Calculus IV: Vector Calculus (Line Integrals, Surface Integrals, Vector Fields, Greens' Thm, Divergence Thm, Stokes Thm, etc) **Full Course**
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This course includes
- 5.3 hours of video
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Course content
1 modules • 39 lessons • 5.3 hours of video
Calculus IV: Vector Calculus (Line Integrals, Surface Integrals, Vector Fields, Greens' Thm, Divergence Thm, Stokes Thm, etc) **Full Course**
39 lessons
• 5.3 hours
Calculus IV: Vector Calculus (Line Integrals, Surface Integrals, Vector Fields, Greens' Thm, Divergence Thm, Stokes Thm, etc) **Full Course**
39 lessons
• 5.3 hours
- What is VECTOR CALCULUS?? **Full Course Introduction** 06:45
- Curves, Parameterizations, and the Arclength Parameterization 10:04
- What is a LINE INTEGRAL? // Big Idea, Derivation & Formula 14:02
- Line Integrals: Full Example 05:40
- Line Integrals in 3D // Formula & Three Applications 05:49
- Intro to VECTOR FIELDS // Sketching by hand & with computers 12:09
- The Gradient Vector Field 02:18
- Line Integrals of Vector Fields // Big Idea, Definition & Formula 08:40
- Example: Computing the Line Integral of a Vector Field (i.e. Work Done) 06:55
- Line Integrals with respect to x or y // Vector Calculus 11:28
- Flow Integrals and Circulation // Big Idea, Formula & Examples // Vector Calculus 08:43
- Flux Integrals // Big Idea, Formula & Examples // Vector Calculus 11:36
- Conservative Vector Fields // Vector Calculus 06:17
- The Fundamental Theorem of Line Integrals // Big Idea & Proof // Vector Calculus 06:38
- How to Test if a Vector Field is Conservative // Vector Calculus 05:30
- Finding the scalar potential function for a conservative vector field // Vector Calculus 12:06
- Curl or Circulation Density of a Vector Field // Vector Calculus 10:28
- Curl, Circulation, and Green's Theorem // Vector Calculus 07:55
- Divergence, Flux, and Green's Theorem // Vector Calculus 10:33
- Example: Using Green's Theorem to Compute Circulation & Flux // Vector Calculus 08:36
- Describing Surfaces Explicitly, Implicitly & Parametrically // Vector Calculus 11:05
- The Surface Area formula for Parametric Surfaces // Vector Calculus 09:26
- Why is the surface area of a Sphere 4pi times radius squared??? 06:28
- Computing the Surface Area of a surface parametrically // Example 1 // Vector Calculus 08:22
- Computing the Surface Area of a surface parametrically // Example 2 // Vector Calculus 08:07
- Surface Area for Implicit & Explicit Surfaces // Vector Calculus 08:13
- Computing the Surface Area of an Implicitly Defined Surface 07:13
- Surface Integrals // Formulas & Applications // Vector Calculus 08:18
- Orientable vs Non-Orientable Surfaces and the Mobius Strip 06:22
- Flux of a Vector Field Across a Surface // Vector Calculus 06:33
- Computing the Flux Across a Surface // Vector Calculus 08:09
- The CURL of a 3D vector field // Vector Calculus 08:26
- Stokes' Theorem // Geometric Intuition & Statement // Vector Calculus 08:32
- Stokes' Theorem Example // Verifying both Sides // Vector Calculus 13:43
- The Divergence Theorem // Geometric Intuition & Statement // Vector Calculus 07:35
- Divergence Theorem example: Flux across unit cube // Vector Calculus 05:38
- Divergence Theorem for regions bounded by two surfaces // Vector Calculus 05:06
- Deriving Gauss's Law for Electric Flux via the Divergence Theorem from Vector Calculus 10:10
- A unified view of Vector Calculus (Stoke's Theorem, Divergence Theorem & Green's Theorem) 08:18
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