| Simple Calculations with MATLAB | p. 1 |
| Introduction and a Word of Warning | p. 1 |
| Scalar Quantities and Variables | p. 2 |
| Rules for Naming of Variables | p. 4 |
| Precedence: The Order in Which Calculations Are Performed | p. 5 |
| Mathematical Functions | p. 8 |
| Format: The Way in Which Numbers Appear | p. 12 |
| Vectors in MATLAB | p. 13 |
| Initialising Vector Objects | p. 13 |
| Manipulating Vectors and Dot Arithmetic | p. 14 |
| Setting Up Mathematical Functions | p. 17 |
| Some MATLAB Specific Commands | p. 20 |
| Looking at Variables and Their Sizes | p. 22 |
| Accessing Elements of Arrays | p. 23 |
| Tasks | p. 24 |
| Writing Scripts and Functions | p. 27 |
| Creating Scripts and Functions | p. 27 |
| Functions | p. 30 |
| Brief Aside | p. 35 |
| Plotting Simple Functions | p. 36 |
| Evaluating Polynomials and Plotting Curves | p. 41 |
| More on Plotting | p. 44 |
| Functions of Functions | p. 49 |
| Errors | p. 51 |
| Numerical Errors | p. 51 |
| User Error | p. 54 |
| Tasks | p. 57 |
| Loops and Conditional Statements | p. 63 |
| Introduction | p. 63 |
| Loops Structures | p. 63 |
| Summing Series | p. 68 |
| Sums of Series of the Form [characters not reproducible] j[superscript p], p [set membership] [characters not reproducible] | p. 73 |
| Summing Infinite Series | p. 76 |
| Summing Series Using MATLAB Specific Commands | p. 79 |
| Loops Within Loops (Nested) | p. 82 |
| Conditional Statements | p. 83 |
| Constructing Logical Statements | p. 85 |
| The MATLAB Command switch | p. 88 |
| Conditional loops | p. 90 |
| The break Command | p. 92 |
| MATLAB Specific Commands | p. 92 |
| Error Checking | p. 94 |
| Tasks | p. 97 |
| Root Finding | p. 103 |
| Introduction | p. 103 |
| Initial Estimates | p. 104 |
| Fixed Point Iteration | p. 109 |
| Bisection | p. 113 |
| Newton-Raphson and Secant Methods | p. 117 |
| Derivation of the Newton-Raphson Method | p. 117 |
| Repeated Roots of Functions | p. 123 |
| Zeros of Higher-Dimensional Functions(*) | p. 125 |
| MATLAB Routines for Finding Zeros | p. 128 |
| Roots of a Polynomial | p. 128 |
| The Command fzero | p. 128 |
| Tasks | p. 130 |
| Interpolation and Extrapolation | p. 133 |
| Introduction | p. 133 |
| Saving and Reading Data | p. 134 |
| Which Points to Use? | p. 139 |
| Newton Forward Differences and Lagrange Polynomials | p. 141 |
| Linear Interpolation/Extrapolation | p. 147 |
| Calculating Interpolated and Extrapolated Values | p. 148 |
| Splines | p. 150 |
| Curves of Best Fit | p. 152 |
| Interpolation of Non-Smooth Data | p. 155 |
| Insufficient Data Points | p. 158 |
| Minimisation of Functions and Parameter Retrieval | p. 161 |
| Parameter Retrieval | p. 163 |
| Using fmins for Parameter Retrieval | p. 164 |
| Tasks | p. 166 |
| Matrices | p. 169 |
| Introduction | p. 169 |
| Initialising Matrices Within MATLAB | p. 169 |
| Matrix Operations | p. 174 |
| Operations on Elements of Matrices | p. 180 |
| More on Special Matrices | p. 182 |
| Matrices Containing Strings | p. 185 |
| Properties of Matrices and Systems of Equations | p. 186 |
| Determinants of Matrices | p. 190 |
| Elementary Row Operations | p. 191 |
| Solving Many Equations at Once | p. 198 |
| Matrix Decomposition | p. 199 |
| Eigenvalues and Eigenvectors | p. 204 |
| Specific MATLAB Commands | p. 208 |
| Characteristic Polynomials | p. 212 |
| Exponentials of Matrices | p. 214 |
| Tasks | p. 217 |
| Numerical Integration | p. 225 |
| Introduction | p. 225 |
| Integration Using Straight Lines | p. 226 |
| Errors in the Trapezium Method | p. 229 |
| Integration Using Quadratics | p. 230 |
| Integration Using Cubic Polynomials | p. 235 |
| Integrating Using MATLAB Commands | p. 237 |
| Specific Examples of Integrals | p. 238 |
| Infinite Integrals and Removable Singularities | p. 238 |
| Indefinite Integrals | p. 240 |
| Tasks | p. 242 |
| Solving Differential Equations | p. 247 |
| Introduction | p. 247 |
| Euler's Method and Crank-Nicolson | p. 247 |
| Analytical Comparisons | p. 253 |
| Banded Matrices | p. 259 |
| Runge-Kutta Methods | p. 263 |
| Higher-Order Systems | p. 266 |
| Second-Order Systems | p. 266 |
| Bessel's equation | p. 270 |
| Airy's Equation | p. 273 |
| Shooting Methods | p. 274 |
| Boundary-Value Problems | p. 278 |
| Population Dynamics | p. 282 |
| Eigenvalues of Differential Systems | p. 285 |
| Tasks | p. 286 |
| Simulations and Random Numbers | p. 291 |
| Introduction | p. 291 |
| Statistical quantities | p. 291 |
| Averages | p. 291 |
| Other Statistical Measures | p. 293 |
| Random Numbers and Distributions | p. 295 |
| Normal Distribution | p. 298 |
| Calculating Probabilities | p. 299 |
| Permutations | p. 300 |
| Maps and White Noise | p. 300 |
| Modelling Discrete Systems | p. 307 |
| Periodicity and Chaos | p. 309 |
| Random Motion | p. 316 |
| Tasks | p. 319 |
| A Mathematical Introduction to Matrices | p. 323 |
| Special Matrices | p. 330 |
| Inverses of Matrices | p. 331 |
| Glossary of Useful Terms | p. 335 |
| Arithmetic and Logical Operators | p. 335 |
| Symbols | p. 343 |
| Plotting Commands | p. 347 |
| General MATLAB Commands | p. 365 |
| Solutions to Tasks | p. 389 |
| Solutions for Tasks from Chapter 1 | p. 389 |
| Solutions for Tasks from Chapter 2 | p. 394 |
| Solutions for Tasks from Chapter 3 | p. 400 |
| Solutions for Tasks from Chapter 4 | p. 408 |
| Solutions for Tasks from Chapter 5 | p. 414 |
| Solutions for Tasks from Chapter 6 | p. 418 |
| Solutions for Tasks from Chapter 7 | p. 429 |
| Solutions for Tasks from Chapter 8 | p. 436 |
| Solutions for Tasks from Chapter 9 | p. 454 |
| Index | p. 459 |
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