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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 | |