Review of Ordinary Differential Equations: analytical methods, stability – Fourier series, orthogonal functions, Fourier integrals, Fourier transform – Partial Differential Equations: first-order PDEs, method of characteristics, linear advection equation, Burgers’ equation, shock formation, Rankine-Hogoniot jump condition; classification, canonical forms; Laplace equation, min-max principle, cylindrical coordinates; heat equation, method of separation of variables, similarity transformation method; wave equation, d’Alembert solution – Calculus of Variations: standard 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, Van Nostrand Reinhold (1992).

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

4. Strauss, W. A., Partial Differential Equations: An Introduction, 2nd ed., John Wiley (2008).

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).

Course Outcomes (COs):

CO1: Develop a general understanding of linear algebra in terms of vector spaces and its appli- cation to differential equations and Fourier analysis.

CO2: Ability to use Fourier analysis techniques for solving PDE and for signal analysis.

CO3: Formulate physical problems in terms of ODE/PDE and obtain analytical solutions.

CO4: Use commercial/open-source math packages for solving ODE and performing signal analysis.