8 Class Schedule

Class times: MWF 9:30-10:20 pm in A223 CEB (A building).

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

The below schedule is subject to change.

08/24/15 M Vectors and scalars. Fields. Vector analysis.
08/26/15 W Products of vectors and their interpretation.
08/28/15 F Vector differentiation in Cartesian and polar coordinates.
08/31/15 M Intro to curve geometry. The twisted cubic.
09/02/15 W Frenet-Serret Formulae.
09/04/15 F Due: HW 1. Grad. Total derivatives.
09/07/15 M LABOR DAY .
09/09/15 W Geometry of planes and lines. Div, curl.
09/11/15 F Due: HW 2. Interpretaion. Conservative fields.
09/14/15 75 min M Helmholtz theorem. Vector integration. Surface integrals. Flux.
09/16/15 75 min W Divergence and Stokes theorems.
09/18/15 F No lecture.
09/21/15 M Due: HW 3. Coordinate changes: Jacobian matrix. Orthogonal coordinates.
09/23/15 W PDE. Orthogonal coordinates. Partial derivatives.
09/25/15 F Due: HW 4. Domains and their boundaries. Simple BC. Properly posedness.
09/28/15 M Properly posedness example. Properties of the heat equation.
09/30/15 W Properties of the Laplace equation.
10/02/15 F Due: HW 5. Properties of the wave equation. Improperly posed Laplace problem.
10/05/15 M Improperly posed wave equation problem. Classification of 2D second order equations. Example.
10/07/15 W Classification of nD second order equations. Example. Coordinate changes.
10/09/15 F Due: HW 6. Diagonalization by rotation of the coordinate system.
10/12/15 M Diagonalization by rotation of the coordinate system.
10/14/15 W Characteristic coordinates. Characteristics. General solution of the 1D wave equation.
10/16/15 F Due: HW 7. 2D parabolic and elliptic transformations.
10/19/15 M Uniqueness. Energy methods for the Laplace equation.
10/21/15 W Remarks on variational methods. Energy methods for the heat and wave equation.
10/23/15 F Due: HW 8. Introduction to Green's functions. Green's function solution of the one-dimensionalPoisson equation in infinite space. Green's function solution of the two-dimensional Poisson equation in infinite space. Start of finite domain case. Finite domain integral.
10/26/15 M Finite domain. Panel methods. Start of Poisson integral formulae. Poisson integral formulae.
10/28/15 W Mid term review.
10/30/15 F Mid Term Exam
11/02/15 M Mean value theorem. Smoothness. Maximum/minimum property. First order equations.
11/04/15 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.
11/06/15 F Due: HW 9 and 10. D'Alembert solution of the wave equation. Method of images.
11/09/15 M Laplace transform solution. Unidirectional viscous flow.
11/11/15 W VETERANS DAY
11/13/15 F Due: HW 11. Laplace transform solution. Steady supersonic flow.
11/16/15 M Intro to separation of variables: comparison with systems of ordinary differential equations.
11/18/15 W Separation of variables. Solution of the Sturm-Liouville eigenvalue problem.
11/20/15 F Due: HW 12. Finding the solution.
11/23/15 M Separation of variables: dealing with inhomogeneous boundary conditions.
11/25/15 W Thanksgiving.
11/27/15 F Thanksgiving.
11/30/15 M Due: HW 13. Inhomogeneous boundary conditions concluded. Solution due to unit-impulse initial condition. Solution of the inhomogeneous partial differential equation: Duhamel principle.
12/02/15 W Sturm-Liouville theorem. Application to a problem with convection.
12/04/15 F Due: HW 14. Finish problem with convection. Multi-dimensional unsteady problems in cylindrical coordinates.
12/10/15 Thursday 3-5 pm FINAL EXAM (in the usual classroom)
12/15/15 Grades due FAMU/FSU 5:00/4:00 pm
12/16/15 Grades available online