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Introduction to Numerical Methods and Matlab Programming for Engineers

by Todd Young and Martin J. Mohlenkamp

Copyright © 2008, 2009, 2014, 2017, 2020, 2021, 2023 Todd Young and Martin J. Mohlenkamp.

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Adoption of this book for classroom use is encouraged, but instructors are asked to notify the authors of such usage. To obtain the source files contact the authors.

You can access the book as a single pdf file, as separate files for each part, or as separate files for each lecture. Programs mentioned are included here with the lecture(s) in which they are mentioned.

Whole Book

• Front matter
• Part I: Matlab and Solving Equations
  • Lecture 1: Vectors, Functions, and Plots in Matlab
  • Lecture 2: Matlab Programs
  • Lecture 3: Newton's Method and Loops (mynewton.m)
  • Lecture 4: Controlling Error and Conditional Statements
  • Lecture 5: The Bisection Method and Locating Roots (mybisect.m)
  • Lecture 6: Secant Methods (mysecant.m)
  • Lecture 7: Symbolic Computations
• Part II: Linear Algebra
  • Lecture 8: Matrices and Matrix Operations in Matlab
  • Lecture 9: Introduction to Linear Systems
  • Lecture 10: Some Facts About Linear Systems
  • Lecture 11: Accuracy, Condition Numbers and Pivoting
  • Lecture 12: LU Decomposition
  • Lecture 13: Nonlinear Systems - Newton's Method
  • Lecture 14: Eigenvalues and Eigenvectors
  • Lecture 15: Vibrational Modes and Frequencies
  • Lecture 16: Numerical Methods for Eigenvalues
  • Lecture 17: The QR Method
  • (placeholder) 18
• Part III: Functions and Data
  • Lecture 19: Polynomial and Spline Interpolation
  • Lecture 20: Least Squares Fitting: Noisy Data
  • Lecture 21: Integration: Left, Right and Trapezoid Rules
  • Lecture 22: Integration: Midpoint and Simpson's Rules (mysimpweights.m)
  • Lecture 23: Plotting Functions of Two Variables (mywedge.m; mywasher.m; mythreecorners.m)
  • Lecture 24: The Gradient and Max-Min Problems
  • Lecture 25: Double Integrals for Rectangles (mylowerleft.m; mydblsimpweights.m)
  • Lecture 26: Double Integrals for Non-rectangles (mywedge.m; mywasher.m)
  • Lecture 27: Numerical Differentiation
  • Lecture 28: The Main Sources of Error
• Part IV: Differential Equations
  • Lecture 29: Reduction of Higher Order Equations to Systems
  • Lecture 30: Euler Methods (myeuler.m; mymodeuler.m)
  • Lecture 31: Higher Order Methods
  • (placeholder) 32
  • Lecture 33: ODE Boundary Value Problems and Finite Differences (myexactbeam.m)
  • Lecture 34: Finite Difference Method -- Nonlinear ODE (mynonlinheat.m)
  • Lecture 35: Parabolic PDEs - Explicit Method (myheat.m)
  • Lecture 36: Solution Instability for the Explicit Method (myexpmatrix.m)
  • Lecture 37: Implicit Methods
  • Lecture 38: Insulated Boundary Conditions (myheatdisk.m)
  • Lecture 39: Finite Difference Method for Elliptic PDEs (mypoisson.m)
  • (placeholder) 40
  • Lecture 41: Finite Elements (mywasher.m)
  • Lecture 42: Determining Internal Node Values (myfiniteelem.m)
• Back matter

Last modified: Thu Aug 24 12:16:18 UTC 2023