Vector Calculus Courses and Certifications

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

Jonathan Walters

Stewart Calculus - Vector Functions

Explore vector-valued functions through limits, derivatives, integrals, curvature, arc length, and tangent and normal vectors.

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

Math for AI Beginner Part 2 : Vector Calulus

Learn vector calculus for AI applications: gradient, divergence, curl and their identities, plus line, surface and volume integrals via Green's, Gauss's and Stokes' theorems.

• Coursera
• 7 weeks, 1 hour a week
• Self-Paced
• Paid Course

Multivariable Calculus 3: Theorems and Applications

Compute line and surface integrals, identify conservative fields and potential functions, and apply the Divergence and Stokes' theorems to fluid flow, electromagnetism, and diffusion problems.

• MITx Online
• Self-Paced
• Free Online Course

Professor Leonard

Calculus 3 - TNB (Frenet-Serret) Frames, Curvature, Torsion, Encapsulation

Compute Frenet–Serret frames, curvature, torsion, and osculating geometry for vector-valued curves.

• YouTube
• 2 hours 37 minutes
• Self-Paced
• Free Video

Professor Leonard

Green's Theorem - Calculus 3 Lecture

Explains Green’s Theorem and its application to line integrals around simple closed curves in non-conservative vector fields.

• YouTube
• 1 hour 46 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus 3 - Arc Length/Parameterization, TNB (Frenet-Serret) Intro

Learn to compute arc length for space curves, reparameterize vector functions by arc length, and begin using Frenet–Serret frames.

• YouTube
• 2 hours 13 minutes
• Self-Paced
• Free Video

Krista King

Calculus III - Multivariable Calculus, Vector Analysis, and Differential Equations

Master multivariable calculus, vectors, and differential equations through comprehensive coverage of partial derivatives, multiple integrals, 3D geometry, and solution techniques.

• YouTube
• 1 day 6 hours 43 minutes
• Self-Paced
• Free Video

Steve Brunton

Gauss's Divergence Theorem

Learn why Gauss’s Divergence Theorem is true and how it connects mass conservation in physics to partial differential equations.

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

Multidimensional Analysis and Geometry: Introduction to the Derivative in Higher Dimensions - Lecture 2

Explore the derivative in higher dimensions, focusing on linear approximations for functions in 3D space. Learn how classical definitions evolve to handle multivariable calculus concepts.

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

Dot Physics

Mathematical Method to Test for Conservative Fields

Learn a mathematical technique to determine if a vector field is conservative by calculating its curl and verifying if it equals zero.

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

Steve Brunton

Div, Grad, and Curl

A lecture on divergence, gradient, and curl in engineering mathematics.

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

Steve Brunton

Directional Derivative, Continuity Equation, and Examples of Vector Fields

Explores directional derivatives, the continuity equation, and examples of vector fields in an engineering mathematics lecture.

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

Steve Brunton

Gauss's Divergence Theorem

A focused engineering mathematics lecture on Gauss’s Divergence Theorem.

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

NPTEL;  IIT Kharagpur

Integral and Vector Calculus

Explore Riemann and multiple integration alongside vector fields and Green’s, Gauss’s, and Stokes’ theorems.

• YouTube
• 1 day 6 hours
• Self-Paced
• Free Video