By the end of this course, a student will learn:
- basic tools of complex analysis (power series expansions, Laurent series, complex integration and residue caclulus, etc.)
- standard facts from linear algebra, linear independence, determinants, eigenvalues and eigenvectors, Jordan forms. inner product spaces.
- basic linear algebra needed to find eigenvalues and eigenvectors
- system of linear differential equations, basic theory, fundamental matrices, higher order linear differential equations, mechanical vibrations, resonance phenomenon, correspondence between linear second order differential equations and physical spring systems
- computation of Laplace transforms, and use to solve differential equations with discontinuous forcing functions, distributions and delta functions.
- Fourier series expansions, Fourier integral, Fourier transform.
- partial diffrential equations, heat conduction problem