Partial Differential Equations (PDE)
PDE support covering boundary-value problems, Sturm-Liouville theory, Fourier/Laplace transforms, and classical equations.
Course Content
Weekly contentThis module covers ODE fundamentals through conceptual framing and problem solving.
This module covers Special functions and classical equations through conceptual framing and problem solving.
This module covers Sturm-Liouville theory and orthogonal functions through conceptual framing and problem solving.
This module covers Transform methods through conceptual framing and problem solving.
This module covers Introduction to partial differential equations through conceptual framing and problem solving.
This module covers First-order PDEs through conceptual framing and problem solving.
This module covers Higher-order homogeneous PDEs with constant coefficients through conceptual framing and problem solving.
This module covers Classical PDEs: Laplace, Poisson, heat, and wave equations through conceptual framing and problem solving.
This module covers Solution methods: separation of variables and transforms through conceptual framing and problem solving.
Targeted Learning Outcomes
- Form initial-value and boundary-value problems for ODEs and PDEs
- Use Sturm-Liouville structure to build eigenvalue and eigenfunction solutions
- Apply orthogonal functions and Fourier expansions in PDE solutions
- Manage ODE and PDE solution workflows with Laplace and Fourier transforms
- Solve standard Laplace, Poisson, heat, and wave equation exam problems
Recommended Prerequisites
- Calculus, including limits, derivatives, and integrals
- Linear algebra with vectors, matrices, and the basic eigenvalue idea
- Basic differential equations background is preferred