Explore related topics
This course includes
- 5h 28m of video
- 39 lessons
- Level: Beginner
- Spoken in English
- Your place is remembered
- Free in full, no card
Lessons
4 sections · 39 lessons · 5h 28m total length
Lessons 1 to 1010 lessons · 1h 24m
- What is VECTOR CALCULUS?? **Full Course Introduction**7m
- Curves, Parameterizations, and the Arclength Parameterization10m
- What is a LINE INTEGRAL? // Big Idea, Derivation & Formula14m
- Line Integrals: Full Example6m
- Line Integrals in 3D // Formula & Three Applications6m
- Intro to VECTOR FIELDS // Sketching by hand & with computers12m
- The Gradient Vector Field2m
- Line Integrals of Vector Fields // Big Idea, Definition & Formula9m
- Example: Computing the Line Integral of a Vector Field (i.e. Work Done)7m
- Line Integrals with respect to x or y // Vector Calculus11m
Lessons 11 to 2010 lessons · 1h 28m
- Flow Integrals and Circulation // Big Idea, Formula & Examples // Vector Calculus9m
- Flux Integrals // Big Idea, Formula & Examples // Vector Calculus12m
- Conservative Vector Fields // Vector Calculus6m
- The Fundamental Theorem of Line Integrals // Big Idea & Proof // Vector Calculus7m
- How to Test if a Vector Field is Conservative // Vector Calculus6m
- Finding the scalar potential function for a conservative vector field // Vector Calculus12m
- Curl or Circulation Density of a Vector Field // Vector Calculus10m
- Curl, Circulation, and Green's Theorem // Vector Calculus8m
- Divergence, Flux, and Green's Theorem // Vector Calculus11m
- Example: Using Green's Theorem to Compute Circulation & Flux // Vector Calculus9m
Lessons 21 to 3010 lessons · 1h 20m
- Describing Surfaces Explicitly, Implicitly & Parametrically // Vector Calculus11m
- The Surface Area formula for Parametric Surfaces // Vector Calculus9m
- Why is the surface area of a Sphere 4pi times radius squared???6m
- Computing the Surface Area of a surface parametrically // Example 1 // Vector Calculus8m
- Computing the Surface Area of a surface parametrically // Example 2 // Vector Calculus8m
- Surface Area for Implicit & Explicit Surfaces // Vector Calculus8m
- Computing the Surface Area of an Implicitly Defined Surface7m
- Surface Integrals // Formulas & Applications // Vector Calculus8m
- Orientable vs Non-Orientable Surfaces and the Mobius Strip6m
- Flux of a Vector Field Across a Surface // Vector Calculus7m
Lessons 31 to 399 lessons · 1h 16m
- Computing the Flux Across a Surface // Vector Calculus8m
- The CURL of a 3D vector field // Vector Calculus8m
- Stokes' Theorem // Geometric Intuition & Statement // Vector Calculus9m
- Stokes' Theorem Example // Verifying both Sides // Vector Calculus14m
- The Divergence Theorem // Geometric Intuition & Statement // Vector Calculus8m
- Divergence Theorem example: Flux across unit cube // Vector Calculus6m
- Divergence Theorem for regions bounded by two surfaces // Vector Calculus5m
- Deriving Gauss's Law for Electric Flux via the Divergence Theorem from Vector Calculus10m
- A unified view of Vector Calculus (Stoke's Theorem, Divergence Theorem & Green's Theorem)8m
What you need
- No prior experience: this course starts from zero.
Description
This playlist on vector calculus covers approximately six weeks of my Calculus IV course. It follows my full semester multivariable calculus course here: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd The major topics are line integrals, surface integrals, vector fields, conservative fields, Green's theorem, divergence theorem and Stokes' Theorem
Who this course is for
- Anyone starting Science from nothing.
Those two are our reading of the course's level. The description is the author's own.