MATH401: Green's functions and variational methods Outline of the course and schedule of lectures outline.pdf Office hours: Thursday 11am to 1pm in my Math office MATH236. By appointment only, so please email me (wachs@math.ubc.ca) before if you intend to come. Lectures notes: Lecture 0: warm up for ODEs Green's functions for ODEs and steady-state PDEs Lecture Green(a): General notions on solving ODEs and PDEs Lecture Green(b): Introduction to generalized functions Lecture Green(c): Green's functions for ODEs Lecture Green(d): Boundary conditions and self-adjoint problems Lecture Green(e): Modified Green's functions and solvability condition Lecture Green(f): Green's functions and eigenfunction expansion Lecture Green(g): Green's functions for PDEs and free-space Green's functions Lecture Green(h): Method of images for simple BCs, solvability condition and modified Green's functions Lecture Green(i): General theory of Green's functions for the Laplacian operator Lecture Green(j): The maximum principle Lecture Green(k): Green's functions by eigenfunction expansion Green's functions for time-dependent PDEs Lecture TD-Green(a): Green's functions for time-dependent PDEs and free-space Green's functions Lecture TD-Green(b): The heat equation: maximum principle, method of images and eigenfunction expansion Lecture TD-Green(c): The wave equation in 1, 2 and 3 dimensions Variational methods Lecture VarMeth(a): Eigenvalue problems and the Rayleigh quotient Lecture VarMeth(b): Bounds on eigenvalues Lecture VarMeth(c): Euler-Lagrange equations Lecture VarMeth(d): Rayleigh-Ritz method Lecture VarMeth(e): Minimization with constraints Assignments: Assignment 1: MATH401_HW1.pdf, due to Monday Jan 18th, end of lecture Assignment 2: MATH401_HW2.pdf, due to Wednesday Jan 27th, end of lecture Assignment 3: MATH401_HW3.pdf, due to Friday Feb 5th, end of lecture Assignment 4: MATH401_HW4.pdf, due to Wednesday March 2nd, end of lecture Assignment 5: MATH401_HW5.pdf, due to Monday March 14th, end of lecture Assignment 6: MATH401_HW6.pdf, due to Monday March 23rd, end of lecture Assignment 7: MATH401_HW7.pdf, due to Friday April 1st, end of lecture Assignment 8: MATH401_HW8.pdf, due to Friday April 8th, end of lecture, or at the latest April 13th by email or dropped in the cardboard box in front of my office Solutions to assignments: Assignment 1: MATH401_HW1_solutions.pdf Assignment 2: MATH401_HW2_solutions.pdf Assignment 3: MATH401_HW3_solutions.pdf Assignment 4: MATH401_HW4_solutions.pdf Assignment 5: MATH401_HW5_solutions.pdf Assignment 6: MATH401_HW6_solutions.pdf Assignment 7: MATH401_HW7_solutions.pdf Assignment 8: MATH401_HW8_solutions.pdf Mid-term exam: