8 Class Schedule

Class times: MWF 12:30-1:20 pm in A235 CEB (A building).

We will start with vector analysis, then proceed to partial differential equations.

• 01/07 W Vectors and scalars. Fields. Vector analysis.
• 01/09 F Products of vectors and their interpretation.
• 01/12 M Vector differentiation in Cartesian and polar coordinates. Intro to curve geometry.
• 01/14 W The twisted cubic. Frenet-Serret Formulae.
• 01/16 F Due: HW 1. Grad. Total derivatives.
• 01/19 M Martin Luther King day.
• 01/21 W Div, curl.
• 01/23 F Due: HW 2. Conservative fields. Helmholtz theorem. Vector integration.
• 01/26 M Surface integrals. Flux.
• 01/28 W Divergence and Stokes theorems. Coordinate changes: Jacobian matrix.
• 01/30 F Due: HW 3. Orthogonal coordinates.
• 02/02 M PDE. Domains and their boundaries. Simple BC. Properly posedness.
• 02/04 W Properly posedness example. Properties of the heat equation.
• 02/06 F Due: HW 4. Properties of the Laplace equation.
• 02/09 M Improperly posed Laplace and wave equation problems.
• 02/11 W Classification of second order equations.
• 02/13 F Due: HW 5. Example. Coordinate changes.
• 02/16 M Diagonalization by rotation of the coordinate system.
• 02/18 W Characteristic coordinates.
• 02/20 F Due: HW 6. 2D parabolic and elliptic transformations.
• 02/23 M Uniqueness. Energy methods for the Laplace equation. Remarks on variational methods.
• 02/25 W Energy methods for the heat and wave equation. Introduction to Green;s functions.
• 02/27 F Due: HW 7. Green's function solution of the one-di-men-sion-al Poisson equation in infinite space.
• 03/02 M Green's function solution of the two-di-men-sion-alPoisson equation in infinite space. Start of finite domain case.
• 03/04 W Mid Term Exam
• 03/06 F Due: HW 8. Finite domain integral.
• 03/09 M Spring Break
• 03/11 W Spring Break
• 03/13 F Spring Break
• 03/16 M Finite domain. Panel methods. Start of Poisson integral formulae.
• 03/18 W Poisson integral formulae. Smoothness. Mean value theorem. Maximum/minimum property.
• 03/20 F Due: HW 9. First order equations.
• 03/23 M Example linear first order equation. Start of one-way traffic: conservation law, characteristics.
• 03/25 W Shocks. Expansion shocks. Entropy condition. Burger’s equation. Need for the viscous equation to determine the conservation law.
• 03/27 F (Last day to drop) Due: HW 10. D'Alembert solution of the wave equation. Method of images.
• 03/30 M Intro to separation of variables. Solution of the Sturm-Liouville eigenvalue problem.
• 04/01 W Separation of variables. Finding the solution.
• 04/03 F Due: HW 11. Explanation of the solution process in terms of functional analysis.
• 04/06 M Jury selection, no class.
• 04/08 W Long class: Separation of variables: dealing with inhomogeneous boundary conditions.
• 04/10 F Due: HW 12. Long class: inhomogeneous boundary conditions continued. Solution due to unit-impulse initial condition. Solution of the inhomogeneous equation: Duhamel principle.
• 04/13 M Laplace transform solution. Unidirectional viscous flow.
• 04/15 W Laplace transform solution. Steady supersonic flow.
• 04/17 F Due: HW 13. Sturm-Liouville theorem. Application to a problem with convection.
• 04/20 M Completion of the problem with convection.
• 04/22 W Multi-dimensional unsteady problems in cylindrical coordinates.
• 04/24 F Due: HW 14. Review.
• 04/29, Wednesday, 12:30-2:30 pm, in A235: Final Exam