Partial Differential Equations Course
This course focuses on mastering 2D heat diffusion through partial differential equations, covering model justification, domain setup, separation of variables, eigenfunction expansions, initial data representation, long-time decay analysis, time scale estimation, and connections to numerical parameters in practical devices.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
This Partial Differential Equations Course provides 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
Before starting, you can change the chapters and workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workloadWhat our students say
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