Books

Computational Physics: From Equations to Simulation

by Alexander Godunov

Forthcoming from World Scientific (2027)

Contents:

Part I: Computational Physics in Practice

1. The Nature of Computational Physics
2. The Computational Environment: Tools and Infrastructure
3. Computational Workflow: From Physics Problem to Simulation
4. Numerical Errors and Uncertainty in Computation

Part II: Numerical Methods in Computational Physics

5. Interpolation
6. Numerical Differentiation
7. Numerical Integration
8. Linear Systems and Eigenvalue Problems
9. Initial Value Problems for Ordinary Differential Equations
10. Boundary Value Problems for Ordinary Differential Equations
11. Solving Nonlinear Equations

Part III: Simulation and Advanced Computational Methods

12. Monte Carlo Methods
13. Optimization and Data Fitting
14. Molecular Dynamics Simulation
15. Parallel Computing: An Orientation to HPC
16. AI and Machine Learning in Physics

• Appendix A. Practical Computing Setups and Tools
• Appendix B. Common Numerical Routines in Scientific Software
• Appendix C. Random Number Generators in Practice

Pragmatic Mathematics for Scientists and Engineers

by Alexander Godunov and John A. Adam

World Scientific ISBN: 978-9811291333 (2024) ISBN: 978-9811291333 (hardcover)

Contents:

1. Infinite Series
2. Complex Numbers
3. Vectors
4. Matrices
5. Partial Differentiation
6. Line Integrals and Multiple Integrals
7. Fourier Series and Transforms
8. First-Order Ordinary Differential Equations
9. Second-Order Linear Differential Equations
10. The Green's Function Method
11. Calculus of Variations
12. Functions of Complex Variables

Introductory Computational Physics

by Andi Klein and Alexander Godunov

Cambridge University Press: ISBN 978-0521828628 (2006) ISBN: 978-0521828628 (hardcover)

Contents:

1. Introduction
2. Basics
3. Short introduction to Linux
4. Interpolation I
5. Interpolation II
6. Taking derivatives
7. Numerical integration
8. Solution of nonlinear equations
9. Differential equations
10. Matrices
11. Random processes and Monte Carlo simulation

• A. The ROOT system
• B. Free scientific libraries
• C. FORTRAN and C++
• D. Program listings.