Some useful textbooks and lecture notes.

1. R. J. LeVeque: Finite Volume Methods for Hyperbolic Problems, Cambridge Texts in Applied Mathematics, 2002.

2. R. J. LeVeque, Numerical methods for conservation laws, Birkhauser-Verlag.

3. R. J. LeVeque, Finite Difference methods for ordinary and partial differential equations, SIAM.

4. E. Godlewski and P. Raviart, Hyperbolic Systems of Conservation Laws, Ellipses-Edition Marketing, Paris, 1991

5. E. Godlewski and P. Raviart, Numerical approximation of hyperbolic systems of conservation laws, Springer.

6.  J. W. Thomas, Numerical Partial Differential Equations: conservation laws and elliptic equations, Springer.

7. J.S. Hestheven, Numerical methods for conservation laws: From Analysis to Algorithms, SIAM publisher.

8. E. F. Toro: Reimann Solvers and Numerical Methods for Fluid Dynamics, Springer, 1999.

9. C. B. Laney: Computational Gas Dynamics. Cambridge university press, 1998

10. A. Quarteroni and P. Valli, Numerical approximation of Partial Differential Equations, Springer

11. Hirsch C. Numerical Computation of Internal and External Flows. Volume 1-Fundamentals of Computational Fluid Dynamics (Elsevier,2nd edition,2007)

12. John A. Trangenstein, Numerical Solution of Hyperbolic Partial Differential Equations, Cambridge University Press, 2009. 

13. Lecture notes on conservation laws  by Prof. Siddhartha Mishra, Prof. Ulrik Skre Fjordholm and Prof. Remi Abgrall

14. Lecture notes on Hyperbolic Conservation Laws by Prof. G.D. Veerappa Gowda

Some usefule links:

1. Lecture series on Hyperbolic equations and structure preserving numerical methods and other topics

2. Journal of Computational Physics Seminar series

3. ICERM, Brown

4. Journal abbreviations

5. NCM: ATM schools

6. MTTS

7. Mathematics Stock Exchange

8. Conference: HYP 

Advice for Students

1. Learn any one of the programming languages C/C++/Fortran/Matlab/Python

2. Learn to write your project reports/CV in Latex/Lyx. Click here to know more. 

3. You can download Lyx from here. Click here.

4. You can install texlive software on Ubuntu for preparing documents from terminal with the following commands;

• Install Latex distribution by the command sudo apt-get install texlive-full 

• For text-editior (need for editing Latex documents) use the command sudo apt-get install texmaker

• Once you install, type as texmaker to open the editor 

5. For plotting graphs, you can use Visit software and can be installed as;  

• To install Visit, first you need to download executables form Visit

• Choose the Visit according to your system(Windows/Mac/Ubuntu/Linux)

• Unpack the Zip folder, go to bin folder then open the terminal there and type ./Visit