2.086 | Fall 2012 | Undergraduate

Numerical Computation for Mechanical Engineers


Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Recitation / labs: 1 session / week, 3 hours / session

Prerequisites: 2.001 Mechanics and Materials I, 2.003J Dynamics and Control I

Co-requisite: 2.005 Thermal-Fluids Engineering I

This course is geared toward undergraduate students. A more advanced graduate-level treatment can be found in 16.920J/2.097J/6.339J Numerical Methods for Partial Differential Equations.


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

Course Objectives


An understanding (in some cases review) of the mathematical ingredients on which numerical methods are based: calculus; probability; linear algebra; and differential equations.

An understanding of the basic “canon” of numerical approaches and numerical methods relevant to MechE: To what problems does an approach or method apply? How does the method work? What are the limitations and pros/cons? What can go wrong? What are the sources of error and uncertainty?

An understanding of elementary programming concepts and of the basic MATLAB architecture/environment, data types, syntax, and mathematical/numerical routines.


The ability to formulate an engineering problem in a mathematical form appropriate for subsequent computational treatment and to choose an appropriate numerical approach.

The ability to select, test, and use (or reject) third-party numerical programs with confidence.

The ability to solve mechanical engineering problems by computational approaches through a combination of ad hoc MATLAB scripts (typically rather short) and validated and informed calls to MATLAB or third-party numerical routines.

Attitudes and Professional Values

A commitment to always provide with any numerical prediction or recommendation some indication of error and uncertainty—and associated engineering implications—due to numerical treatment (and modeling error, however the latter is the emphasis of other MechE subjects).

Course Delivery

The course delivery includes lectures, recitations, reading assignments from the textbook Math, Numerics, and Programming (for Mechanical Engineers), problem sets, quizzes, and MATLAB exercises. These elements are summarized in the class calendar.

Lectures will comprise motivation/engineering demonstrations, blackboard review of key concepts, animations of numerical techniques, and examples of MATLAB implementations. The lectures will emphasize the math and numerics, but also the connection to MATLAB programming.

Recitations will comprise mini-lectures on MATLAB topics, programming of the assigned MATLAB exercises, and discussion of the problem sets. The recitations will emphasize MATLAB programming, but with connection to the math and numerics.

Reading assignments will be provided at the beginning of each Unit.

The problem sets will include “theory,” formulation, implementation (MATLAB), and interpretation and assessment. The write-up of each problem set should be succinct but should clearly answer all questions and, as necessary, show all supporting work and evidence. MATLAB programs associated with the problem set should not be submitted unless specifically requested in a question but should be kept on file until the end of the semester (after final subject grades are assigned).

The quizzes will cover the math, numerics, and programming concepts explicitly covered in lectures, recitations, assigned MATLAB exercises, and problems sets; a detailed study guide will be provided prior to each quiz. Quizzes will take place during the usual lecture period but will typically be less than the full 1.5 hours (the remainder of the period to be devoted to lecture/new material).

The MATLAB exercises for each recitation will be distributed prior to recitation. Students should review these exercises and even sketch the necessary MATLAB programs prior to recitation in order to make good progress during recitation. On the due date (Monday of the following week with exceptions for holidays) by 5 PM students should upload to the course website a folder containing the completed scripts and functions for the assignment. All of the scripts should be in a single file, with each script preceded by a comment line which indicates the exercise number; each function .m file should contain a comment line which indicates the exercise number.


Assessment is based on three components: five problem sets, four (in-class) quizzes, and the cumulative MATLAB exercises for the entire semester.

Problem sets 1–3 and 5 (200/19)% each
Problem Set 4 (400/19)%
Four quizzes (125/19)% each
Cumulative MATLAB exercises (200/19)%

Note the preponderance of MATLAB exercises will be during the first month of the semester.

Policy on Collaboration

Students may discuss all class material and assignments at length with one another, including derivations and code. But there can be no written transcript, no code transfer, and no electronic record whatsoever of a session: upon terminating a discussion, the blackboard must be erased, the paper recycled, the screen cleared, and all files deleted; any take-away must be exclusively in each student’s own head. Students choosing to collaborate must list their collaborators in the header of their submitted assignments.

Learning Resource Types
menu_book Online Textbook
theaters Demonstration Videos
grading Exams with Solutions
assignment Programming Assignments