This book covers the basics of numerical methods, while avoiding the definition-theorem-proof style and instead focusing on numerical examples and simple pseudo-codes.

The book is divided into ten chapters. Starting with floating number calculations and continuing up to ordinary differential equations, including "Euler backwards". The final chapter discusses practical error estimations. Exercises (including several in MATLAB) are provided at the end of each chapter. Suitable for readers with minimal mathematical knowledge, the book not only offers an elementary introduction to numerical mathematics for programmers and engineers but also provides supporting material for students and teachers of mathematics.

Autorentext

Gisbert Stoyan worked for more than 10 years on industrial problems at the WIAS in Berlin and was teaching numerical mathematics at ELTE University (Budapest, Hungary) for over 30 years. He has written research papers mostly on the numerical solution of partial differential equations. A three-volume textbook published in Hungarian brings together his experiences in areas including (along with the basic topics like numerical linear algebra, nonlinear equations) strongly stable methods for ODEs, multigrid algorithms, finite element praxis and theory, finite elements for Navier-Stokes equations, and methods for first-order hyperbolic equations. Agnes Baran received her PhD in Mathematics in 2008 at the University of Debrecen. Her doctoral thesis on high-order finite element methods for Stokes equations was supervised by Gisbert Stoyan. Since 2008, she works as an Assistant Professor at the Faculty of Informatics at the the University of Debrecen where she teaches courses on numerical analysis for students of Mathematics and Computer Science.

Inhalt

Floating point arithmetic.- Norms, condition numbers.- Solution of systems of linear equations.- The least squares problem.- Eigenvalue problems.- Interpolation.- Nonlinear equations and systems.- Numerical integration.- Ordinary differential equations.- Practical error estimation.- Bibliography.- Index.