Partial Differential Equations Course
Master PDEs for 2D heat diffusion: derive governing equations, solve eigenvalue problems, build Fourier series solutions, and estimate decay time scales to connect rigorous analysis with realistic engineering and mathematical applications.

4 to 360 hours of flexible workload
valid certificate in your country
What Will I Learn?
This Partial Differential Equations Course gives you a focused, hands-on path to mastering 2D heat diffusion. You will justify the parabolic model, set up domains and mixed boundaries, apply separation of variables, and build eigenfunction expansions. Learn to represent localized initial data, analyze long-time decay, estimate realistic time scales, and connect exact solutions to practical numerical parameters in real devices.
Elevify Differentials
Develop Skills
- Analyze PDE steady states: verify zero solutions and long-time decay rates.
- Solve 2D heat equations: set up domains, boundary data, and physical models fast.
- Apply separation of variables: build eigenproblems and orthogonal mode bases.
- Construct Fourier series solutions: compute coefficients and assemble modal sums.
- Estimate thermal time scales: use k, L, H to predict rapid convergence to steady.
Suggested Summary
Before starting, you can change the chapters and workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workload.What our students say
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