Partial Differential Equations Courses and Certifications

Analysis of Transport Phenomena: Scaling

Model heat and mass transfer, fluid flow, and chemical reactions using dimensional analysis, similarity solutions for linear and nonlinear diffusion, and Green functions with the method of images.

• MITx Online
• 3 weeks, 10-12 hours/week
• Self-Paced
• Free Online Course

Analysis of Transport Phenomena: Series Expansions

Apply Fourier series, Sturm–Liouville theory, and generalized expansions with Bessel functions and Legendre polynomials to model diffusion, convection, fluid dynamics, and phase transformations.

• MITx Online
• 6 weeks, 10-12 hours/week
• Self-Paced
• Free Online Course

Mathematical Methods for Engineers II

Solve engineering problems numerically: finite differences for wave and heat equations, conservation laws and shocks, sparse matrices, multigrid and Krylov solvers, constrained optimization and duality.

• MIT OpenCourseWare
• Self-Paced
• Free Online Course

Professor Leonard

Using Partial Fractions in Differential Equations

Review partial fractions and apply them to solve differential equations by separation of variables.

• YouTube
• 40 minutes
• Self-Paced
• Free Video

3Blue1Brown

Differential Equations - A Tourist's Guide

Discover the fundamentals of differential equations through visual explanations, covering partial differential equations, heat equations, Fourier series, and Laplace transforms.

• YouTube
• 3 hours 17 minutes
• Self-Paced
• Free Video

Tom Rocks Maths

Oxford Calculus - Partial Differentiation, Critical Points, PDEs, and Fourier Series

Master advanced calculus concepts including partial differentiation, critical points, PDEs, Jacobians, Taylor's theorem, heat equations, and Fourier series with Oxford methodology.

• YouTube
• 6 hours 28 minutes
• Self-Paced
• Free Video

Differential Equations: Fourier Series and Partial Differential Equations

3 ratings

Learn to use Fourier series to solve differential equations with periodic input signals and to solve boundary value problems involving the heat equation and wave equation.

• edX
• 11 weeks, 5-8 hours a week
• No Longer Offered
• Free Online Course

IIT Madras;  NPTEL

Differential equations for engineers

1 rating

Develops analytical methods for ordinary and partial differential equations, including wave, heat, and Laplace equations, for engineering applications.

• Swayam
• 12 weeks
• Available until Oct 9, 2026
• Free Online Course

Solving Differential Equations in Science and Engineering

Discover how differential equations help explain the world. Learn to analyze, solve, and apply them across real-world systems in this foundational course – using pen, paper and mathematics.

• edX
• 12 weeks, 6-7 hours a week
• Self-Paced
• Free Online Course (Audit)

IIT Kharagpur;  NPTEL

Introduction to CFD

Learn to develop computational fluid dynamics codes by numerically solving fluid-flow conservation equations and model PDEs.

• Swayam
• 12 weeks
• Available until Oct 9, 2026
• Free Online Course

Finite Element Methods

Derives finite element formulations, shape functions, and stiffness matrices to solve ordinary and partial differential equations in one, two, and three dimensions.

• Swayam
• 16 weeks
• Available until Oct 28, 2026
• Free Online Course

IIT Bombay;  NPTEL

Phase Field Modelling: The Materials Science, Mathematics and Computational Aspects

Model solid-solid transformations and microstructure evolution using phase-field methods, mathematical equations, and GNU Octave computations.

• Swayam
• 12 weeks
• Available until Oct 9, 2026
• Free Online Course

Numerical Methods for PDEs and Their Applications: Wolfram U Colloquium

A research colloquium on numerical methods that turn partial differential equations into quantitative predictions, with a developer’s view of FEM in Wolfram Language.

• Wolfram U
• 3 hours
• Self-Paced
• Free Online Course

The Royal Institution

The Extraordinary Theorems of John Nash

Cédric Villani explores how John Nash’s revolutionary ideas opened new chapters in game theory and geometric analysis.

• YouTube
• 1 hour
• Self-Paced
• Free Video

Richard Behiel

The Hydrogen Atom: Introduction to Quantum Physics - Part 1

Dive into quantum physics fundamentals through an exploration of the hydrogen atom, covering electron behavior, Schrödinger's equation, and essential mathematical concepts in spherical coordinates.

• YouTube
• 19 minutes
• Self-Paced
• Free Video