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.