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| Simple Calculations with MATLAB | |
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| Introduction and a Word of Warning | |
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| Scalar Quantities and Variables | |
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| Rules for Naming of Variables | |
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| Precedence: The Order in Which Calculations Are Performed | |
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| Mathematical Functions | |
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| Format: The Way in Which Numbers Appear | |
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| Vectors in MATLAB | |
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| Initialising Vector Objects | |
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| Manipulating Vectors and Dot Arithmetic | |
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| Setting Up Mathematical Functions | |
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| Some MATLAB Specific Commands | |
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| Looking at Variables and Their Sizes | |
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| Accessing Elements of Arrays | |
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| Tasks | |
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| Writing Scripts and Functions | |
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| Creating Scripts and Functions | |
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| Functions | |
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| Brief Aside | |
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| Plotting Simple Functions | |
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| Evaluating Polynomials and Plotting Curves | |
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| More on Plotting | |
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| Functions of Functions | |
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| Errors | |
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| Numerical Errors | |
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| User Error | |
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| Tasks | |
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| Loops and Conditional Statements | |
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| Introduction | |
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| Loops Structures | |
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| Summing Series | |
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| Sums of Series of the Form [characters not reproducible] j[superscript p], p [set membership] [characters not reproducible] | |
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| Summing Infinite Series | |
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| Summing Series Using MATLAB Specific Commands | |
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| Loops Within Loops (Nested) | |
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| Conditional Statements | |
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| Constructing Logical Statements | |
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| The MATLAB Command switch | |
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| Conditional loops | |
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| The break Command | |
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| MATLAB Specific Commands | |
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| Error Checking | |
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| Tasks | |
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| Root Finding | |
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| Introduction | |
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| Initial Estimates | |
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| Fixed Point Iteration | |
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| Bisection | |
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| Newton-Raphson and Secant Methods | |
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| Derivation of the Newton-Raphson Method | |
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| Repeated Roots of Functions | |
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| Zeros of Higher-Dimensional Functions(*) | |
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| MATLAB Routines for Finding Zeros | |
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| Roots of a Polynomial | |
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| The Command fzero | |
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| Tasks | |
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| Interpolation and Extrapolation | |
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| Introduction | |
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| Saving and Reading Data | |
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| Which Points to Use? | |
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| Newton Forward Differences and Lagrange Polynomials | |
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| Linear Interpolation/Extrapolation | |
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| Calculating Interpolated and Extrapolated Values | |
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| Splines | |
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| Curves of Best Fit | |
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| Interpolation of Non-Smooth Data | |
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| Insufficient Data Points | |
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| Minimisation of Functions and Parameter Retrieval | |
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| Parameter Retrieval | |
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| Using fmins for Parameter Retrieval | |
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| Tasks | |
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| Matrices | |
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| Introduction | |
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| Initialising Matrices Within MATLAB | |
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| Matrix Operations | |
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| Operations on Elements of Matrices | |
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| More on Special Matrices | |
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| Matrices Containing Strings | |
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| Properties of Matrices and Systems of Equations | |
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| Determinants of Matrices | |
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| Elementary Row Operations | |
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| Solving Many Equations at Once | |
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| Matrix Decomposition | |
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| Eigenvalues and Eigenvectors | |
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| Specific MATLAB Commands | |
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| Characteristic Polynomials | |
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| Exponentials of Matrices | |
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| Tasks | |
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| Numerical Integration | |
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| Introduction | |
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| Integration Using Straight Lines | |
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| Errors in the Trapezium Method | |
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| Integration Using Quadratics | |
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| Integration Using Cubic Polynomials | |
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| Integrating Using MATLAB Commands | |
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| Specific Examples of Integrals | |
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| Infinite Integrals and Removable Singularities | |
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| Indefinite Integrals | |
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| Tasks | |
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| Solving Differential Equations | |
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| Introduction | |
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| Euler's Method and Crank-Nicolson | |
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| Analytical Comparisons | |
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| Banded Matrices | |
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| Runge-Kutta Methods | |
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| Higher-Order Systems | |
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| Second-Order Systems | |
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| Bessel's equation | |
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| Airy's Equation | |
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| Shooting Methods | |
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| Boundary-Value Problems | |
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| Population Dynamics | |
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| Eigenvalues of Differential Systems | |
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| Tasks | |
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| Simulations and Random Numbers | |
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| Introduction | |
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| Statistical quantities | |
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| Averages | |
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| Other Statistical Measures | |
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| Random Numbers and Distributions | |
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| Normal Distribution | |
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| Calculating Probabilities | |
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| Permutations | |
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| Maps and White Noise | |
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| Modelling Discrete Systems | |
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| Periodicity and Chaos | |
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| Random Motion | |
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| Tasks | |
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| A Mathematical Introduction to Matrices | |
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| Special Matrices | |
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| Inverses of Matrices | |
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| Glossary of Useful Terms | |
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| Arithmetic and Logical Operators | |
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| Symbols | |
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| Plotting Commands | |
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| General MATLAB Commands | |
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| Solutions to Tasks | |
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| Solutions for Tasks from Chapter 1 | |
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| Solutions for Tasks from Chapter 2 | |
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| Solutions for Tasks from Chapter 3 | |
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| Solutions for Tasks from Chapter 4 | |
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| Solutions for Tasks from Chapter 5 | |
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| Solutions for Tasks from Chapter 6 | |
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| Solutions for Tasks from Chapter 7 | |
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| Solutions for Tasks from Chapter 8 | |
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| Solutions for Tasks from Chapter 9 | |
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| Index | |