Readings

All readings are from the textbook: Masayuki Yano, et al. Math, Numerics, and Programming (for Mechanical Engineers). V2.1, August 2013. Files for each available unit are provided in the following table, courtesy of the authors. The entire textbook is available for download as a single file.

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

Textbook UNITS READING ASSIGNMENTS Supporting Videos
Entire Textbook as a Single File (PDF - 29.0MB)    

This resource may not render correctly in a screen reader.Unit I. (Numerical) Calculus; Elementary Programming Concepts (PDF - 2.6MB)

  • Chapter 1: Motivation
  • Chapter 2: Interpolation
  • Chapter 3: Differentiation
  • Chapter 4: Elements of a Program and MATLAB Basics
  • Chapter 5: MATLAB Arrays
  • Chapter 6: Functions in MATLAB
  • Chapter 7: Integration

Math and Numerics

  • Chapter 1
  • Sections 2.1, 3.1, and 7.1

MATLAB

  • Chapter 4
  • Sections 5.1, 5.2, and 5.4

The Macro-Me Robot

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

This resource may not render correctly in a screen reader.Unit II. Monte Carlo Methods (PDF - 1.9MB)

  • Chapter 8: Introduction
  • Chapter 9: Introduction to Random Variables
  • Chapter 10: Statistical Estimation: Bernoulli (Coins)
  • Chapter 11: Statistical Estimation: The Normal Density
  • Chapter 12: Monte Carlo: Areas and Volumes
  • Chapter 13: Monte Carlo: General Integration Procedures
  • Chapter 14: Montel Carlo: Failure Probabilities

Math and Numerics

  • Chapters 8, 9, 10, 11, and 12

MATLAB

  • Sections 6.1–6.4, and 5.3
  

This resource may not render correctly in a screen reader.Unit III. Linear Algebra 1: Matrices and Least Squares; Regression (PDF - 2.3MB)

  • Chapter 15: Motivation
  • Chapter 16: Matrices and Vectors: Definitions and Operations
  • Chapter 17: Least Squares
  • Chapter 18: MATLAB Linear Algebra (Briefly)
  • Chapter 19: Regression: Statistical Inference

Math and Numerics

  • Chapters 11, 15, 16, 17, and 19

MATLAB

  • 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.)

This resource may not render correctly in a screen reader.Unit IV. (Numerical) Differential Equations (PDF - 1.1MB)

  • Chapter 20: Motivation
  • Chapter 21: Initial Value Problems
  • Chapter 22: Boundary Value Problems
  • Chapter 23: Partial Differential Equations

Math and Numerics

  • Chapter 20
  • Sections 21.1.1–21.1.5, and 21.2

MATLAB:

  • Section 6.5–6.6

Macro-Me Suspension

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 - 13.7MB)

  • Chapter 24: Motivation
  • Chapter 25: Linear Systems
  • Chapter 26: Gaussian Elimination and Back Substitution
  • Chapter 27: Gaussian Elimination: Sparse Matrices
  • Chapter 28: Sparse Matrices in MATLAB

Math and Numerics:

  • Chapters 24, 25, 26, and 27
MATLAB
  • Chapter 28
  

This resource may not render correctly in a screen reader.Unit VI: Nonlinear Equations (PDF)

  • Chapter 29: Newton Iteration

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.)