MAT 207B Methods of Applied Mathematics Lecture Notes Page (Winter 2025)
Lecture 01: Variational Problems I (on Monday, January 6)
Lecture 02: Variational Problems II (on Wednesday, January 8)
Lecture 03: Variational Problems III (on Friday, January 10)
Lecture 04: The Isoperimetric Problem (on Monday, January 13)
Lecture 05: Natural Boundary Conditions (on Wednesday, January 15)
Lecture 06: Applications of Calculus of Variations to Data Interpolation and Approximation (on Friday, January 17)
Lecture 07: Basics of PDEs I - String (1D wave) equation; separation of variables (on Wednesday, January 22)
Lecture 08: Basics of PDEs II - Uniqueness of the solution (1); heat equation (on Friday, January 24)
Lecture 09: Basics of PDEs III - Laplace's/Poisson's equations; uniqueness of the solution (2); well-posed problems (on Monday, January 27)
Lecture 10: Basics of PDEs IV - Harmonic functions; the fundamental solution of the Laplacian (on Wednesday, January 29)
Lecture 11: Basics of PDEs V - Dirichlet/Neumann problems; a fast and accurate Laplace/Poisson solver on a rectangle (on Friday, January 31)
Lecture 12: Fourier Series I (on Monday, February 3)
Lecture 13: Fourier Series II (on Wednesday, February 5)
Lecture 14: Fourier Series III (on Friday, February 7)