This website, which is under construction, is designed to go along with Prof. Dinshaw S. Balsara's textbook. The website is designed with the philosophy that a good education should be available anywhere, at any time to anyone.

The book is designed for scientists, engineers and mathematicians who want to obtain computational solutions to physical problems. Specifically, we focus on physical problems that are governed by partial differential equations (PDEs). We focus on the most popular classes of PDEs -- elliptic, parabolic and hyperbolic -- for which good methods are desired. In each instance, a physical and intuitive introduction is given to the computational problem which is then backed up with sufficient algorithmic and mathematical detail so as to give the reader a firm grasp of the methods. The problem sets associated with the book are analytical as well as computational so as to give the student a firm grounding in theory and numerical implementation.

The book comes with associated videos of the lectures. Slides with voice-over are also available. The movies might help in introducing the subject, while the slides help with reviewing the subject matter. The slides should be easy to view over the internet. A large number of example codes are also provided for each chapter on this website.

The slides with voice-over are light-weight and can be viewed on a smartphone or tablet. We have also tried to compress most of the movies to make them similarly light-weight.

# Contents

- Chapter 1: An overview of PDEs
- Chapter 2: Finite Difference Approximations
- Chapter 3: Scalar Advection and Linear Hyperbolic Systems
- Chapter 4: Non-Linear Conservation Laws; the Scalar Case
- Chapter 5: The Hydrodynamical Riemann Problem
- Appendix A: Introduction to MHD and the Multidimensional Riemann problem
- Appendix B: Introduction to Parallel Computing with Coarray Fortran
- Appendix C: Les Houches Summer School Lectures on Computational Astrophysics