Week 1 (September 12—16)
- Introduction: PDE Motivations and Context (Section 1.1)
- Introduction: Initial and Boundary Value Problems (Section 1.2)
- First order PDEs (Section 2.1)
Week 2 (September 19—23)
- First order PDEs (Section 2.1 (end))
- Homogeneous 1D Wave equation (Section 2.3)
- Homogeneous 1D Wave equation--end (Section 2.3)
Week 3 (Sept. 26—30)
- 1D Wave equation reloaded: characteristic coordinates and more
(Section 2.4 and Section 2.5)
- 1D Wave equation: IBVP (Section 2.6)
- Wave equation: Energy integral (Section 2.7)
Week 4 (October 3—7)
- 1D Heat equation: method of self-similar solutions (Section 3.1)
- Heat equation (Misc.) (Section 3.2)
- Heat equation (Misc.) -- end
- Tutorial 4
- Home Assignment 4
Problems to Section 2.6 (1--5)
- Quiz 2 (Thu, Oct. 6, Lecture): covers Home Assignment 3
Week 5 (October 10—14)
- 1D wave equation: Separation of variables (the first blood)
(Section 4.1)
- Eigenvalue problems (examples) (Section 4.2)
- Ortogonal systems (Section 4.3)
Week 6 (October 17—21)
- Ortogonal systems (Section 4.3 (end))
- Ortogonal systems and Fourier series
(Section 4.4)
- Other Fourier series
(Section 4.5)
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Week 7 (October 24—28)
- Fourier transform, Fourier integral
(Section 5.1)
- Properties of Fourier transform
(Section 5.2)
- Applications of Fourier transform to PDEs
(Section 5.3)
Week 8 (Oct. 31—Nov. 4)
- Separation of variables for heat equation
(Section 6.1)
Separation of variables: Misc equations (Section 6.2)
- Laplacian in polar and spherical coordinates
(Section 6.3)
Laplacian: separation of variables in polar coordinates
(Section 6.4)
- Laplace operator in the disk. II
(Section 6.5)
Week 9 (November 7—11)
- General properties of Laplace equation
(Section 7.1)
- Potential theory and around
(Section 7.2)
Green function
(Section 7.3)
- Separation of variable in spherical coordinates
(Section 8.1)
Notes below are subject to modifications
Week 10 (November 14—18)
- Separation of variable in spherical coordinates
(Section 8.1 (end))
- Wave equation in 3D and 2D
(Section 9.1)
- Wave equation in 3D and 2D (end);
Wave equation: energy method
(Section 9.2)
- Term Test 2. Covers Chapters 4--7.
Solving HA 6—9 is a good preparation
Week 11 (November 21—26)
- Functionals, extremums and variations
(Section 10.1)
- Functionals, extremums and variations .II
(Section 10.2)
- Variational methods in physics
(Section 10.3)
Week 12 (Nov. 30—Dec. 04)
- Distributions
(Section 11.1)
- Distributions: more
(Section 11.2)
- Applications of distributions
(Section 11.3)
Weak solutions
(Section 11.4)
- Tutorial 12
- Bonus Quiz: covers Home Assignment 11
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