ISBN-10:
0521852889
ISBN-13:
9780521852883
Pub. Date:
06/30/2005
Publisher:
Cambridge University Press
Numerical Methods in Engineering with MATLAB / Edition 1

Numerical Methods in Engineering with MATLAB / Edition 1

by Jaan Kiusalaas

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Product Details

ISBN-13: 9780521852883
Publisher: Cambridge University Press
Publication date: 06/30/2005
Edition description: Older Edition
Pages: 608
Product dimensions: 7.01(w) x 8.98(h) x 0.75(d)

About the Author

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 thirty years. He is also the coauthor or author of numerous books.

Table of Contents

Preface to the First Edition ix

Preface to the Second Edition xi

1 Introduction to MATLAB 1

1.1 Quick Overview 1

1.2 Data Types and Variables 4

1.3 Operators 9

1.4 Flow Control 11

1.5 Functions 15

1.6 Input/Output 19

1.7 Array Manipulation 20

1.8 Writing and Running Programs 24

1.9 Plotting 25

2 Systems of Linear Algebraic Equations 27

2.1 Introduction 27

2.2 Gauss Elimination Method 33

2.3 LU Decomposition Methods 40

Problem Set 2.1 51

2.4 Symmetric and Banded Coefficient Matrices 54

2.5 Pivoting 64

Problem Set 2.2 73

*2.6 Matrix Inversion 80

*2.7 Iterative Methods 82

Problem Set 2.3 93

3 Interpolation and Curve Fitting 100

3.1 Introduction 100

3.2 Polynomial Interpolation 100

3.3 Interpolation with Cubic Spline 116

Problem Set 3.1 122

3.4 Least-Squares Fit 125

Problem Set 3.2 137

4 Roots of Equations 142

4.1 Introduction 142

4.2 Incremental Search Method 143

4.3 Method of Bisection 145

4.4 Methods Based on Linear Interpolation 148

4.5 Newton-Raphson Method 154

4.6 Systems of Equations 159

Problem Set 4.1 164

*4.7 Zeros of Polynomials 171

Problem Set 4.2 178

5 Numerical Differentiation 181

5.1 Introduction 181

5.2 Finite Difference Approximations 181

5.3 Richardson Extrapolation 186

5.4 Derivatives by Interpolation 189

Problem Set 5.1 194

6 Numerical Integration 198

6.1 Introduction 198

6.2 Newton-Cotes Formulas 199

6.3 Romberg Integration 208

Problem Set 6.1 212

6.4 Gaussian Integration 216

Problem Set 6.2 230

*6.5 Multiple Integrals 233

Problem Set 6.3 244

7 Initial Value Problems 248

7.1 Introduction 248

7.2 Taylor Series Method249

7.3 Runge-Kutta Methods 254

Problem Set 7.1 264

7.4 Stability and Stiffness 270

7.5 Adaptive Runge-Kutta Method 274

7.6 Bulirsch-Stoer Method 281

Problem Set 7.2 288

8 Two-Point Boundary Value Problems 295

8.1 Introduction 295

8.2 Shooting Method 296

Problem Set 8.1 306

8.3 Finite Difference Method 310

Problem Set 8.2 319

9 Symmetric Matrix Eigenvalue Problems 325

9.1 Introduction 325

9.2 Jacobi Method 327

9.3 Inverse Power and Power Methods 343

Problem Set 9.1 350

9.4 Householder Reduction to Tridiagonal Form 357

9.5 Eigenvalues of Symmetric Tridiagonal Matrices 364

Problem Set 9.2 373

10 Introduction to Optimization 380

10.1 Introduction 380

10.2 Minimization Along a Line 382

10.3 Powell's Method 389

10.4 Downhill Simplex Method 399

Problem Set 10.1 406

Appendices 415

A1 Taylor Series 415

A2 Matrix Algebra 418

List of Computer Programs 423

Chapter 2 423

Chapter 3 423

Chapter 4 424

Chapter 6 424

Chapter 7 424

Chapter 8 424

Chapter 9 425

Chapter 10 425

Index 427

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