Math 222: Partial Differential Equations II TR 9:00-10:15 AM in COB 262: Syllabus (PDF) Note that the syllabus has changed to reflect the new grading percentages as discussed in class Discussion Section: Fridays from 10:30 AM - 11:20 AM in COB 209 Office Hours: Wednesdays from 2:30 - 3:30 PM and Thursdays from 1:00 - 2:00 PM in COB 347 Sections from Texts: Ablowitz and Fokas, Section 4.5 Shearer and Levy, Chapter 8 Shearer and Levy, Chapter 9 Ablowitz and Fokas, Section 4.6 Lecture 1 (01/20): Introduction to 2nd order linear PDEs, derivation of Laplace's equation, and ODE BVP Lecture 2 (01/22): ODE BVP and existence and uniqueness of solutions to the Poisson equation There will be no discussion section this week. HW 1 Discussion Sections: 01/30 and 02/06 Additional problems will be added depending on how far in the material we get this week. Lecture 3 (01/27): The Maximum Principle for elliptic PDEs Lecture 4 (01/29): The Maximum Principle for elliptic PDEs and parabolic PDEs Lecture 5 (02/03): Separation of Variables for elliptic PDEs (Dirichlet problems in rectangular domains) Lecture 6 (02/05): Separation of Variables for elliptic PDEs (Neumann problems in rectangular domains and Dirichlet problems in circular domains) HW 2 Discussion Sections: 02/13 and 02/20 Lecture 7 (02/10): Introduced integral representations and Poisson's formula and Green's identities Lecture 8 (02/12): Green's identities and Fourier Transforms: motivation and definition and properties Lecture 9 (02/17): Exam 1 Exam 1 Solutions Lecture 10 (02/19): Fourier Transform properties and Dirac delta function and distributions Link to website with Fourier transform examples. HW 3 Discussion Sections: 02/27 and 03/06 Additional problems will be added depending on how far in the material we get this week. Lecture 11 (02/24): Delta functions and Distributions: definition (linearity and continuity) and test functions and examples Lecture 12 (02/26): Regular and Singular distributions and Convergence of distributions Lecture 13 (03/03): Convergence of distributions, Distributional derivatives, Translation of a derivative, Multiplication of a distribution by a C-infinity function Lecture 14 (03/05): NO CLASS HW 4 Discussion Sections: 03/13 and 03/20 Additional problems will be added depending on how far in the material we get this week. Lecture 15 (03/10): Fourier Transforms of districbutions and delta functions and Solution of PDEs using Fourier Transforms Research Projects Information (discussed in class today) Link to convolution page on wikipedia as discussed in class today Lecture 16 (03/12): Solution of PDEs using Fourier Transforms and Review for Exam 2 Lecture 17 (03/17): Work on Research Projects Lecture 18 (03/19): Exam 2 Lecture 19 (03/31): CLASS CANCELLED Lecture 20 (04/02): Introduction to Green's functions: Boundary value problem HW 5 Discussion Sections: 04/03 and 04/10 and 04/17 and 04/24 Lecture 21 (04/07): Fundamental solution of Laplace's equation in n-dimensions and Solving Poisson's equation using the fundamental solution Lecture 22 (04/09): Solving Poisson's equation using the fundamental solution and Green's function to solve the BVP Lecture 23 (04/14): Symmetry of Green's function and Method of images - half space Lecture 24 (04/16): Method of images - half space and sphere and Solving the PDEs using the Green's function Plots of fundamental solutions and Green's functions Lecture 25 (04/21): Solving the PDEs using the Green's function and Green's functions generally for linear PDEs Solution to Laplace's equation in a sphere in 3D
Lecture 26 (04/23): Green's functions generally for linear PDEs, Equations of motion for fluid dynamics and nondimensionalization, and Review for Exam 3 Lecture 27 (04/28): Equations of motion for fluid dynamics and nondimensionalization and the fundamental solution HW 6 Discussion Section: 05/01 Lecture 28 (04/30): Exam 3 Lecture 29 (05/05): Equations of motion for fluid dynamics and nondimensionalization and the fundamental solution Lecture 30 and Discussion Section (05/07 and 05/08):Practice presentations Final Project Presentations Tuesday, May 12, 2015 3:00 PM in COB 262 |