MATH401: Green's functions and variational methods

• 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.

• 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

• 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
• Assignment 5: MATH401_HW5.pdf, due Wednesday March 14th 2018, end of lecture
• Assignment 6: MATH401_HW6.pdf, due Wednesday March 21st 2018, end of lecture
• Assignment 7: MATH401_HW7.pdf, due Wednesday April 4th 2018, end of lecture
• Assignment 8: MATH401_HW8.pdf, due Friday April 6th, end of lecture, or at the latest April 10th end of the day by email or dropped in the cardboard box in front of my office

• 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

• midterm2016_MATH401.pdf
• solutions: midterm2016_MATH401_solutions.pdf

• midterm2017_MATH401.pdf
• solutions: midterm2017_MATH401_solutions.pdf