Elementary Numerical Mathematics for Programmers and Engineers

1. Front Matter

   Pages i-ix

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2. Floating Point Arithmetic

   • Gisbert Stoyan, Agnes Baran

   Pages 1-14

3. Norms, Condition Numbers

   • Gisbert Stoyan, Agnes Baran

   Pages 15-35

4. Solution of Systems of Linear Equations

   • Gisbert Stoyan, Agnes Baran

   Pages 37-67

5. The Least Squares Problem

   • Gisbert Stoyan, Agnes Baran

   Pages 69-84

6. Eigenvalue Problems

   • Gisbert Stoyan, Agnes Baran

   Pages 85-109

7. Interpolation

   • Gisbert Stoyan, Agnes Baran

   Pages 111-133

8. Nonlinear Equations and Systems

   • Gisbert Stoyan, Agnes Baran

   Pages 135-160

9. Numerical Integration

   • Gisbert Stoyan, Agnes Baran

   Pages 161-183

10. Numerical Solution of Ordinary Differential Equations

    • Gisbert Stoyan, Agnes Baran

    Pages 185-209

11. Practical Error Estimation

    • Gisbert Stoyan, Agnes Baran

    Pages 211-216

12. Back Matter

    Pages 217-220

    PDF

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.

• 65-01, 65-04
• numerical analysis
• Gaussian elimination
• least squares
• eigenvalue problems
• interpolation
• nonlinear equations
• numerical integration
• practical error estimation

“The book is well-written and the typesetting is attractive. … Elementary Numerical Mathematics for Programmers and Engineers covers the standard topics well. Results are never simply stated and the main ideas are always fleshed out either through derivations or highly insightful examples. The authors also use clear and consistent notation throughout the book. I would particularly recommend this book to someone who is trying to learn numerical mathematics independently without the help of an instructor.” (Jason M. Graham, MAA Reviews, maa.org, February, 2017)

• Faculty of Informatics, ELTE University, Budapest, Hungary

  Gisbert Stoyan

• Faculty of Informatics, University of Debrecen, Debrecen, Hungary

  Agnes Baran

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.

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