Review of Ordinary Differential Equations: analytical methods, stability – Fourier series, orthog- onal functions, Fourier integrals, Fourier transform – Partial Differential Equations: first-order PDEs, method of characteristics, linear advection equation, Burgers’ equation, shock forma- tion, Rankine-Hogoniot jump condition; classification, canonical forms; Laplace equation, min- max principle, cylindrical coordinates; heat equation, method of separation of variables, similar- ity transformation method; wave equation, d’Alembert solution – Calculus of Variations: stan- dard variational problems, Euler-Lagrange equation and its applications, isoperimetric problems, Rayleigh-Ritz method, Hamilton’s principle of least action.

Same as Reference

1. Brown, J. W. and Churchill, R. V., Fourier Series and Boundary Value Problems, 8th ed., McGraw-Hill, (2012).

2. Bleecker, D. D. and Csordas, G., Basic Partial Differential Equations, Chapman & Hall (1995).

3. Myint-U, T. and Debnath, L., Linear Partial Differential Equations for Scientists and Engi- neers, 4th ed., Birkhauser (2006).

4. Strauss, W. A., Partial Differential Equations: An Introduction, 2nd ed., John Wiley (2007).

5. Kot, M., A First Course in the Calculus of Variations, American Math Society (2014).

6. Gelfand, I. M. and Fomin, S. V., Calculus of Variations, Prentice Hall (1963).

7. Arfken, G. B., Weber, H. J., and Harris, F. E., Mathematical Methods for Physicists, 7th ed., Academic Press (2012).

8. Greenberg, M. D., Advanced Engineering Mathematics, 2nd ed., Pearson (1998).