2.086 | Fall 2014 | Undergraduate

Numerical Computation for Mechanical Engineers


Course Meeting Times

Recitations: 1 session / week, 3 hours / session

The primary student-faculty contact opportunities are (i) the 3-hour weekly recitation, focused on MATLAB® skills and more generally the application of the course material as motivated by the assignments, and (ii) the several weekly office hours with the course staff.

Course Content

Elementary programming concepts, including variable types, data structures, operations, flow control, and functions; MATLAB environment, syntax, (sparse) matrix operations, and numerical computation built-in functions. Introductory linear algebra, and probability and statistical estimation. Formulation of engineering problems in forms suitable for efficient numerical computation. Numerical methods relevant to engineering, including approximation (interpolation, least squares, statistical regression), numerical integration and differentiation, solution of linear and nonlinear algebraic systems of equations and eigenproblems, discretization of ordinary differential equations. Deterministic and Monte Carlo approaches.

Course Objectives


The student should assimilate:

  • An understanding (in some cases review) of the mathematical ingredients on which numerical methods are based: Calculus; probability and statistics; linear algebra; and ordinary differential equations.
  • An understanding of the basic “canon” of numerical approaches and numerical methods relevant to MechE and engineering more broadly: To what problems does an approach or method apply? How does the method work? How does the method compare to alternatives (in terms of appropriate computational metrics)? What can go wrong? What are the sources of error and uncertainty?
  • An understanding of (i) elementary programming concepts, and (ii) the basic MATLAB architecture / environment, data types, syntax, and mathematical / numerical routines.


The student should develop:

  • The ability (i) to formulate an engineering problem in a mathematical form appropriate for subsequent computational treatment, and (ii) to choose an appropriate numerical approach.
  • The ability to select and critically apply third-party numerical codes and software packages.
  • The ability to solve mechanical engineering problems by computational approaches through a combination of (i) ad hoc custom MATLAB scripts (typically rather short), and (ii) informed calls to MATLAB or third-party numerical routines.
  • The ability to create and interpret meaningful test cases to confirm correct implementation of a computational approach.

Attitudes and Professional Values

The student should adopt:

  • A commitment to (i) always test codes thoroughly, and (ii) always provide, with any numerical prediction or recommendation, some indication of the error and uncertainty–and associated engineering implications–due to numerical treatment (and to modeling assumptions, which however is the focus of other MechE subjects).

Course Textbook

The textbook for the course is the online textbook: Masayuki Yano, et al. Math, Numerics, and Programming (for Mechanical Engineers). V2.1, August 2013. Unpublished manuscript. The manuscript is available for download in the Readings section.

The less-is-more variant of the textbook is available in the Nutshells & GUIs section: Masayuki Yano, et al. Math, Numerics, & Programming for Mechanical Engineers… in a Nutshell. V1.1, 2014. Unpublished manuscript. 


This course is based on MATLAB. MIT students can run MATLAB on their own laptops, or use the shared machines in the class recitation / lab room.

[Note to OCW Users: MIT OpenCourseWare does not provide student access or discounts for MATLAB software. It can be purchased from The MathWorks®. For more information about MATLAB Pricing and Licensing, contact The MathWorks® directly.]


Assignments (5 in total; equally weighted) 80%
Mini Quizzes (7 in total; equally weighted) 20%

Formal assessment is based on two components: Five assignments, and seven mini quizzes. The nominal subject grade is a weighted sum of the assignment grades and the mini quiz grades: The weight for each assignment is 16%; the weight for each mini quiz is 20 / 7%. Final letter grades are decided in accordance with the descriptions provided in MIT Regulations of the Faculty and are informed by the nominal subject grade but also by instructor evaluation of student effort, independence, and progress.

The mini quizzes will be of duration 20 minutes and will be given at the beginning of the recitation period. In order to obtain credit for the mini quiz, you must take the mini quiz in the allocated period—please make sure to arrive at your recitation on time as no allowances can be made for tardiness—and in the recitation to which you are permanently assigned.

The mini quizzes will focus exclusively on the math and numerics component of 2.086, with no reference to MATLAB. The material for the quizzes will be derived exclusively from the Required Reading nutshells, with each quiz focused on the specific nutshell indicated in the Schedule-cum-Syllabus. (Note that any material in nutshell appendices is solely for your intellectual enjoyment; you are not responsible for this appendix material, and you will not be quizzed on this appendix material.) The nutshells include “Check You Are With The Program” (CYAWTP) questions which should serve as your study guide: The mini quiz questions will be similar to the CYAWTPs in terms of material exercised, scope, and difficulty, but (unlike the CYAWTPs) presented in multiple-choice format.

You may bring to the mini quizzes any material you wish but only in hardcopy form: no electronic devices of any variety are permitted.

Collaboration Policy


No collaboration is permitted on the assignments. In particular, you cannot view in any medium, or incorporate in any form into your own computer codes, any computer codes or excerpts of computer codes developed for 2.086 assignments by current or former 2.086 students, or any third-party consultants.

You may of course incorporate code suggestions from 2.086 staff including the templates provided with each assignment.

Note that codes submitted in assignments may be compared to each other and to a historical database for similarity beyond the anticipated.

Mini Quizzes

No collaboration of any kind is permitted on the mini quizzes. Furthermore, as each mini quiz will be administered asynchronously to the different recitation sections (and also in make-up oral sessions as needed), the mini quizzes should not be discussed with any parties, except 2.086 instructors, until the end of the semester.

Required Reading

We encourage collaboration on the Required Reading and in particular on the “Check You Are with the Program” (CYAWTP) questions in the Nutshells as preparation for the mini quizzes.


All cases of infringement related either to assignments or mini quizzes will be referred to the relevant MIT committees for adjudication and action.

Missed-Work Policy

Excused Absences

In order to obtain an excused absence from a particular course requirement (assignment or mini quiz), you will need either (i) a medical justification, or (ii) an explicit waiver from the Office of the Dean for Student Life. (In some cases, and with advance notice, professional travel may qualify as an excused absence; please speak to an instructor at least two weeks before the anticipated absence.)


No credit will be received for the late submission of an assignment unless the student has obtained, prior to the due date, an excused absence. A student with an excused absence for an assignment should discuss the situation with an instructor, who will then establish a new due date; there is no grade penalty in the case of an excused absence.

Mini Quizzes

No credit will be received for a mini quiz which is not taken in your designated recitation section on the date indicated in the calendar, and in the specific period reserved for the mini quiz (the beginning of recitation), unless the student has received, prior to the day of the quiz, an excused absence. A student with an excused absence for a mini quiz will be given a make-up oral mini quiz by an instructor.

Course Info

Learning Resource Types
Online Textbook
Demonstration Videos
Programming Assignments