An elementary first course for students in mathematics and engineering Practical in approach: examples of code are provided for students to debug, and tasks – with full solutions – are provided at the end of each chapter Includes a glossary of useful terms, with each term supported by an example of the syntaxes commonly encountered
Author(s): Stephen R. Otto, James P. Denier
Edition: 1st Edition.
Publisher: Springer
Year: 2005
Language: English
Pages: 479
Preface......Page 7
The Structure of This Text......Page 8
Contents......Page 11
1.1 Introduction and a Word of Warning......Page 16
1.2 Scalar Quantities and Variables......Page 17
1.3 Format: The Way in Which Numbers Appear......Page 27
1.4 Vectors in MATLAB......Page 28
1.5 Setting Up Mathematical Functions......Page 32
1.6 Some MATLAB Speci.c Commands......Page 35
1.7 Accessing Elements of Arrays......Page 38
1.8 Tasks......Page 39
2.1 Creating Scripts and Functions......Page 42
2.2 Plotting Simple Functions......Page 51
2.3 Functions of Functions......Page 64
2.4 Errors......Page 66
2.5 Tasks......Page 72
3.2 Loops Structures......Page 78
3.3 Summing Series......Page 83
3.4 Conditional Statements......Page 98
3.5 Conditional loops......Page 105
3.6 MATLAB Speci.c Commands......Page 107
3.7 Error Checking......Page 109
3.8 Tasks......Page 112
4.1 Introduction......Page 118
4.2 Initial Estimates......Page 119
4.3 Fixed Point Iteration......Page 124
4.4 Bisection......Page 128
4.5 Newton–Raphson and Secant Methods......Page 132
4.6 Repeated Roots of Functions......Page 138
4.7 Zeros of Higher-Dimensional Functions(*)......Page 140
4.8 MATLAB Routines for Finding Zeros......Page 143
4.9 Tasks......Page 145
5.1 Introduction......Page 148
5.2 Saving and Reading Data......Page 149
5.3 Which Points to Use?......Page 154
5.4 Newton Forward Di.erences and Lagrange Polynomials......Page 156
5.5 Calculating Interpolated and Extrapolated Values......Page 163
5.6 Splines......Page 165
5.7 Curves of Best Fit......Page 167
5.8 Interpolation of Non-Smooth Data......Page 170
5.9 Minimisation of Functions and Parameter Retrieval......Page 176
5.10 Tasks......Page 181
6.1 Introduction......Page 184
6.2 Properties of Matrices and Systems of Equations......Page 201
6.3 Elementary Row Operations......Page 206
6.4 Matrix Decomposition......Page 214
6.5 Eigenvalues and Eigenvectors......Page 219
6.6 Speci.c MATLAB Commands......Page 223
6.7 Characteristic Polynomials......Page 227
6.8 Exponentials of Matrices......Page 229
6.9 Tasks......Page 232
7.1 Introduction......Page 240
7.2 Integration Using Straight Lines......Page 241
7.3 Integration Using Quadratics......Page 245
7.4 Integration Using Cubic Polynomials......Page 250
7.5 Integrating Using MATLAB Commands......Page 252
7.6 Speci.c Examples of Integrals......Page 253
7.7 Tasks......Page 257
8.2 Euler’s Method and Crank–Nicolson......Page 262
8.3 Banded Matrices......Page 274
8.4 Runge–Kutta Methods......Page 278
8.5 Higher-Order Systems......Page 281
8.6 Boundary-Value Problems......Page 293
8.7 Population Dynamics......Page 297
8.8 Eigenvalues of Di.erential Systems......Page 300
8.9 Tasks......Page 301
9.2 Statistical quantities......Page 306
9.3 Random Numbers and Distributions......Page 310
9.4 Maps and White Noise......Page 315
9.5 Tasks......Page 334
A: A Mathematical Introduction to Matrices......Page 338
A.1 Special Matrices......Page 345
A.2 Inverses of Matrices......Page 346
B.1 Arithmetic and Logical Operators......Page 350
B.2 Symbols......Page 358
B.3 Plotting Commands......Page 362
B.4 General MATLAB Commands......Page 380
C.1 Solutions for Tasks from Chapter 1......Page 404
C.2 Solutions for Tasks from Chapter 2......Page 409
C.3 Solutions for Tasks from Chapter 3......Page 415
C.4 Solutions for Tasks from Chapter 4......Page 423
C.5 Solutions for Tasks from Chapter 5......Page 429
C.6 Solutions for Tasks from Chapter 6......Page 433
C.7 Solutions for Tasks from Chapter 7......Page 444
C.8 Solutions for Tasks from Chapter 8......Page 451
C.9 Solutions for Tasks from Chapter 9......Page 469
Index......Page 474
