This is a short book of about 200 pages (having in view a little bit more than a one-semester course), but with elementary detailed explanations how and why numerical methods work - for non-mathematicians, together with algorithms in a pseudo-code, with exercises for self-study and for written examinations.
An analysis has shown that there is no book on the market fulfilling the above aims. Students like short books, not bibles, and are acknowledging detailed explanations without much preassumptions concerning their knowledge. They will get an idea of the mathematics behind the numerical algorithms, moreover , they learn to write numerical programs.
This book gives an introduction into numerical methods on an elementary level for undergraduate students in engineering and informatics, with very few prerequisites assumed (from calculus and algebra, but quoting the most important at the beginning of the chapters, even remembering mathematical facts learned at the high school).
The book is self-contained, remembers in about 25 boxes mathematical prerequites or formulates there important insights and summaries, contains also several tables showing computing results, moreover 11 pseudo-code algorithms together with 25 test examples, and 23 figures.
Table of contents:
1. Floating point calculations (integer numbers; floating point numbers; calculation with floating point numbers, rounding; spread of errors; summary; exercises)
2. Norms and condition numbers (norms; error estimates; exercises)
3. Linear systems of equations (Gaussian elimination; LU decomposition; algorithms, number of arithmetical operations; general matrices; Cholesky decomposition; banded matrices; exercises)
4. Least squares (linear regression; Gaussian normal equations; algorithm; exercises)
5. Eigenvalue problems (general properties; power method; inverse iteration; exercises)
6. Interpolation (interpolational problems; Lagrange interpolation; Hermite interpolation, piecewise polynomial interpolation, exercises)
7. Nonlinear equations (bisectioning; Newton's method; systems of equations; Gauss-Newton method, exercises)
8. Numerical integration (elementary quadrature formulae; interpolational quadrature formulae; compound formulae; practical points of view; multi-dimensional integrals; exercises)
9. Initial value problems for ordinary differential equations (motivation; initial value problems; Euler's method; error estimation for Euler's method; the improved Euler's method; implicit Euler' method; exercises)