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