Partial Differential Equations (PDEs)
Fourier methods, separation, Green's functions and numerics.
What you’ll learn
- Turn word problems into clear mathematical models
- Use the right theorem or method without guessing
- Blend analytic techniques with numerical intuition
- Check your own work with simple sanity checks and visuals
Curriculum
M1
Fundamentals & classification — 3 lessons
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What is a PDE? ICs/BCs & types14m
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Classification: elliptic/parabolic/hyperbolic14m
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Separation of variables (overview)12m
M2
Fourier series & orthogonality — 2 lessons
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Fourier series & orthogonality16m
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Sine/cosine series & convergence notes14m
M3
Heat equation — 3 lessons
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Heat equation: separation & eigenfunctions16m
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Heat with boundary conditions14m
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Inhomogeneous heat & sources12m
M4
Wave equation — 2 lessons
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Wave equation: d'Alembert & separation16m
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Vibrating string & boundary conditions14m
M5
Laplace/Poisson — 2 lessons
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Laplace's equation & harmonic functions16m
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Poisson equation & Green's identity14m
M6
Transforms & Green’s functions — 2 lessons
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Transforms (Fourier/Laplace) for PDEs16m
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Green's functions: idea & examples14m
M7
Numerical PDE — 2 lessons
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Finite differences for PDEs16m
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Stability/consistency (brief)12m
Projects
- Model a real-world system (growth, decay, motion, or heat flow) or dataset
- Write a short report comparing analytic and numerical solutions
- Create study notes and formula sheets you can reuse in exams
Prerequisites
- Prior exposure to high-school algebra and functions
- For ODE/PDE: at least Calculus I (or concurrent)
- Willingness to pause and re-watch explanations until they click
Who is this for?
- Students currently in a university math course who want a second pass
- STEM majors building a stronger analysis foundation
- Self-taught learners filling in gaps before ML/AI or physics
Outcomes
- Less “formula hunting”, more structured problem-solving
- A reusable set of notes, diagrams, and checklists
- More confidence walking into problem sets and exams
Resources
- Starter project / template (ZIP)
- Setup & study checklists (PDF)
- Core formulas / syntax cheatsheet (PDF)
Tip: Right-click → “Save link as…” if your browser opens the file.
FAQ
Is this beginner-friendly?
Yes. We start from mental models and build up with guided practice and plenty of worked examples.
Will I need extra software?
We stick to free or standard tools. Any optional extras are clearly marked and have alternatives.
Do I get updates?
Yes—lifetime access with updates as the field, tools, and exam expectations evolve.