Vector Fields Courses and Certifications

Krista King

Vector Calculus - Introduction to Vectors, Vector Functions, and Vector Fields

Master vector calculus from 3D geometry through advanced theorems including dot/cross products, line integrals, Green's theorem, and surface integrals in this comprehensive playlist.

• YouTube
• 12 hours 10 minutes
• Self-Paced
• Free Video

Calculus through Data & Modelling: Vector Calculus

53 ratings at Coursera

Learn line integrals over vector fields, conservative fields and potential functions, and Green's Theorem, applying its discrete Shoelace form to measure polygon areas in a data project.

• Coursera
• 3 weeks, 2 hours a week
• Self-Paced
• Paid Course

NPTEL;  IIT Madras

Electro Magnetic Fields

1 rating

A complete survey of electromagnetic fields from Coulomb’s law and electrostatics through induction, waves, radiation, and transmission lines.

• YouTube
• 1 day 17 hours
• Self-Paced
• Free Video

Mathemaniac

Lie Groups, Algebras, and Brackets - Visual Introduction to Lie Theory

Discover Lie theory through visual intuition, exploring groups, algebras, rotations in higher dimensions, exponentials, matrix operations, and the geometric meaning behind abstract concepts.

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

Ross Dynamics Lab

Normal Forms for Vector Fields

Learn how nonlinear coordinate transformations reduce autonomous vector fields near equilibria to normal forms and reveal topological equivalence, including Takens–Bogdanov cases.

• YouTube
• 1 hour 20 minutes
• Self-Paced
• Free Video

Michael Penn

Multivariable Calculus - Two Surface Integrals Over Vector Fields

Work through two surface integrals involving vector fields in a focused multivariable calculus lesson.

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

Electrostatics and magnetostatics

Introduces static electric and magnetic fields through scalar and vector fields and the integral and differential operators used to describe them.

• Polimi OPEN KNOWLEDGE
• 7 hours
• Self-Paced
• Free Certificate

Calculus IV - Vector Calculus - Line Integrals, Surface Integrals, Vector Fields, Green's Theorem, Divergence Theorem, Stokes Theorem

A six-week vector calculus course linking line and surface integrals through vector fields, Green’s, Stokes’, and divergence theorems.

• YouTube
• 5 hours
• Self-Paced
• Free Video

3Blue1Brown

The Hairy Ball Theorem

Explore the fascinating Hairy Ball Theorem through stunning visual proofs and discover its unexpected applications in topology, vector fields, and mathematical reasoning.

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

Tobias Osborne

Symplectic Geometry and Classical Mechanics

Explore the mathematical foundations connecting symplectic geometry with classical mechanics through comprehensive lectures covering geometric structures and physical applications.

• YouTube
• 1 day 4 hours 53 minutes
• Self-Paced
• Free Video

Physics with Professor Matt Anderson

Electric Charge and Field - Module 16

Explore electric charge fundamentals, Coulomb's Law, and electric field concepts through practical examples and vector analysis in this comprehensive physics module.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

3Blue1Brown

How AI Videos Actually Work - Diffusion Models, CLIP, and the Math of Turning Text into Images

Explore the mathematical foundations of AI video generation through diffusion models, CLIP embeddings, and the intricate process of transforming text prompts into visual content.

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

Steve Brunton

Potential Flow Part 2 - Details and Examples

Explore contour integrals and examples of potential flows, showing how Laplace’s equation establishes idealized fluid-flow vector fields.

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

Tom Rocks Maths

Oxford Calculus - Gradient and Divergence Explained

A visual and computational introduction to gradient and divergence, connecting their formal definitions and physical interpretations to the Laplacian.

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

Dave Churchill

AI for Video Games - COMP 4303 (2021-01)

Master AI programming techniques for video games including pathfinding, procedural generation, steering behaviors, and bot development using C++ and real game examples.

• YouTube
• 1 day 1 hour 39 minutes
• Self-Paced
• Free Video