Lecture 09/04 (Section 6.1): Extremal values of continuous functions on a compact domain. Maximum principle for a two-point boundary value problem.

Lecture 09/04 (Section 6.1–6.2): Maximum principle for a two-point boundary value problem (continued) and for the linear heat equation.

Lecture 23/04 (Section 6.2–6.3): Maximum principle for the linear heat equation and for numerical methods. The nonlinear heat equation.

Lecture 30/04 (Section 6.3–6.4): Numerical method for the nonlinear heat equation. Harmonic functions in two dimensions.

Lecture 02/05 (Section 6.4–6.5): Harmonic functions in two dimensions and maximum principles. Numerical method for Laplace's equation in 2D. Definition of discrete harmonic function.

Lecture 07/05 (Section 6.5): Maximum principle for discrete harmonic functions.

Lecture 09/05 (Section 6.5): Existence and uniqueness of solutions of the discrete Poisson problem.