Numerical Methods in Engineering with MATLABÂ®

Numerical Methods in Engineering with MATLABr is a text for engineering students and a reference for practicing engineers. The choice of numerical methods was based on their relevance to engineering problems. Every method is discussed thoroughly and illustrated with problems involving both hand computation and programming. MATLAB M-files accompany each method and are available on the book website. This code is made simple and easy to understand by avoiding complex book-keeping schemes, while maintaining the essential features of the method. MATLAB was chosen as the example language because of its ubiquitous use in engineering studies and practice. This new edition includes the new MATLAB anonymous functions, which allow the programmer to embed functions into the program rather than storing them as separate files. Other changes include the addition of rational function interpolation in Chapter 3, the addition of Ridder's method in place of Brent's method in Chapter 4, and the addition of downhill simplex method in place of the Fletcher-Reeves method of optimization in Chapter 10.

Jaan Kiusalaas is a Professor Emeritus in the Department of Engineering Science and Mechanics at the Pennsylvania State University. He has taught numerical 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 Numerical Methods in Engineering with Python, second edition.

Preface to the First Edition	p. ix
Preface to the Second Edition	p. xi
Introduction to MATLAB	p. 1
Quick Overview	p. 1
Data Types and Variables	p. 4
Operators	p. 9
Flow Control	p. 11
Functions	p. 15
Input/Output	p. 19
Array Manipulation	p. 20
Writing and Running Programs	p. 24
Plotting	p. 25
Systems of Linear Algebraic Equations	p. 27
Introduction	p. 27
Gauss Elimination Method	p. 33
LU Decomposition Methods	p. 40
Problem Set 2.1	p. 51
Symmetric and Banded Coefficient Matrices	p. 54
Pivoting	p. 64
Problem Set 2.2	p. 73
Matrix Inversion	p. 80
Iterative Methods	p. 82
Problem Set 2.3	p. 93
Interpolation and Curve Fitting	p. 100
Introduction	p. 100
Polynomial Interpolation	p. 100
Interpolation with Cubic Spline	p. 116
Problem Set 3.1	p. 122
Least-Squares Fit	p. 125
Problem Set 3.2	p. 137
Roots of Equations	p. 142
Introduction	p. 142
Incremental Search Method	p. 143
Method of Bisection	p. 145
Methods Based on Linear Interpolation	p. 148
Newton-Raphson Method	p. 154
Systems of Equations	p. 159
Problem Set 4.1	p. 164
Zeros of Polynomials	p. 171
Problem Set 4.2	p. 178
Numerical Differentiation	p. 181
Introduction	p. 181
Finite Difference Approximations	p. 181
Richardson Extrapolation	p. 186
Derivatives by Interpolation	p. 189
Problem Set 5.1	p. 194
Numerical Integration	p. 198
Introduction	p. 198
Newton-Cotes Formulas	p. 199
Romberg Integration	p. 208
Problem Set 6.1	p. 212
Gaussian Integration	p. 216
Problem Set 6.2	p. 230
Multiple Integrals	p. 233
Problem Set 6.3	p. 244
Initial Value Problems	p. 248
Introduction	p. 248
Taylor Series Method	p. 249
Runge-Kutta Methods	p. 254
Problem Set 7.1	p. 264
Stability and Stiffness	p. 270
Adaptive Runge-Kutta Method	p. 274
Bulirsch-Stoer Method	p. 281
Problem Set 7.2	p. 288
Two-Point Boundary Value Problems	p. 295
Introduction	p. 295
Shooting Method	p. 296
Problem Set 8.1	p. 306
Finite Difference Method	p. 310
Problem Set 8.2	p. 319
Symmetric Matrix Eigenvalue Problems	p. 325
Introduction	p. 325
Jacobi Method	p. 327
Inverse Power and Power Methods	p. 343
Problem Set 9.1	p. 350
Householder Reduction to Tridiagonal Form	p. 357
Eigenvalues of Symmetric Tridiagonal Matrices	p. 364
Problem Set 9.2	p. 373
Introduction to Optimization	p. 380
Introduction	p. 380
Minimization Along a Line	p. 382
Powell's Method	p. 389
Downhill Simplex Method	p. 399
Problem Set 10.1	p. 406
Appendices	p. 415
Taylor Series	p. 415
Matrix Algebra	p. 418
List of Computer Programs	p. 423
	p. 423
	p. 423
	p. 424
	p. 424
	p. 424
	p. 424
	p. 425
	p. 425
Index	p. 427
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Numerical Methods in Engineering with MATLABÂ®

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