Guide to scientific computing. (Q2782242)

This textbook gives an introduction to a wide class of problems in scientific computing. It includes seven chapters with the following titles: NEWLINENEWLINENEWLINE(1) Number representations and errors. NEWLINENEWLINENEWLINE(2) Iterative solution of equations.NEWLINENEWLINENEWLINE(3) Approximate evaluations of functions.NEWLINENEWLINENEWLINE(4) Interpolation.NEWLINENEWLINENEWLINE(5) Numerical calculus.NEWLINENEWLINENEWLINE(6) Differential equations and NEWLINENEWLINENEWLINE(7) Linear equations. NEWLINENEWLINENEWLINEHere are some details. NEWLINENEWLINENEWLINEIn Chapter 1 floating point computer arithmetic is considered, and in Chapter 2 the bisection method, the secant method and Newton's method for the numerical solution of nonlinear equations are treated. NEWLINENEWLINENEWLINEIn Chapter 3 the approximate evaluation of infinite series is considered, and Chapter 4 is devoted to polynomial and spline interpolation. In Chapter 5 numerical integration, numerical differentiation as well as minimization problems for functions of one variable are considered, and Chapter 6 is devoted to initial- and boundary value problems for ordinary differential equations. NEWLINENEWLINENEWLINEFinally, Chapter 7 contains sections on the Gaussian elimination, Jacobi- and Gauss-Seidel iteration, the LU decomposition and eigenvalue problems. Additionally, for each considered topic some MATLAB routines are introduced. NEWLINENEWLINENEWLINEThis textbook addresses to students taking a first course on that topic. It is not the intention to treat the considered topics in a detailed and rigorous manner but the basic ideas are always presented. The presentation is clear and lively, and many examples, figures, exercises and hints for their solution are included.