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Calculus 3D
United States
เข้าร่วมเมื่อ 7 ก.พ. 2015
I've been teaching college-level math for over 25 years. In 2015 I started recording screencasts of my lectures. The result is Calculus 3D, a channel with videos from a traditional Calculus 3 course. I hope you find them helpful as you advance in your study of mathematics.
Currently, I'm working on splitting up the longer full-lecture videos into shorter ones with more graphics and explanatory callouts. These shorter videos are designated by chapter/section/video number. So, "Video 16.2.1" is short for chapter 16/section 2/video number 1. The chapter and section numbering more-or-less follows Stewart's text. The homework playlists have video solutions to the problems linked to below.
Currently, I'm working on splitting up the longer full-lecture videos into shorter ones with more graphics and explanatory callouts. These shorter videos are designated by chapter/section/video number. So, "Video 16.2.1" is short for chapter 16/section 2/video number 1. The chapter and section numbering more-or-less follows Stewart's text. The homework playlists have video solutions to the problems linked to below.
Video 16.8.4: More Notes on Stokes' Theorem
Notes 3-5. See th-cam.com/video/w9evXX4K4-g/w-d-xo.html for Notes 1 and 2.
3. Circulation around boundary curve C is equal to the total curling of F around points on S.
4. Curl F = 0 ( the 0 vector) means F is irrotational.
5. For given boundary curve, C, the flux integral of the curl F is independent of surface, S.
Thumbnail is from mathbox.org/math/fieldlines.
3. Circulation around boundary curve C is equal to the total curling of F around points on S.
4. Curl F = 0 ( the 0 vector) means F is irrotational.
5. For given boundary curve, C, the flux integral of the curl F is independent of surface, S.
Thumbnail is from mathbox.org/math/fieldlines.
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Video 16.5 Addendum: A Point-Wise Interpretation of Curl
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-Green's Theorem gives us a way to interpret curl at a point. -A line integral over a closed curve can represent how much a vector field is circulatiing around that closed curve.
Video 16.8.3: Notes on Stokes'
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Note that the rim curve, C, does not need to lie in a single plane, even though I often draw it that way. This video covers: 1. The relationship between Green's Theorem and Stokes' Theorem 2. Using Stokes' Theorem to develop an interpretation of the Curl of a vector field at a point. Intro is from mathbox.org/math/fieldlines.
Video 16.8.2: Using Stokes' Theorem to Evaluate a Line Integral
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Video 16.8.2: Using Stokes' Theorem to Evaluate a Line Integral
Video 16.8.1: Introduction to Stokes' Theorem
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Stokes' Theorem and how it relates to Green's Theorem. The intro animation was plotted with the awesome grapher from www.math3d.org/.
16.6.3B: Parameterizing the Lower Half of an Ellipsoid
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16.6.3B: Parameterizing the Lower Half of an Ellipsoid
Video 16.4.6: Conservative Vector Fields, Path Independence, and Line Integrals on Closed Curves
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Video 16.4.6: Conservative Vector Fields, Path Independence, and Line Integrals on Closed Curves
Video 16.4.7: Green's Theorem Ties Up a Loose End
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Green's Theorem helps us understand where the conservative vector field test comes from (for a planar field).
Video 16.4.5: Using a Line Integral of Compute the Area of a Region
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Video 16.4.5: Using a Line Integral of Compute the Area of a Region
Video 16.4.4: Green's Theorem Extended to a Region with a Hole
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Video 16.4.4: Green's Theorem Extended to a Region with a Hole
Video 16.4.3: Green's Theorem on a Heart-Shaped Region
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Video 16.4.3: Green's Theorem on a Heart-Shaped Region
Video 16.4.2: Partial Proof of Green's Theorem
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Video 16.4.2: Partial Proof of Green's Theorem
Video 16.4.1: Green's Theorem with a Quick Example
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Video 16.4.1: Green's Theorem with a Quick Example
Video 16.1.1: Introduction to Vector Fields (Redux)
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Special thanks to TuxRiders for providing data and the following tutorial on Paraview: th-cam.com/video/CByh84hOslU/w-d-xo.htmlsi=f44gjGr1csTfOJ7I.
Video 16.3.4: Recovering a Potential Function from F(x,y)
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Example of finding a potential function given what turns out to be a conservative vector field.
Video 16.3.3: Showing a 2D Vector Field is Conservative
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Video 16.3.3: Showing a 2D Vector Field is Conservative
Video 16.3.2: Evaluating a Line Integral using the Fundamental Theorem of Line Integrals
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Video 16.3.2: Evaluating a Line Integral using the Fundamental Theorem of Line Integrals
Video 16.3.1: The Fundamental Theorem of Line Integrals
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Video 16.3.1: The Fundamental Theorem of Line Integrals
Video 16.2.8: The Sign of a Line Integral Over a Vector Field From Its Graph
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Video 16.2.8: The Sign of a Line Integral Over a Vector Field From Its Graph
Video 16.2.7: Evaluating a Line Integral in Differential Form
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Video 16.2.7: Evaluating a Line Integral in Differential Form
Video 16.2.6: Differential Form of a Line Integral
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Video 16.2.6: Differential Form of a Line Integral
Video 16.2.5: Computing a Line Integral W.R.T. a Vector Field
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Video 16.2.5: Computing a Line Integral W.R.T. a Vector Field
Video 16.2.4: Line Integrals W.R.T. a Vector Field
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Video 16.2.4: Line Integrals W.R.T. a Vector Field
Video 16.2.2: Arc Length Line Integrals Part 2
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Video 16.2.2: Arc Length Line Integrals Part 2
Video 16.2.1:Introduction to Line Integrals w.r.t. Arc Length
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Video 16.2.1:Introduction to Line Integrals w.r.t. Arc Length
Video 16.2.3: Example of Arc Length Integration
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Video 16.2.3: Example of Arc Length Integration
16.8.2b: Evaluate a Line Integral Using Stoke's Theorem
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16.8.2b: Evaluate a Line Integral Using Stoke's Theorem
16.8.2c: Evaluate a Line Integral Using Stoke's Theorem
มุมมอง 651ปีที่แล้ว
16.8.2c: Evaluate a Line Integral Using Stoke's Theorem