Table of Contents
Sample Problems and Numerical Methods. Some Basic Issues. Getting Started in Mathcad.
2. Solving Equations of One Variable.
Bisection Method. Regula Falsi and Secant Methods. Newton's Method. Muller's Method. Mathcad's Methods.
3. Solving Systems of Linear Equations: Direct Methods.
Gaussian Elimination. Gaussian Elimination with Row Pivoting. Gaussian Elimination for Tridiagonal Systems. Mathcad's Methods.
4. Solving Systems of Linear Equations: Iterative Methods.
Jacobi Method. Gauss-Seidel Method. Successive Overrelaxation. Mathcad's Methods.
5. Systems of Nonlinear Equations.
Newton's Method for Systems of Equations. Fixed-Point Iteration for Nonlinear Systems. Minimum of a Nonlinear Function. Mathcad's Methods.
6. LU Factorization.
LU Factorization from Gaussian Elimination. LU Factorization of Tridiagonal Matrices. LU Factorization with Pivoting. Direct LU Factorization. Applications of LU Factorization. Mathcad's Methods.
7. Eigenvalues, Eigenvectors, and QR Factorization.
Power Method. QR Factorization. Finding Eigenvalues Using QR Factorization. Mathcad's Methods.
Polynomial Interpolation. Hermite Interpolation. Rational Function Interpolation. Spline Interpolation. Mathcad's Methods.
9. Function Approximation.
Least Squares Approximation. Continuous Least-Squares Approximation. Function Approximation at a Point. Mathcad's Methods.
10. Fourier Methods.
Fourier Approximation and Interpolation. Fourier Transforms for n = 2r. Fast Fourier Transforms for General n. Mathcad's Methods.
11. Numerical Differentiation and Integration.
Differentiation. Basic Numerical Integration. Better Numerical Integration. Gaussian Quadrature. Mathcad's Methods.
12. Ordinary Differential Equations: Initial-Value Problems.
Taylor Methods. Runge-Kutta Methods. Multistep Methods. Stability. Mathcad's Methods.
13. Systems of Ordinary Differential Equations.
Higher-Order ODEs. Systems of Two First-Order ODE. Systems of First-Order ODE-IVP. Stiff ODE and Ill-Conditioned Problems. Mathcad's Methods.
14. Ordinary Differential Equations: Boundary-Value Problems.
Shooting Method for Solving Linear BVP. Shooting Method for Solving Nonlinear BVP. Finite-Difference Method for Solving Linear BVP. Finite-Difference Method for Nonlinear BVP. Mathcad's Methods.
15. Partial Differential Equations.
Classification of PDE. Heat Equation: Parabolic PDE. Wave Equation: Hyperbolic PDE. Poisson Equation: Elliptic PDE. Finite-Element Method for Solving an Elliptic PDE. Mathcad's Methods.
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