8 Class Schedule

Class times: MWF 9:30-10:24 pm in A223 CEB (A building).

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

The below schedule is from last year and subject to change.

08/29/16 M Vectors and scalars. Fields. Vector analysis.
08/31/16 W Products of vectors and their interpretation.
09/02/16 F HERMINE
09/05/16 M LABOR DAY
09/07/16 W Triple products. Vector differentiation in Cartesian and polar coordinates. Grad. Total derivatives.
09/09/16 F Due: HW 1. Geometry of planes and lines. Div, curl.
09/12/16 M Interpretation. Helmholtz theorem.
09/14/16 W Conservative fields. Vector integration.
09/16/16 F Due: HW 2. Surface integrals. Flux. Divergence and Stokes theorems.
09/19/16 M Coordinate changes: Jacobian matrix. Orthogonal coordinates.
09/21/16 W PDE. Differentiating the unit vectors. Partial derivatives.
09/23/16 F Domains and their boundaries. Simple BC. Properly posedness. Properly posedness example. Due: HW 3.
09/26/16 M Properties of the heat, Laplace, and wave equations.
09/28/16 W Improperly posed Laplace problem. Improperly posed wave equation problem.
09/30/16 F Due: HW 4. One-way wave equation equation. Classification of 2D second order equations. Example.
10/03/16 M Classification of nD second order equations. Example. Coordinate changes.
10/05/16 W Diagonalization by rotation of the coordinate system.
10/07/16 F Due: HW 5. Diagonalization by rotation of the coordinate system. Coordinate stretching.
10/10/16 M Further simplification. 2D case: Characteristic coordinates. Characteristics.
10/12/16 W General solution of the 1D wave equation.
10/14/16 F Due: HW 6. 2D parabolic and elliptic transformations.
10/17/16 M Introduction to Green's functions. Green's function solution of the one-dimensionalPoisson equation in infinite space. (SKIP: Uniqueness. Energy methods for the Laplace equation. Remarks on variational methods. Energy methods for the heat and wave equation.)
10/19/16 W Green's function solution of the two-dimensional Poisson equation in infinite space. Start of finite domain case. Finite domain integral.
10/21/16 F Due: HW 7. Mid term review.
10/24/16 M Finite domain.
10/26/16 W Mid Term Exam
10/28/16 F Due: HW 8. Panel methods. Poisson integral formulae.
10/31/16 M Mean value theorem. Smoothness. Maximum / minimum property. First order equations.
11/02/16 W Example linear first order equation. SKIP: One-way traffic: conservation law, characteristics. Shocks. Expansion shocks. Entropy condition. Burger’s equation. Need for the viscous equation to determine the conservation law.
11/04/16 F Due: HW 9. Burgers' equation, shocks, expansion fans. Fourier transform solution of the linearized Korteweg-De Vries equation.
11/07/16 M D'Alembert solution of the wave equation.
11/09/16 W Method of images. Laplace transform solution.
11/11/16 F VETERANS DAY
11/14/16 M Due: HW 10. Laplace transform solution. Unidirectional viscous flow.
11/16/16 W Steady supersonic flow.
11/18/16 F Due: HW 11. Intro to separation of variables. Comparison with systems of ordinary differential equations. Solution of the Sturm-Liouville eigenvalue problem.
11/21/16 M Finding the solution.
11/23/16 W THANKSGIVING
11/25/16 F THANKSGIVING
11/28/16 M Due: HW 12. Separation of variables: dealing with inhomogeneous boundary conditions.
11/30/16 W Inhomogeneous boundary conditions concluded.
12/02/16 F Due: HW 13. Sturm-Liouville theorem. Solution due to unit-impulse initial condition. Solution of the inhomogeneous partial differential equation: Duhamel principle.
12/05/16 M Due: HW 14. SKIP: Application to a problem with convection. Multi-dimensional unsteady problems in cylindrical coordinates.
12/07/16 W FINAL EXAM I
12/09/16 F FINAL EXAM II