Numerical Methods in Engineering with Python

by Jaan Kiusalaas

• ISBN13: 9780521191326
• ISBN10: 0521191327
• Edition: 2nd
• Format: Hardcover
• Copyright: 2010-01-29
• Publisher: Cambridge University Press
• More Book Details
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Summary

This text is for engineering students and a reference for practising engineers, especially those who wish to explore Python. This new edition features 18 additional exercises and the addition of rational function interpolation. Brent's method of root finding was replaced by Ridder's method, and the Fletcher-Reeves method of optimization was dropped in favor of the downhill simplex method. Each numerical method is explained in detail, and its shortcomings are pointed out. The examples that follow individual topics fall into two categories: hand computations that illustrate the inner workings of the method and small programs that show how the computer code is utilized in solving a problem. This second edition also includes more robust computer code with each method, which is available on the book Web site. This code is made simple and easy to understand by avoiding complex bookkeeping schemes, while maintaining the essential features of the method.

Author Biography

Jaan Kiusalaas is a Professor Emeritus in the Department of Engineering Science and Mechanics at Pennsylvania State University. He has taught computer methods, including finite element and boundary element methods, for more than 30 years. He is also the co-author of four other books-Engineering Mechanics: Statics, Engineering Mechanics: Dynamics, Mechanics of Materials, and an alternate version of this work with MATLAB code.

Table of Contents

Preface to the First Edition	p. viii
Preface to the Second Edition	p. x
Introduction to Python	p. 1
General Information	p. 1
Core Python	p. 3
Functions and Modules	p. 15
Mathematics Modules	p. 17
numpy Module	p. 18
Scoping of Variables	p. 24
Writing and Running Programs	p. 25
Systems of Linear Algebraic Equations	p. 27
Introduction	p. 27
Gauss Elimination Method	p. 33
LU Decomposition Methods	p. 40
	p. 51
Symmetric and Banded Coefficient Matrices	p. 54
Pivoting	p. 64
	p. 73
Matrix Inversion	p. 79
Iterative Methods	p. 82
	p. 93
Other Methods	p. 97
Interpolation and Curve Fitting	p. 99
Introduction	p. 99
Polynomial Interpolation	p. 99
Interpolation with Cubic Spline	p. 114
	p. 121
Least-Squares Fit	p. 124
	p. 135
Roots of Equations	p. 139
Introduction	p. 139
Incremental Search Method	p. 140
Method of Bisection	p. 142
Methods Based on Linear Interpolation	p. 145
Newton-Raphson Method	p. 150
Systems of Equations	p. 155
	p. 160
Zeroes of Polynomials	p. 166
	p. 174
Numerical Differentiation	p. 177
Introduction	p. 177
Finite Difference Approximations	p. 177
Richardson Extrapolation	p. 182
Derivatives by Interpolation	p. 185
	p. 189
Numerical Integration	p. 193
Introduction	p. 193
Newton-Cotes Formulas	p. 194
Romberg Integration	p. 202
	p. 207
Gaussian Integration	p. 211
	p. 225
Multiple Integrals	p. 227
	p. 239
Initial Value Problems	p. 243
Introduction	p. 243
Taylor Series Method	p. 244
Runge-Kutta Methods	p. 249
	p. 260
Stability and Stiffness	p. 266
Adaptive Runge-Kutta Method	p. 269
Bulirsch-Stoer Method	p. 277
	p. 284
Other Methods	p. 289
Two-Point Boundary Value Problems	p. 290
Introduction	p. 290
Shooting Method	p. 291
	p. 301
Finite Difference Method	p. 305
	p. 314
Symmetric Matrix Eigenvalue Problems	p. 319
Introduction	p. 319
Jacobi Method	p. 321
Power and Inverse Power Methods	p. 337
	p. 345
Householder Reduction to Tridiagonal Form	p. 351
Eigenvalues of Symmetric Tridiagonal Matrices	p. 358
	p. 367
Other Methods	p. 373
Introduction to Optimization	p. 374
Introduction	p. 374
Minimization along a Line	p. 376
Powell's Method	p. 382
Downhill Simplex Method	p. 392
	p. 399
Other Methods	p. 406
Taylor Series	p. 407
Matrix Algebra	p. 410
List of Program Modules (by Chapter)	p. 416
Index	p. 419
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