Math Methods II
This is the course page of PHY422A.
Class notes
Handout 2022
Outline
Group Theory
Lectures 1&2
Lecture 3&4
Lectures 4 end
Representations
SU(2): first look
Lie generalities
SU(2) Reps
Lie Groups and Algebra
SU(2) applications
Roots and weights
Lorentz
Partial Differential Equations
pde 1: introduction
pde 2
pde 3
pde 4
Sturm-Liouville theory
Green's fn ODE
Riemann method
Green's fn PDE 1
Green's fn PDE 2
Videos lectures
Group Theory
Course introduction
Lecture 1: Symmetry and Groups.
Lecture 2: Symmetry and Groups 2.
Lecture 3: Finite groups.
Lecture 4: Finite groups 2.
Lecture 5: Representations 1
Lecture 5 (supplementary)
Lecture 6: Representations 2
Lecture 7: Representations 3
Lecture 8: Reps final.
Lecture 9: First look at SU(2)
Lecture 10: Lie groups and algebras: Generalities 1
Lecture 11: Lie groups and algebras: Generalities 2
Lecture 12: SU(2) reps
Lecture 13: SU(2), SO(2).
Lecture 14: Clarifications
Lecture 15: SO(3)
Lecture 16: SU(2) applications - I
Lecture 17: SU(2) applications - II
Lecture 18: Roots and weights - I
Lecture 19: Roots and weights - II; SU(3).
Lecture 20: Guest lecture on Young Tableaux
Lecture 21: STR and Lorentz group.
Lecture 22: Lorentz group II
Supplementary lecture: Quotient group.
Partial Differential Equations
Lecture 23: First look at PDEs
Lecture 24: Classification of PDEs; boundary conditions.
Lecture 25: General methods in 2d.
Lecture 26: PDEs in 2d - Characteristic curves
Lecture 27: 2d Wave Eq
Lecture 28: PDEs & BCs
Lecture 29 Part 1: Sturm-Liouville theory
Lecture 29 Part 2: Sturm-Liouville theory
Lecture 30: Green's function for ODEs -1
Lecture 31: Green's function for ODEs - 2
Lecture 32: Riemann's method
Lecture 33: Green's function for PDEs -1
Lecture 34: Green's function for PDEs -2
Lecture 35: Green's function for PDEs -3
Lecture 36: Green's function for PDEs -4