This textbook gives an introduction to a wide class of problems in scientific computing. It includes seven chapters with the following titles:
(1) Number representations and errors.
(2) Iterative solution of equations.
(3) Approximate evaluations of functions.
(4) Interpolation.
(5) Numerical calculus.
(6) Differential equations and
(7) Linear equations.
Here are some details.
In 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.
In 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.
Finally, 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.
This 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.