An introduction to numerical methods : a MATLAB approach /: a MATLAB approach. (©2012)

• Record Type: Book
• Further Information: Note: Abdelwahab Kharab, Ronald B. Guenther.
• Other Names: Kharab, Abdelwahab; Guenther, Ronald B
• Contents: Introduction; About MATLAB and MATLAB graphical user interface (GUI); 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; Applied problems System of Linear Equations ; Matrices and matrix operations; Naïve Gaussian elimination; Gaussian elimination with scaled partial pivoting; Lu decomposition; Iterative methods; Applied problems Interpolation; Polynomial interpolation theory; Newton’s divided-difference interpolating polynomial; The error of the interpolating polynomial; Lagrange interpolating polynomial; Applied problems Interpolation with Spline Functions ; Piecewise linear interpolation; Quadratic spline; Natural cubic splines; Applied problems The Method of Least Squares ; Linear least squares; Least-squares polynomial; Nonlinear least squares; Trigonometric least-squares polynomial; Applied problems Numerical Optimization ; Analysis of single-variable functions; Line search methods; Minimization using derivatives; Applied problems Numerical Differentiation ; Numerical differentiation; Richardson’s formula; Applied problems Numerical Integration; Trapezoidal rule; Simpson’s rule; Romberg algorithm; Gaussian quadrature; Applied problems Numerical Methods for Linear Integral Equations ; Introduction; Quadrature rules; The successive approximation method; Schmidt’s method; Volterra-type integral equations; Applied problems Numerical Methods for Differential Equations ; Euler’s Method; Error Analysis; Higher-order Taylor series methods; Runge-Kutta methods; Adams-Bashforth methods; Predictor-corrector methods; Adams-Moulton methods; Numerical stability; Higher-order equations and systems of differential equations; Implicit methods and stiff systems; Phase plane analysis: chaotic differential equations; Applied problems Boundary-Value Problems; Finite-difference methods; Shooting methods; Applied problems Eigenvalues and Eigenvectors ; Basic theory; The power method; The quadratic method; Eigenvalues for boundary-value problems; Bifurcations in differential equations; Applied problems Partial Differential Equations; Parabolic equations; Hyperbolic equations; Elliptic equations; Nonlinear partial differential equations; Introduction to finite-element method; Applied problems Bibliography and References Appendix A: Calculus Review; Appendix B: MATLAB Built-in Functions; Appendix C: Text MATLAB Functions; Appendix D: MATLAB GUI Answers to Selected Exercises Index
• Edition: 3rd ed
• Publisher Details: Boca Raton, FL : CRC Press
• Publication Date: 2012
• Copyright Date: 2012
• Extent: 1 online resource (567 pages), illustrations
• Subjects: 518; Numerical analysis -- Data processing; Numerical analysis -- Data processing; Electronic books
• Languages: English
• ISBNs: 9781439869000; 1439869006
• Notes: Note: Includes bibliographical references and index.
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