Mathematical Methods in Aerospace Engineering

a
Course
Postgraduate
Semester
Sem. I
Subject Code
AE601
Subject Title
Mathematical Methods in Aerospace Engineering

Syllabus

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, similar- ity 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.

Text Books

Same as Reference

References

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 Engineers, 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).

Course Outcomes (COs):
CO1: Develop a general understanding of linear algebra in terms of vector spaces and its application 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.