Numerical Computation for Mechanical Engineers

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)
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.)
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
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.)
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
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.)