Vector Calculus Courses and Certifications

Professor Leonard

Calculus 3 Lecture - How to Find Divergence and Curl of Vector Fields

Explains what divergence and curl mean and how to compute them for vector fields.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

Professor Leonard

Line Integrals on Conservative Vector Fields - Independence of Path: Calculus 3 Lecture

Learn how conservative vector fields make line integrals path independent using the Fundamental Theorem of Line Integrals.

• YouTube
• 1 hour 54 minutes
• Self-Paced
• Free Video

NPTEL-NOC IITM

Green's Theorem: Derivation and Examples - Lecture 23

Derive and explore Green's Theorem through detailed examples, enhancing understanding of this fundamental concept in vector calculus.

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

Dot Physics

Derivatives of Vectors in Polar Coordinates

Explore the derivation process for first and second derivatives of position vectors in polar coordinate systems.

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

NPTEL-NOC IITM

Optimization: Vector Case - Part 2

Dive into advanced vector optimization techniques and their practical applications in mathematical problem-solving.

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

Dot Physics

Calculate the Flux Through the Surface of a Wedge - Two Methods

Learn to calculate flux through a wedge surface using traditional integration and Python-based random number methods, enhancing your vector calculus and computational skills.

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

Richard Behiel

Understanding Buoyancy Through Vector Calculus - A Mathematical Meditation

Explore the physics of buoyancy through vector calculus, examining molecular collisions and fluid dynamics while building fundamental mathematical understanding of dot products, divergence theorem, and normal vectors.

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

Michael Penn

Differential Forms - The Exterior Derivative and Vector Calculus

Reframes classical vector calculus operators using the exterior derivative, Hodge operator, and differential forms.

• YouTube
• 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

Michael Penn

Multivariable Calculus - What Is a Vector Field

An introduction to vector fields, with graphical examples and the definition of conservative vector fields.

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

Steve Brunton

Deriving the Heat Equation in 2D and 3D and in N Dimensions with Control Volumes and Vector Calculus

Derive the heat equation in two, three, and N dimensions using control volumes, Gauss’s theorem, and vector calculus.

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

Career Certificate

Mathematics for Engineers

7849 ratings at Coursera

Learn matrix algebra, differential equations, vector calculus, and numerical methods with MATLAB programming, and apply them to engineering problems in a capstone project.

• Coursera
• 12 weeks, 10 hours a week
• Self-Paced
• Paid Course
• 5 courses

张量分析

系统讲解张量定义、运算、分解与导数，并结合工程案例理解张量分析的实际应用。

• XuetangX
• Self-Paced
• Free Online Course

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

Career Certificate

Electrodynamics

987 ratings at Coursera

Work from vector calculus, field, flux and circulation through electrostatics and magnetostatics to in-depth solutions of Maxwell's equations, with special relativity linking magnetism to electricity.

• Coursera
• 4 weeks, 10 hours a week
• Self-Paced
• Paid Course
• 4 courses