Laplace transforms and their application to the solution of ode initial value problems. Applications to physical problems. Brief introduction to numerical solutions of ode's. Definition and classification of partial differential equations. Sources of PDE's from the physical sciences and other disciplines. Examples of PDE's: wave equation, vibrating strings, heat, sound, and electricity. Fourier series, graphical considerations, orthogonal functions, computation of Fourier series, use of Fourier series in solving classes of PDE's. Variables separable solutions. Bessel functions, Legendre polynomials, Laplace's equation, harmonic functions. A brief look at numerical solutions of PDE's.
Contact hours:
5 lectures/tutorials per week.Assessment:
2 tests (25%), 3 or 4 assignments (15%) and final exam (60%).Prerequisite: 1.30831
Text:
Kreyszig, E., 2000, Advanced engineering mathematics, 8th Edition, John Wiley, New York