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| Getting Started | |
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| Algorithms | |
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| Convergence | |
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| Floating Point Numbers | |
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| Floating Point Arithmetic | |
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| Rootfinding | |
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| Bisection Method | |
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| Method of False Position | |
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| Fixed Point Iteration | |
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| Newton's Method | |
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| The Secant Method and Muller's Method | |
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| Accelerating Convergence | |
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| Roots of Polynomials | |
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| Systems of Equations | |
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| Gaussian Elimination | |
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| Pivoting Strategies | |
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| Norms | |
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| Error Estimates | |
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| LU Decomposition | |
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| Direct Factorization | |
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| Special Matrices | |
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| Iterative Techniques for Linear Systems: Basic Concepts and Methods | |
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| Iterative Techniques for Linear Systems: Conjugate-Gradient Method | |
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| Nonlinear Systems | |
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| Eigenvalues and Eigenvectors | |
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| The Power Method | |
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| The Inverse Power Method | |
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| Deflation | |
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| Reduction to Tridiagonal Form | |
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| Eigenvalues of Tridiagonal and Hessenberg Matrices | |
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| Interpolation and Curve Fitting | |
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| Lagrange Form of the Interpolating Polynomial | |
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| Neville's Algorithm | |
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| The Newton Form of the Interpolating Polynomial and Divided Differences | |
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| Optimal Interpolating Points | |
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| Piecewise Linear Interpolation | |
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| Hermite and Hermite Cubic Interpolation | |
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| Regression | |
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| Numerical Differentiation and Integration | |
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| Continuous Theory and Key Numerical Concepts | |
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| Euler's Method | |
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| Higher-Order One-Step Methods | |
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| Multistep Methods | |
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| Convergence Analysis | |
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| Error Control and Variable Step Size Algorithms | |
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| Systems of Equations and Higher-Order Equations | |
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| Absolute Stability and Stiff Equations | |
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| Numerical Methods for Initial Value Problems of Ordinary Differential Equations | |
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| Continuous Theory and Key Numerical Concepts | |
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| Euler's Method | |
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| Higher-Order One-Step Methods | |
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| Multistep Methods | |
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| Convergence Analysis | |
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| Error Control and Variable Step Size Algorithms | |
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| Systems of Equations and Higher-Order Equations | |
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| Absolute Stability and Stiff Equations | |
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| Second-Order One-Dimensional Two-Point Boundary Value Problems | |
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| Finite Difference Method | |
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| The Linear Problem with Dirichlet Boundary Conditions | |
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| Finite Difference Method | |
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| The Linear Problem with Non-Dirichlet Boundary Conditions | |
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| Finite Difference Method | |
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| Nonlinear Problems | |
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| The Shooting Method | |
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| Linear Boundary Value Problems | |
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| The Shooting Method | |
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| Nonlinear Boundary Value Problems | |
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| Finite Difference Method for Elliptic Partial Differential Equations | |
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| The Poisson Equation on a Rectangular Domain | |
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| Dirichlet Boundary Conditions | |
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| The Poisson Equation on a Rectangular Domain | |
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| Non-Dirichlet Boundary Conditions | |
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| Solving the Discrete Equations: Relaxation Schemes | |
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| Local Mode Analysis of Relaxation and the Multigrid Method | |
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| Irregular Domains | |
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| 10 | |
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| The Heat Equation with Dirichlet Boundary Conditions | |
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| Stability | |
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| More General Parabolic Equations | |
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| Non-Dirichlet Boundary Conditions | |
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| Polar Coordinates | |
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| Problems in Two Space Dimensions | |
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| Finite Difference Method for Hyperbolic Partial Differential Equations and the Convection-Diffusion Equation | |
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| Advection Equation | |
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| Upwind Differencing | |
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| Advection Equation | |
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| MacCormack Method | |
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| Convection-Diffusion Equation | |
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| The Wave Equation | |
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| Appendices | |
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| Important Theorems from Calculus | |
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| Algorithm for Solving a Tridiagonal System of Linear Equations | |
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| References | |
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| Index | |
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| Answers to Selected Problems | |