An introduction to numerical methods : a MATLAB approach /: a MATLAB approach. (2005)

• Record Type: Book
• Further Information: Note: Abdelwahab Kharab, Ronald B. Guenther.
• Other Names: Kharab, Abdelwahab; Guenther, Ronald B
• Contents: INTRODUCTION; About the software MATLAB; An Introduction to MATLAB; Taylor Series; NUMBER SYSTEM AND ERRORS; Floating-Point Arithmetic; Round-Off Errors; Truncation Error; Interval Arithmetic; ROOTS OF EQUATIONS; The Bisection Method; The Method of False Position; Fixed-Point Iteration; The Secant method; Newton's Method; Convergence of the Newton and Secant Methods; Multiple Roots and the Modified Newton Method; Newton's Method for Nonlinear Systems; SYSTEM OF LINEAR EQUATIONS; Matrices and Matrix Operations; Naïve Gaussian Elimination; Gaussian Elimination with Scaled Partial Pivoting; LU Decomposition; Iterative Methods; INTERPOLATION; Polynomial Interpolation Theory; Newton's Divided Difference Interpolating Polynomial; The Error of the Interpolating Polynomial; Lagrange Interpolating Polynomial; INTERPOLATION WITH SPLINE FUNCTIONS; Piecewise Linear Interpolation; Quadratic Spline; Natural Cubic Splines; THE METHOD OF LEAST SQUARES; Linear Least Squares; Least Squares Polynomial; Nonlinear Least Squares; Trigonometric Least Squares Polynomial; NUMERICAL OPTIMIZATION; Analysis of Single-Variable Functions; Line Search Methods; Minimization Using Derivatives; NUMERICAL DIFFERENTIATION; Numerical Differentiation; Richardson's Formula; NUMERICAL INTEGRATION; Trapezoidal Rule; Simpson's Rule; Romberg Algorithm; Gaussian Quadrature; NUMERICAL METHODS FOR DIFFERENTIAL EQUATIONS; Euler's Method; Error Analysis; Higher Order Taylor Series Methods; Runge-Kutta Methods; Multistep Methods; Adams-Bashforth Method; Predictor-Corrector Methods; Adams-Moulton Method; Numerical Stability; Higher Order Equations and Systems of Differential Equations; Implicit Methods and Stiff Systems; Phase Plane Analysis: Chaotic Differential Equations; BOUNDARY-VALUE PROBLEMS; Finite-Difference Methods; Shooting Methods; EIGENVALUES AND EIGENVECTORS; Basic Theory; The Power Method; The Quadratic Method; Eigenvalues for Boundary-Value Problems; Bifurcations in Differential Equations; PARTIAL DIFFERENTIAL EQUATIONS; Parabolic Equations; Hyperbolic Equations; Elliptic Equations; Introduction to Finite Element Method; Bibliography and References; Appendices; Calculus Review; MATLAB Built-in Functions; Text MATLAB Functions; Answers to Selected Exercises; Index; ; Each chapter also contains a section of Applied Problems.
• Edition: 2nd ed
• Publisher Details: Place of publication not identified : Chapman and Hall/CRC
• Publication Date: 2005
• Extent: 1 online resource (624 pages), (100 illustrations)
• Subjects: 518; Numerical analysis -- Data processing
• Languages: English
• ISBNs: 9781420057058; 1420057057
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.