This book can be used by students starting a curriculum in the applied sciences. The focus is on various practical aspects of numerical analysis and on how the presented methods can be implemented with the MATLAB package. The chapters are structured through an introduction, motivating examples from applications, mathematical explanations of the methods, MATLAB programs, many examples illustrating the methods and some exercises (with a selection of answers). A bibliography and an author and subject index end the volume.
A first set of topics are those related to solving linear or nonlinear equations (Newton’s method, Gaussian elimination, Jacobi method, Gauss-Seidel method). Then methods for problems of linear algebra are presented (LU factorization, QR factorization, eigenvalue problems). Other topics are related to interpolation, least squares approximation, Fourier methods including the fast Fourier transform. Finally, the other chapters deal with numerical differentiation and integration, ordinary and partial differential equations simulation (Runge-Kutta, shooting methods, finite elements).
This book concentrates on implementation with pedagogical goals i.e. the theorem-proof format is avoided for entertaining discussions. Moreover, many of the almost 600 pages of this volume contain examples and numerical values up to the fourth decimal.