one of the following course designators: MATH, PHYS, CHEM, BIOL, STAT, APMA, or EEEB. One technical elective (3000-level or higher), with the approval of your ME faculty adviser, may be substituted for this purpose.
- 12
9 points required; 6 must be MECE courses.
Mechanical Engineering Program Early Decision Track
| First Year | ||
|---|---|---|
| Semester I | ||
| MATH UN1101 | CALCULUS I | |
| Choose one of the following Physics courses depending on track: | ||
| INTRO TO MECHANICS ＆ THERMO | ||
| PHYSICS I:MECHANICS/RELATIVITY | ||
| ACCELERATED PHYSICS I | ||
| Choose a one-semester Chemistry lecture: | ||
| GENERAL CHEMISTRY I-LECTURES | ||
| GENERAL CHEMISTRY II-LECTURES | ||
| INTENSVE ORGANIC CHEMISTRY | ||
| 2ND TERM GEN CHEM (INTENSIVE) | ||
| ENGL CC1010 (taken Semester l or ll) | UNIVERSITY WRITING | |
| Choose one of the following Computer Science courses (taken Semester l or lll): | ||
| Introduction to Computer Science and Programming in Java | ||
| Introduction to Computer Science and Programming in MATLAB | ||
| INTRO TO COMP FOR ENG/APP SCI | ||
| PHED UN1001 | PHYSICAL EDUCATION ACTIVITIES | |
| ENGI E1102 (taken Semester l or ll) | THE ART OF ENGINEERING | |
| Semester II | ||
| MATH UN1102 | CALCULUS II | |
| Choose one of the following Physics courses depending on track: | ||
| INTRO ELEC/MAGNETSM ＆ OPTCS | ||
| PHYSICS II: THERMO, ELEC ＆ MAG | ||
| ACCELERATED PHYSICS II | ||
| CHEM UN15001 | GENERAL CHEMISTRY LABORATORY | |
| ENGL CC1010 (taken Semester l or ll) | UNIVERSITY WRITING | |
| ENME E3105 | MECHANICS | |
| PHED UN1002 | PHYSICAL EDUCATION ACTIVITIES | |
| ENGI E1102 (taken Semester l or ll) | THE ART OF ENGINEERING | |
| Second Year | ||
| Semester III | ||
| APMA E2000 - APMA E2001 (taken Semester lll or lV) | MULTV. CALC. FOR ENGI ＆ APP SCI | |
| ORCA E2500 (taken Semester lll or lV)2 | FOUNDATIONS OF DATA SCIENCE | |
| Choose one of the following Physics courses depending on track:3 | ||
| INTRO-CLASSCL ＆ QUANTUM WAVES | ||
| PHYSICS III:CLASS/QUANTUM WAVE | ||
| Choose one of the following Required Nontechnical Electives: | ||
| EURPN LIT-PHILOS MASTERPIECS I | ||
| CONTEMP WESTERN CIVILIZATION I | ||
Global Core (3–4) | ||
| MECE E34144 | Mechanics of Solids for Mechanical Engineers | |
| Choose one of the following Computer Science courses (taken Semester l or lll): | ||
| Introduction to Computer Science and Programming in Java | ||
| Introduction to Computer Science and Programming in MATLAB | ||
| INTRO TO COMP FOR ENG/APP SCI | ||
| Semester IV | ||
| APMA E2000 - APMA E2001 (taken Semester lll or lV) | MULTV. CALC. FOR ENGI ＆ APP SCI | |
| ORCA E2500 (taken Semester lll or lV)2 | FOUNDATIONS OF DATA SCIENCE | |
| Choose one of the following Mathematics: | ||
| INTRO TO APPLIED MATHEMATICS | ||
Linear Algebra and ODE6, 7 | ||
| Choose one of the following Required Nontechnical Electives: | ||
| EURPN LIT-PHILOS MASTRPIECS II | ||
| CONTEMP WESTRN CIVILIZATION II | ||
Global Core (3–4) | ||
| ELEN E1201 | INTRO-ELECTRICAL ENGINEERING | |
| MECE E3408 | COMPUTER GRAPHICS ＆ DESIGN | |
| Third Year | ||
| Semester V | ||
| MECE E3018 | MECHANICAL ENGINEERING LAB I | |
| MECE E3100 | INTRO TO MECHANCIS OF FLUIDS | |
| MECE E3301 | THERMODYNAMICS | |
| MECE E1008 (taken Semester V or Vl) | INTRO TO MACHINING | |
| HUMA UN1121 or UN1123 | MASTERPIECES OF WESTERN ART | |
| Nontech Electives (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll)8 | ||
| Semester VI | ||
| MECE E3028 | MECHANICAL ENGINEERING LAB II | |
| ENME E3106 | DYNAMICS AND VIBRATIONS | |
| MECE E3311 | HEAT TRANSFER | |
| MECE E3610 | MATERIALS/PROCESSES IN MANUFAC | |
| MECE E1008 (taken Semester V or Vl) | INTRO TO MACHINING | |
| ECON UN1105 - ECON UN1155 | PRINCIPLES OF ECONOMICS | |
| Technical Electives (taken Semester Vl, Vll, or Vlll)9,10 | ||
| Nontech Electives (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll)8 | ||
| Fourth Year | ||
| Semester VII | ||
| MECE E3409 | MACHINE DESIGN | |
| MECE E3420 | ENG DES-CONCPT/DESIGN GENERATN | |
| Technical Electives (taken Semester Vl, Vll, or Vlll)9, 10 | ||
| Nontech Electives (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll)8 | ||
| Semester VIII | ||
| MECE E3430 | ENGINEERING DESIGN | |
| EEME E3601 | CLASSICAL CONTROL SYSTEMS | |
| Technical Electives (taken Semester Vl, Vll, or Vlll)9, 10 | ||
| Nontech Electives (Students must complete the 27-point requirement.) (taken Semester V, Vl, Vll, or Vlll)8 | ||
- 1
May substitute Physics Lab PHYS UN1494 INTRO TO EXPERIMENTAL PHYS-LAB (3) or PHYS UN3081 INTERMEDIATE LABORATORY WORK (2).
- 2
Offered in spring semester.
- 3
May substitute EEEB UN2001 ENVIRONMENTAL BIOLOGY I, BIOL UN2005 INTRO BIO I: BIOCHEM,GEN,MOLEC, or higher.
- 4
Required for class of 2025 and beyond.
- 5
Students who take APMA E2101 INTRO TO APPLIED MATHEMATICS must complete an additional 3 point course in math or basic science with one of the following course designators: MATH, PHYS, CHEM, BIOL, STAT, APMA, or EEEB. One technical elective 3000-level or higher), with the approval of your ME faculty adviser, may be substituted for this purpose.
- 6
Linear algebra may be fulfilled by either APMA E3101 APPLIED MATH I: LINEAR ALGEBRA or MATH UN2010 LINEAR ALGEBRA.
- 7
Ordinary differential equations may be fulfilled by either MATH UN2030 ORDINARY DIFFERENTIAL EQUATIONS or MATH UN3027 Ordinary Differential Equations.
- 8
Not required for Combined Plan students.
- 9
If APMA E2101 INTRO TO APPLIED MATHEMATICS is taken instead of Linear Algebra and ODE, students must complete an additional 3-point course in math or basic science with one of the following course designators: MATH, PHYS, CHEM, BIOL, STAT, APMA, or EEEB. One technical elective (3000-level or higher), with the approval of your ME faculty adviser, may be substituted for this purpose.
- 10
9 points required; 6 must be MECE courses.