The Fundamental Theorem of Line Integrals // Big Idea & Proof // Vector Calculus

ক্লাস39টি ক্লাস

• ✓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)

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