Partial Differential Equations Course
This course provides a practical introduction to solving 2D heat diffusion problems using partial differential equations, focusing on separation of variables, eigenfunction expansions, and estimating physical time scales for real-world applications.

flexible workload of 4 to 360h
valid certificate in your country
What will I learn?
This Partial Differential Equations Course offers a focused, practical approach 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 localised initial data, analyse long-time decay, estimate realistic time scales, and connect exact solutions to practical numerical parameters in real devices.
Elevify advantages
Develop skills
- Analyse PDE steady states: verify zero solutions and long-time decay rates.
- Solve 2D heat equations: set up domains, boundary data, and physical models quickly.
- 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
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