MATH401: Green's functions and variational methods Outline of the course and schedule of lectures outline.pdf MID TERM EXAM: February 16th 2018, 12:00pm in SCRF200, duration: 50min. Office hours: - Thursday 11:00am-12:00pm, with me in my Math office MATH236.
By appointment only, so please email me (wachs_at_math.ubc.ca) before if you intend to come. - Monday 1:00pm-2:00pm, with Sarafa Adewale Iyaniwura (TA) in LSK300.
Same for Sarafa, please email him (iyaniwura_at_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 Monday Jan 15th 2018, end of lecture
- Assignment 2: MATH401_HW2.pdf, due Friday Jan 26th 2018, end of lecture
- Assignment 3: MATH401_HW3.pdf, due Friday February 9th 2018, end of lecture
- Assignment 4: MATH401_HW4.pdf, due Wednesday February 13th 2018, end of lecture
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
Mid-term exam in Spring 2016: Mid-term exam in Spring 2017: |