### MAT 207B Methods of Applied Mathematics *Lecture Notes* Page (Winter 2018)

Lecture 01: Variational Problems I (on Monday, January 8)
Lecture 02: Variational Problems II (on Wednesday, January 10)
Lecture 03: Variational Problems III (on Friday, January 12)
Lecture 04: The Isoperimetric Problem (on Wednesday, January 17)
Lecture 05: Natural Boundary Conditions (on Friday, January 19)
Lecture 06: Applications of Calculus of Variations to Data Interpolation and Approximation (on Monday, January 22)
Lecture 07: Basics of PDEs I - String (1D wave) equation; separation of variables (on Wednesday, January 24)
Lecture 08: Basics of PDEs II - Uniqueness of the solution (1); heat equation (on Friday, January 26)
Lecture 09: Basics of PDEs III - Laplace's/Poisson's equations; uniqueness of the solution (2); well-posed problems (on Monday, January 29)
Lecture 10: Basics of PDEs IV - Harmonic functions; the fundamental solution of the Laplacian (on Wednesday, January 31)
Lecture 11: Basics of PDEs V - Dirichlet/Neumann problems; a fast and accurate Laplace/Poisson solver on a rectangle (on Friday, February 2)
Lecture 12: Fourier Series I (on Monday, February 5)
Lecture 13: Fourier Series II (on Wednesday, February 7)
Lecture 14: Fourier Series III (on Friday, February 9)
Lecture 15: Fourier Series IV (on Monday, February 12)
Lecture 16: Fourier Series V (on Wednesday, February 14)
Lecture 17: Basics of *L*^{2} Theory I (on Friday, February 16)
Lecture 18: Basics of *L*^{2} Theory II (on Wednesday, February 21)
Lecture 19: Basics of *L*^{2} Theory III (on Friday, February 23)
Lecture 20: The Sturm-Liouville Problem I (on Monday, February 26)
Lecture 21: The Sturm-Liouville Problem II (on Wednesday, February 28)
Lecture 22: Green's Functions I (on Friday, March 2; Monday, March 5)
Lecture 23: Green's Functions II (on Monday, March 5; Wednesday, March 7)
Lecture 24: Green's Functions III (on Wednesday, March 7; Friday, March 9)
Lecture 25: Eigenfunction Expansion (on Friday, March 9; Monday, March 12)
Lectures 26, 27, 28: Laplacian Eigenfunctions: Foundations and Applications (on Monday, March 12; Wednesday, March 14; Friday, March 16)