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)
  • Lecture 15: Fourier Series IV (on Monday, February 10)
  • Lecture 16: Fourier Series V (on Wednesday, February 12)
  • Lecture 17: Basics of L2 Theory I (on Friday, February 14)
  • Lecture 18: Basics of L2 Theory II (on Wednesday, February 19)
  • Lecture 19: Basics of L2 Theory III (on Friday, February 21)
  • Lecture 20: The Sturm-Liouville Problem I (on Monday, February 24)
  • Lecture 21: The Sturm-Liouville Problem II (on Wednesday, February 26)
  • Lecture 22: Green's Functions I (on Friday, February 28; Monday, March 3)
  • Lecture 23: Green's Functions II (on Monday, March 3; Wednesday, March 5)
  • Lecture 24: Green's Functions III (on Wednesday, March 5; Friday, March 7)
  • Lecture 25: Eigenfunction Expansion (on Friday, March 7; Monday, March 10)
  • Lectures 26, 27, 28: Laplacian Eigenfunctions: Foundations and Applications (on Monday, March 10; Wednesday, March 12; Friday, March 14)

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