An introduction to programming and numerical methods in MATLAB / S.R. Otto, J.P. Denier.

Includes index.Simple Calculations with MATLABp. 1 Introduction and a Word of Warningp. 1 Scalar Quantities and Variablesp. 2 Rules for Naming of Variablesp. 4 Precedence: The Order in Which Calculations Are Performedp. 5 Mathematical Functionsp. 8 Format: The Way in Which Numbers Appearp. 12 Vectors in MATLABp. 13 Initialising Vector Objectsp. 13 Manipulating Vectors and Dot Arithmeticp. 14 Setting Up Mathematical Functionsp. 17 Some MATLAB Specific Commandsp. 20 Looking at Variables and Their Sizesp. 22 Accessing Elements of Arraysp. 23 Tasksp. 24 Writing Scripts and Functionsp. 27 Creating Scripts and Functionsp. 27 Functionsp. 30 Brief Asidep. 35 Plotting Simple Functionsp. 36 Evaluating Polynomials and Plotting Curvesp. 41 More on Plottingp. 44 Functions of Functionsp. 49 Errorsp. 51 Numerical Errorsp. 51 User Errorp. 54 Tasksp. 57 Loops and Conditional Statementsp. 63 Introductionp. 63 Loops Structuresp. 63 Summing Seriesp. 68 Sums of Series of the Form [characters not reproducible] j[superscript p], p [set membership] [characters not reproducible]p. 73 Summing Infinite Seriesp. 76 Summing Series Using MATLAB Specific Commandsp. 79 Loops Within Loops (Nested)p. 82 Conditional Statementsp. 83 Constructing Logical Statementsp. 85 The MATLAB Command switchp. 88 Conditional loopsp. 90 The break Commandp. 92 MATLAB Specific Commandsp. 92 Error Checkingp. 94 Tasksp. 97 Root Findingp. 103 Introductionp. 103 Initial Estimatesp. 104 Fixed Point Iterationp. 109 Bisectionp. 113 Newton-Raphson and Secant Methodsp. 117 Derivation of the Newton-Raphson Methodp. 117 Repeated Roots of Functionsp. 123 Zeros of Higher-Dimensional Functions(*)p. 125 MATLAB Routines for Finding Zerosp. 128 Roots of a Polynomialp. 128 The Command fzerop. 128 Tasksp. 130 Interpolation and Extrapolationp. 133 Introductionp. 133 Saving and Reading Datap. 134 Which Points to Use?p. 139 Newton Forward Differences and Lagrange Polynomialsp. 141 Linear Interpolation/Extrapolationp. 147 Calculating Interpolated and Extrapolated Valuesp. 148 Splinesp. 150 Curves of Best Fitp. 152 Interpolation of Non-Smooth Datap. 155 Insufficient Data Pointsp. 158 Minimisation of Functions and Parameter Retrievalp. 161 Parameter Retrievalp. 163 Using fmins for Parameter Retrievalp. 164 Tasksp. 166 Matricesp. 169 Introductionp. 169 Initialising Matrices Within MATLABp. 169 Matrix Operationsp. 174 Operations on Elements of Matricesp. 180 More on Special Matricesp. 182 Matrices Containing Stringsp. 185 Properties of Matrices and Systems of Equationsp. 186 Determinants of Matricesp. 190 Elementary Row Operationsp. 191 Solving Many Equations at Oncep. 198 Matrix Decompositionp. 199 Eigenvalues and Eigenvectorsp. 204 Specific MATLAB Commandsp. 208 Characteristic Polynomialsp. 212 Exponentials of Matricesp. 214 Tasksp. 217 Numerical Integrationp. 225 Introductionp. 225 Integration Using Straight Linesp. 226 Errors in the Trapezium Methodp. 229 Integration Using Quadraticsp. 230 Integration Using Cubic Polynomialsp. 235 Integrating Using MATLAB Commandsp. 237 Specific Examples of Integralsp. 238 Infinite Integrals and Removable Singularitiesp. 238 Indefinite Integralsp. 240 Tasksp. 242 Solving Differential Equationsp. 247 Introductionp. 247 Euler's Method and Crank-Nicolsonp. 247 Analytical Comparisonsp. 253 Banded Matricesp. 259 Runge-Kutta Methodsp. 263 Higher-Order Systemsp. 266 Second-Order Systemsp. 266 Bessel's equationp. 270 Airy's Equationp. 273 Shooting Methodsp. 274 Boundary-Value Problemsp. 278 Population Dynamicsp. 282 Eigenvalues of Differential Systemsp. 285 Tasksp. 286 Simulations and Random Numbersp. 291 Introductionp. 291 Statistical quantitiesp. 291 Averagesp. 291 Other Statistical Measuresp. 293 Random Numbers and Distributionsp. 295 Normal Distributionp. 298 Calculating Probabilitiesp. 299 Permutationsp. 300 Maps and White Noisep. 300 Modelling Discrete Systemsp. 307 Periodicity and Chaosp. 309 Random Motionp. 316 Tasksp. 319 A Mathematical Introduction to Matricesp. 323 Special Matricesp. 330 Inverses of Matricesp. 331 Glossary of Useful Termsp. 335 Arithmetic and Logical Operatorsp. 335 Symbolsp. 343 Plotting Commandsp. 347 General MATLAB Commandsp. 365 Solutions to Tasksp. 389 Solutions for Tasks from Chapter 1p. 389 Solutions for Tasks from Chapter 2p. 394 Solutions for Tasks from Chapter 3p. 400 Solutions for Tasks from Chapter 4p. 408 Solutions for Tasks from Chapter 5p. 414 Solutions for Tasks from Chapter 6p. 418 Solutions for Tasks from Chapter 7p. 429 Solutions for Tasks from Chapter 8p. 436 Solutions for Tasks from Chapter 9p. 454 Indexp. 459

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. Exposure to MATLAB, and programming in general, is becoming essential for students. It is the standard tool of choice for many universities - in both the mathematics and engineering departments - and it is also used extensively in industry. The level is elementary, avoiding deep mathematical descriptions, and the practical approach makes it accessible to anyone with a modest mathematical background.

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