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 equationend (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 selfsimilar solutions (Section 3.1)
 Heat equation (Misc.) (Section 3.2)
 Heat equation (Misc.)  end
 Tutorial 4
 Home Assignment 4
Problems to Section 2.6 (15)
 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)


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)
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
