Partial Education
Complex variables. Lecture #2. Cauchy-Goursat Theorem.
Complex variables. Lecture #1. Parametrized curves, contour integrals.
PDE. Lecture #8. Quasi-linear equations. Cauchy problem.
PDE. Lecture #7. Quasilinear equations. Method of characteristics.
PDE. Lecture #6. Linear Homogeneous equations: Characteristics & Integral surfaces.
PDE. Lecture #5. Linear homogeneous equation in two independent variables.
PDE. Lecture 4A. Derivation of the heat equation
PDE. Lecture A1. Auxiliary Material for Derivation of PDE Models
PDE. Lecture #31. Weak Solution to the Dirichlet Problem for Poisson’s Equation
PDE. Lecture #30. Introduction to Sobolev Spaces. Part IV
PDE. Lecture #29. Introduction to Sobolev Spaces. Part III
PDE. Lecture #28. Introduction to Sobolev spaces. Part II
PDE. Lecture #27. Introduction to Sobolev spaces. Part 1
PDE. Lecture #26. The Harnack convergence theorem
PDE. Lecture #25. Analyticity of harmonic functions. Part II.
PDE. Lecture #24. Analyticity of harmonic functions. Part I.
PDE. Lecture #23. Green’s Function for a ball. Poisson’s integral formula. Harnack's inequality.
Complex variables. Lecture #12. Applications of residue theory: evaluation of improper integrals.
PDE. Lecture #22. Subharmonic functions.
Complex variables. Lecture #11. Residue theory.
PDE. Lecture #21. Green’s Function for Laplacian.
Complex variables. Lecture #6. Sequences and series.
PDE. Lecture #20. The maximum principle.
PDE. Lecture #4. The Transport Equation.
PDE. Lecture #19. Mean—value formulae for harmonic functions.
PDE. Lecture #3. Derivation of linear transport equation.
PDE. Lecture #18. A representation of solutions of Laplace and Poisson equations using potentials.
PDE. Lecture #2. From ODE to PDE.
PDE. Lecture #17. The fundamental solution for the Laplacian. Part 3. Green's formulae.
PDE. Lecture #16. The fundamental solution for the Laplacian. Part 2. Dirac delta-function.