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# Introduction to Numerical Methods and Matlab Programming for Engineers

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

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.

TextPrograms
Wholeby Partsby Section
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
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: An Application of Eigenvectors: Vibrational Modes
Lecture 16: Numerical Methods for Eigenvalues
Lecture 17: The QR Method
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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
Lecture 24: Double Integrals for Rectangles mylowerleft.m; mydblsimpweights.m
Lecture 25: Double Integrals for Non-rectangles mywedge.m; mywasher.m
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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
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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
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Lecture 41: Finite Elements mywasher.m
Lecture 42: Determining Internal Node Values myfiniteelem.m
Back matter