Synopses & Reviews
This book presents the fundamental numerical techniques used in engineering, applied mathematics, computer science, and the physical and life sciences in a way that is both interesting and understandable. Using a wide range of examples and problems, this book focuses on the use of MathCAD functions and worksheets to illustrate the methods used when discussing the following concepts: solving linear and nonlinear equations, numerical linear algebra, numerical methods for data interpolation and approximation, numerical differentiation and integration, and numerical techniques for solving differential equations. For professionals in the fields of engineering, mathematics, computer science, and physical or life sciences who want to learn MathCAD functions for all major numerical methods.
Synopsis
For one/two-semester undergraduate or beginning graduate-level courses in computer and mathematical methods, numerical methods, or numerical analysis. This text presents the fundamental numerical techniques used in engineering, applied mathematics, computer science and the physical and life sciences in a way that is both interesting and understandable to students in those fields. The organization of the chapters and of the material within each chapter, the use of MathCAD functions and worksheets to illustrate the methods and the exercises provided are all designed with student learning as the primary objective.
Description
Includes bibliographical references (p. 667-672) and indexes.
Table of Contents
1. Foundations.
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.
8. Interpolation.
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.