2.086 | Fall 2012 | Undergraduate

Numerical Computation for Mechanical Engineers


All readings are from the textbook: Masayuki Yano, James Douglass Penn, George Konidaris, and Anthony T. Patera. Math, Numerics, and Programming (for Mechanical Engineers). V1.2, September 2012. Files for each available unit are provided in the following table, courtesy of the authors.

Students should read all of the assignments for the unit before proceeding to the associated MATLAB® Exercises and the Problem Sets. In general, students should skip the advanced material in the text, indicated either by blue shading or by blue “Advanced Material” bookends.

Unit I. (Numerical) Calculus; Elementary Programming Concepts (PDF - 2.4MB)

Math and Numerics:

  • Chapter 1
  • Section 2.1; Section 3.1; Section 7.1


  • Chapter 4 (for Recitation session 1)
  • Section 5.1; Section 5.2; Section 5.4 (for Recitation session 2)

The Macro-Me-Robot^1

Video of a 2.086 robot performing IR range finding and odometry. (Courtesy of James Penn. Used with permission.)

Unit II. Monte Carlo Methods (PDF - 2.1MB)

Math and Numerics:

  • Chapters 8, 9, 10, 11, 12, 14


  • Section 6.1, 6.2, 6.3, and 6.4
  • Section 5.3

Bernoulli/Area Estimation Summary (PDF)

Unit III. Linear Algebra 1: Matrices and Least Squares; Regression (PDF - 2.3MB)

Math and Numerics:

  • Chapters 11, 15, 16, 17, 19


  • Chapter 18

The Macro-Me-Robot: Friction Test

Video of a 2.086 robot attempting to push a load on two different surfaces. (Courtesy of James Penn. Used with permission.)

Unit IV. (Numerical) Differential Equations (PDF - 1.2MB)

Math and Numerics:

  • Chapter 20; Sections 21.1.1 to 21.1.5 inclusive; Section 21.2; page 348; Section 21.4 but only the first two paragraphs.


  • Section 6.5, Section 6.6.


Video of a 2.086 robot driving over a small bump at three different velocities. (Courtesy of James Penn. Used with permission.)

Unit V. (Numerical) Linear Algebra 2: Solution of Linear Systems (PDF - 12.7MB)

Math and Numerics:

  • Chapters 24, 25, 26, 27


  • Chapter 28

Unit VI. Linear Algebra 3: Eigenvalue Problems—NOT AVAILABLE    
Unit VII. Nonlinear Equations (PDF)

Math and Numerics, and MATLAB

  • Chapter 29

Robot Arm Demo

Video of a 2.086 robot arm tracking a specified trajectory. (Courtesy of James Penn. Used with permission.)

V1.2 Errata (PDF)    
Learning Resource Types
Online Textbook
Demonstration Videos
Exams with Solutions
Programming Assignments