Numerical Approximation of Partial Differential Equations

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Explores the parabolic heat equation evolution and numerical solution methods.

Covers non-linear ordinary differential equations, including separation, Cauchy problems, and stability conditions.

Explores direction fields, Euler methods, and differential equations through practical exercises and stability analysis.

Covers numerical differentiation, forward differences, Taylor's expansion, Big O notation, and error minimization.

Covers error division and schemes for solving differential equations.

Explores the stability analysis of finite difference methods for solving differential equations.

Introduces the finite difference method for approximating derivatives and solving differential equations in practical applications.

Covers high order methods for space discretisation in linear differential systems.

Covers numerical methods for solving boundary value problems using Crank-Nicolson and FFT.

Covers advanced topics in numerical analysis, focusing on techniques for solving complex mathematical problems.