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| (NOTE: Chapters 2-12 conclude with Summary.) | |
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| Introduction | |
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| Terminology | |
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| MATLAB Overview | |
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| Organization of the Book | |
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| Rating Systems for Exercises | |
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| MATLAB Basics | |
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| Interactive Computing with MATLAB | |
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| Running MATLAB | |
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| Matrices and Vectors | |
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| Additional Types of Variables | |
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| Managing the Interactive Environment | |
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| Plotting in MATLAB | |
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| MATLAB Programming | |
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| Script m-Files | |
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| Function m-Files | |
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| Input and Output | |
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| Flow Control | |
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| Vectorization | |
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| Deus ex Machina | |
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| Organizing and Debugging MATLAB Programs | |
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| Organizing and Documenting m-Files | |
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| Organizing a Numerical Solution | |
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| Debugging | |
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| Numerical Techniques | |
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| Unavoidable Errors in Computing | |
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| Digital Representation of Numbers | |
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| Finite Precision Arithmetic | |
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| Truncation Error of Algorithms | |
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| Finding the Roots of f(x)=0 | |
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| Preliminaries | |
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| Fixed-Point Iteration | |
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| Bisection | |
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| Newton's Method | |
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| The Secant Method | |
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| Hybrid Methods | |
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| Roots of Polynomials | |
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| A Review of Linear Algebra | |
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| Vectors | |
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| Matrices | |
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| Mathematical Properties of Vectors and Matrices | |
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| Special Matrices | |
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| Solving Systems of Equations | |
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| Basic Concepts | |
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| Gaussian Elimination | |
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| Limitations on Numerical Solutions to Ax = b | |
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| Factorization Methods | |
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| Nonlinear Systems of Equations | |
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| Least-Squares Fitting of a Curve to Data | |
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| Fitting a Line to Data | |
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| Least-Squares Fit to a Linear Combination of Functions | |
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| Multivariate Linear Least-Squares Fitting | |
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| Interpolation | |
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| Basic Ideas | |
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| Interpolating Polynomials of Arbitrary Degree | |
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| Piecewise Polynomial Interpolation | |
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| MATLAB's Built in Interpolation Functions | |
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| Numerical Integration | |
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| Basic Ideas and Nomenclature | |
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| Newton-Cotes Rules | |
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| Gaussian Quadrature | |
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| Adaptive Quadrature | |
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| Improper Integrals and Other Complications | |
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| Numerical Integration of Ordinary Differential Equations | |
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| Basic Ideas and Nomenclature | |
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| Euler's Method | |
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| Higher Order One-Step Methods | |
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| Adaptive Stepsize Algorithms | |
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| Coupled ODEs | |
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| Additional Topics | |
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| Bibliography | |
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| Eigenvalues and Eigensystems | |
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| Eigenvectors Map onto Themselves | |
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| Mathematical Preliminaries | |
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| The Power Method | |
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| Built-in Functions for Eigenvalue Computation | |
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| Singular Value Decomposition | |
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| Sparse Matrices | |
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| Storage and Flop Savings | |
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| MATLAB Sparse Matrix Format | |
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| MATLAB Toolbox Functions | |
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| Listings for NMM Toolbox m-Files | |
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| Subject Index | |