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| Foundations | |
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| Sample Problems and Numerical Methods | |
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| Some Basic Issues | |
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| Algorithms and Computer Programs | |
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| Solving Equations of One Variable | |
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| Bisection Method | |
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| Regular Falsi and Secant Methods | |
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| Newton's Method | |
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| Muller's Method | |
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| Methods of Modern Computing | |
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| Solving Systems of Linear Equations | |
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| Direct Methods | |
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| Gaussian Elimination | |
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| Gaussian Elimination with Row Pivoting | |
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| Gaussian Elimination for Tridiagonal Systems | |
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| Methods of Modern Computing | |
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| LU and QR Factorization | |
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| LU Factorization from Gaussian Elimination | |
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| Direct LU Factorization | |
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| Applications of LU Factorization | |
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| Householder and Givens Transformations | |
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| QR Factorization | |
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| Methods of Modern Computing | |
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| Eigenvalues and Eigenvectors | |
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| Power Method | |
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| Inverse Power Method | |
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| QR Method | |
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| Methods of Modern Computing | |
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| Solving Systems of Linear Equations | |
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| Iterative Methods | |
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| Jacobi Method | |
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| Gauss-Seidel Method | |
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| Successive Over Relaxation | |
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| Methods of Modern Computing | |
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| Nonlinear Functions of Several Variables | |
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| Newton's Method for Systems of Equations | |
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| Fixed-Point Iteration for Nonlinear Systems | |
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| Minimum of a Nonlinear Function of Several Variables | |
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| Methods of Modern Computing | |
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| Interpolation | |
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| Polynomial Interpolation | |
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| Hermite Interpolation | |
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| Rational-Function Interpolation | |
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| Spline Interpolation | |
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| Methods of Modern Computing | |
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| Function Approximation | |
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| Least-Squares Approximation | |
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| Continuous Least-Squares Approximation | |
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| Function Approximation at a Point | |
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| Methods of Modern Computing | |
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| Fourier Methods | |
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| Fourier Approximation and Interpolation | |
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| Radix-2 Fast Fourier Transforms | |
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| General Fast Fourier Transforms | |
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| Methods of Modern Computing | |
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| Numerical Differentiation and Integration | |
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| Differentiation | |
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| Basic Numerical Integration | |
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| Better Numerical Integration | |
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| Gaussian Quadrature | |
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| Methods of Modern Computing | |
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| Ordinary Differential Equations | |
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| Initial-Value Problems | |
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| Taylor Methods | |
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| Runge-Kutta Methods | |
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| Multistep Methods | |
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| Stability | |
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| Methods of Modern Computing | |
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| Ordinary Differential Equations | |
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| Higher-Order Equations and First-Order Systems | |
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| Higher-Order ODEs | |
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| Systems of Two First-Order ODE | |
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| Systems of First-Order ODE | |
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| Stiff ODE and Ill-conditioned Problems | |
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| Methods of Modern Computing | |
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| Ordinary Differential Equations | |
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| Boundary-Value Problems | |
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| Shooting Method for Linear BVP | |
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| Shooting Method Nonlinear BVP | |
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| Finite-Difference Method for Linear BVP | |
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| Finite-Difference Method for Nonlinear BVP | |
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| Methods of Modern Computing | |
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| Partial Differential Equations | |
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| Classification of PDE | |
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| Heat equation | |
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| Parabolic PDE | |
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| Wave equation | |
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| Hyperbolic PDE | |
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| Poisson Equation - Elliptic PDE | |
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| Finite Element Method for an Elliptic PDE | |
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| Methods of Modern Computing | |