This text provides a first course in numerical methods and programming taught through the medium of MATLAB. It is designed to give readers their first exposure to any kind of programming. The first three chapters introduce readers to the power of MATLAB without overwhelming them with its advanced features; the text then covers all the elementary material associated with numerical methods, and helps students develop skills in algorithm design. Examples of code are provided to debug, hence accentuating the need for precision, and developing readers? skills in finding errors in their own work. At the end of each chapter, tasks are provided to reinforce the ideas introduced, with full solutions at the back of the book. A glossary of terms is provided, with each term supported by an example of the syntaxes commonly encountered.
Aimed at first and second year undergraduates in mathematics and engineering, this book will also be invaluable for engineers who need to use MATLAB in their work environment.
Author(s): Stephen R. Otto, James P. Denier
Edition: 1
Publisher: Springer
Year: 2005
Language: English
Pages: 468
City: London
An Introduction to Programming and Numerical Methods in MATLAB......Page 1
Preface......Page 5
The Structure of This Text......Page 6
Contents......Page 9
1.1 Introduction and a Word of Warning......Page 14
1.2 Scalar Quantities and Variables......Page 15
1.3 Format: The Way in Which Numbers Appear......Page 25
1.5 Setting Up Mathematical Functions......Page 30
1.6 Some MATLAB Specific Commands......Page 33
1.7 Accessing Elements of Arrays......Page 36
1.8 Tasks......Page 37
2.1 Creating Scripts and Functions......Page 40
2.2 Plotting Simple Functions......Page 49
2.3 Functions of Functions......Page 62
2.4 Errors......Page 64
2.5 Tasks......Page 70
3.2 Loops Structures......Page 75
3.3 Summing Series......Page 80
3.4 Conditional Statements......Page 95
3.5 Conditional loops......Page 102
3.6 MATLAB Specific Commands......Page 104
3.7 Error Checking......Page 106
4.1 Introduction......Page 114
4.2 Initial Estimates......Page 115
4.3 Fixed Point Iteration......Page 120
4.4 Bisection......Page 124
4.5 Newton–Raphson and Secant Methods......Page 128
4.6 Repeated Roots of Functions......Page 134
4.7 Zeros of Higher-Dimensional Functions(*)......Page 136
4.8 MATLAB Routines for Finding Zeros......Page 139
4.9 Tasks......Page 141
5.1 Introduction......Page 144
5.2 Saving and Reading Data......Page 145
5.3 Which Points to Use?......Page 150
5.4 Newton Forward Differences and Lagrange Polynomials......Page 152
5.5 Calculating Interpolated and Extrapolated Values......Page 159
5.6 Splines......Page 161
5.7 Curves of Best Fit......Page 163
5.8 Interpolation of Non-Smooth Data......Page 166
5.9 Minimisation of Functions and Parameter Retrieval......Page 172
5.10 Tasks......Page 177
6.1 Introduction......Page 179
6.2 Properties of Matrices and Systems of Equations......Page 196
6.3 Elementary Row Operations......Page 201
6.4 Matrix Decomposition......Page 209
6.5 Eigenvalues and Eigenvectors......Page 214
6.6 Specific MATLAB Commands......Page 218
6.7 Characteristic Polynomials......Page 222
6.8 Exponentials of Matrices......Page 224
6.9 Tasks......Page 227
7.1 Introduction......Page 234
7.2 Integration Using Straight Lines......Page 235
7.3 Integration Using Quadratics......Page 239
7.4 Integration Using Cubic Polynomials......Page 244
7.5 Integrating Using MATLAB Commands......Page 246
7.6 Specific Examples of Integrals......Page 247
7.7 Tasks......Page 251
8.2 Euler’s Method and Crank–Nicolson......Page 255
8.3 Banded Matrices......Page 267
8.4 Runge–Kutta Methods......Page 271
9.2 Statistical quantities......Page 299
9.3 Random Numbers and Distributions......Page 303
9.4 Maps and White Noise......Page 308
9.5 Tasks......Page 327
A A Mathematical Introduction to Matrices......Page 331
B.1 Arithmetic and Logical Operators......Page 342
B.2 Symbols......Page 350
B.3 Plotting Commands......Page 354
B.4 General MATLAB Commands......Page 372
C.1 Solutions for Tasks from Chapter 1......Page 395
C.2 Solutions for Tasks from Chapter 2......Page 400
C.3 Solutions for Tasks from Chapter 3......Page 406
C.4 Solutions for Tasks from Chapter 4......Page 414
C.5 Solutions for Tasks from Chapter 5......Page 420
C.6 Solutions for Tasks from Chapter 6......Page 424
C.7 Solutions for Tasks from Chapter 7......Page 435
C.8 Solutions for Tasks from Chapter 8......Page 442
C.9 Solutions for Tasks from Chapter 9......Page 460
Index......Page 464
