Applied Mathematics Courses and Certifications

Ordinary Differential Equations : Power series, eigenvalues and Green functions

Master techniques for solving Ordinary Differential Equations using power series, eigenvalues, and Green's functions, covering Legendre polynomials, Bessel functions, and boundary value problems.

• Swayam
• Available until Sep 11, 2026
• Free Online Course

Partial Differential Equations

Comprehensive introduction to partial differential equations, covering linear and nonlinear PDEs, solution methods, and applications in science and engineering. Includes self-assessment problems and discussion forum.

• Swayam
• 15 weeks
• Self-Paced
• Free Online Course

Ordinary Differential Equations

Master fundamental concepts and practical applications of ordinary differential equations, from basic theory to advanced problem-solving using Matlab, with emphasis on real-world mathematical modeling and computational methods.

• XuetangX
• Self-Paced
• Free Online Course

IIT Bombay;  NPTEL

Partial Differential Equations - IITB

Explore partial differential equations, from first-order nonlinear PDEs to the properties of wave, Laplace, and heat equations, with emphasis on qualitative analysis and solution methods.

• Swayam
• 12 weeks
• Self-Paced
• Free Online Course

Analysis and Modeling in Chemical Engineering

Explore analysis and modeling of chemical processes at system and subsystem levels, focusing on general modeling strategies and algorithm development applicable across a wide range of engineering systems.

• Swayam
• Self-Paced
• Free Online Course

Convex Optimization in Control

Explore convex optimization techniques in control systems, focusing on semidefinite programming and LMIs for stability analysis, controller synthesis, and robust control, with practical implementation.

• Swayam
• 12 weeks
• Self-Paced
• Free Online Course

Nonlinear Dynamics and Chaos

Explore the fascinating world of nonlinear dynamics and chaos, analyzing dynamical systems in science and engineering using modern numerical and analytical techniques.

• Swayam
• Self-Paced
• Free Online Course

IISc Bangalore;  NPTEL

First Course on Partial Differential Equations - II

Explore advanced topics in partial differential equations, including Hamilton-Jacobi equations, conservation laws, and multi-dimensional heat and wave equations. Ideal for mathematics and engineering students.

• Swayam
• 8 weeks
• Available until Sep 11, 2026
• Free Online Course

Mathematical Modeling

Master advanced mathematical modeling techniques from power series to optimization, applying theoretical concepts to solve real-world problems across engineering, physics, and economics.

• Swayam
• 15 weeks
• Self-Paced
• Free Online Course

Introduction to Scaling Analysis and Perturbation Methods for Chemical Engineers

Master scaling analysis and perturbation methods for chemical engineering, covering asymptotic techniques, physicochemical modelling, and approximate solutions for complex multiphysics problems in transport and reaction processes.

• Swayam
• Self-Paced
• Free Online Course

IMSC;  NPTEL

Sobolev Spaces and Partial Differential Equations

Explore distributions, Sobolev spaces, and their applications in PDEs. Develop skills in functional analysis for solving elliptic boundary value problems and evolution equations.

• Swayam
• 12 weeks
• Self-Paced
• Free Online Course

Numerical Methods for PDEs and Their Applications: Wolfram U Colloquium

Explore advanced numerical methods for solving partial differential equations with research experts and learn Wolfram Language's finite element approach.

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

Introduction to Functions

Before starting this course you should have familiarity with the coordinate plane, basic algebra and linear relationships of the form y=mx + c.

• Brilliant
• Self-Paced
• Paid Course

Real-World Algebra

This is a great course to use for starting or re-starting your study of math. Before you get started, you should be comfortable with numerical arithmetic (addition, subtraction, multiplication, and division), but no prior experience with algebra is neede…

• Brilliant
• Self-Paced
• Paid Course

Introduction to Partial Differential Equations Video Course: Wolfram U

Learn to classify and solve PDEs, from first-order to second-order equations, using Wolfram Language, with applications in physics, engineering, and finance.

• Wolfram U
• 5 hours
• Self-Paced
• Free Certificate