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What is VECTOR CALCULUS?? **Full Course Introduction**
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Classroom Contents
Calculus IV - Vector Calculus - Line Integrals, Surface Integrals, Vector Fields, Green's Theorem, Divergence Theorem, Stokes Theorem
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- 1 What is VECTOR CALCULUS?? **Full Course Introduction**
- 2 Curves, Parameterizations, and the Arclength Parameterization
- 3 What is a LINE INTEGRAL? // Big Idea, Derivation & Formula
- 4 Line Integrals: Full Example
- 5 Line Integrals in 3D // Formula & Three Applications
- 6 Intro to VECTOR FIELDS // Sketching by hand & with computers
- 7 The Gradient Vector Field
- 8 Line Integrals of Vector Fields // Big Idea, Definition & Formula
- 9 Example: Computing the Line Integral of a Vector Field (i.e. Work Done)
- 10 Line Integrals with respect to x or y // Vector Calculus
- 11 Flow Integrals and Circulation // Big Idea, Formula & Examples // Vector Calculus
- 12 Flux Integrals // Big Idea, Formula & Examples // Vector Calculus
- 13 Conservative Vector Fields // Vector Calculus
- 14 The Fundamental Theorem of Line Integrals // Big Idea & Proof // Vector Calculus
- 15 How to Test if a Vector Field is Conservative // Vector Calculus
- 16 Finding the scalar potential function for a conservative vector field // Vector Calculus
- 17 Curl or Circulation Density of a Vector Field // Vector Calculus
- 18 Curl, Circulation, and Green's Theorem // Vector Calculus
- 19 Divergence, Flux, and Green's Theorem // Vector Calculus
- 20 Example: Using Green's Theorem to Compute Circulation & Flux // Vector Calculus
- 21 Describing Surfaces Explicitly, Implicitly & Parametrically // Vector Calculus
- 22 The Surface Area formula for Parametric Surfaces // Vector Calculus
- 23 Why is the surface area of a Sphere 4pi times radius squared???
- 24 Computing the Surface Area of a surface parametrically // Example 1 // Vector Calculus
- 25 Computing the Surface Area of a surface parametrically // Example 2 // Vector Calculus
- 26 Surface Area for Implicit & Explicit Surfaces // Vector Calculus
- 27 Computing the Surface Area of an Implicitly Defined Surface
- 28 Surface Integrals // Formulas & Applications // Vector Calculus
- 29 Orientable vs Non-Orientable Surfaces and the Mobius Strip
- 30 Flux of a Vector Field Across a Surface // Vector Calculus
- 31 Computing the Flux Across a Surface // Vector Calculus
- 32 The CURL of a 3D vector field // Vector Calculus
- 33 Stokes' Theorem // Geometric Intuition & Statement // Vector Calculus
- 34 Stokes' Theorem Example // Verifying both Sides // Vector Calculus
- 35 The Divergence Theorem // Geometric Intuition & Statement // Vector Calculus
- 36 Divergence Theorem example: Flux across unit cube // Vector Calculus
- 37 Divergence Theorem for regions bounded by two surfaces // Vector Calculus
- 38 Deriving Gauss's Law for Electric Flux via the Divergence Theorem from Vector Calculus
- 39 A unified view of Vector Calculus (Stoke's Theorem, Divergence Theorem & Green's Theorem)
