Textbook: Erwin Kreyszig, Advanced Engineering Mathematics, 1999, 8nd.
Edition, J. Wiley & Sons, pp.582#649, 962#988. Monday: Basic concepts. 1D
wave ...
Partial Di¤erential Equations 1st week, Classical theory
Textbook: Erwin Kreyszig, Advanced Engineering Mathematics, 1999, 8nd Edition, J. Wiley & Sons, pp.582-649, 962-988.
Monday: Basic concepts. 1D wave equation. Vibrating string. Separation of variables, use of Fourier series. D’Alembert’s solution. Chapter 11, §11.1-11.4. Problems: 11.1.2, 11.1.4, 11.1.5, 11.1.6, 11.1.8, 11.1.10–11.1.12, 11.1.15, 11.1.16, 11.1.18, 11.1.19, 11.1.22, 11.1.23, 11.1.25, 11.3.3, 11.3.4, 11.3.7, 11.3.9, 11.3.12–11.3.15, 11.3.17, 11.4.9.
Tuesday: Heat equation. Solution by Fourier series. Chapter 11, §11.5, 11.6 Problems: 11.5.3, 11.5.5, 11.5.8, 11.5.12, 11.5.13, 11.5.17
Wednesday: Rectangular membrane. Use of double Fourier series. Laplacian in polar coordinates. Chapter 11, §11.8, 11.9 Problems: 11.6.3, 11.8.7, 11.8.8, 11.8.9, 11.8.11, 11.8.13, 11.8.19, 11.9.3–11.9.5, 11.9.6(b), 11.9.7, 11.9.9, 11.9.13, 11.9.15
Thursday: Circular membrane. Laplace equation in cylindrical coordinates. Chapter 11, §11.10-11.11 Problems: 11.10.11–11.10.15, 11.11.3–11.11.7, 11.11.9–11.11.11, 11.11.13
Friday: Numerical methods for partial di¤erential equations. Chapter 19, §19.4–19.7 Problems: 19.4.3, 19.4.5, 19.4.9, 19.4.12, 19.5.3, 19.5.4, 19.5.13, 19.6.3, 19.6.9, 19.6.11, 19.7.1, 19.7.5–19.7.7
