### Calculus: Surface integrals and Stokes' theorem

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Parameterizing a surface. Surface integrals. Stokes' theorem.
Introduction to Parametrizing a Surface with Two Parameters. Determining a Position Vector-Valued Function for a Parametrization of Two Parameters. Partial Derivatives of Vector-Valued Functions. Introduction to the Surface Integral. Example of calculating a surface integral part 1. Example of calculating a surface integral part 2. Example of calculating a surface integral part 3. Surface Integral Example Part 1 - Parameterizing the Unit Sphere. Surface Integral Example Part 2 - Calculating the Surface Differential. Surface Integral Example Part 3 - The Home Stretch. Surface Integral Ex2 part 1 - Parameterizing the Surface. Surface Integral Ex2 part 2 - Evaluating Integral. Surface Integral Ex3 part 1 - Parameterizing the Outside Surface. Surface Integral Ex3 part 2 - Evaluating the Outside Surface. Surface Integral Ex3 part 3 - Top surface. Surface Integral Ex3 part 4 - Home Stretch. Conceptual Understanding of Flux in Three Dimensions. Constructing a unit normal vector to a surface. Vector representation of a Surface Integral. Stokes' Theorem Intuition. Green's and Stokes' Theorem Relationship. Orienting Boundary with Surface. Orientation and Stokes. Conditions for Stokes Theorem. Stokes Example Part 1. Part 2 Parameterizing the Surface. Stokes Example Part 3 - Surface to Double Integral. Stokes Example Part 4 - Curl and Final Answer. Evaluating Line Integral Directly - Part 1. Evaluating Line Integral Directly - Part 2. Stokes' Theorem Proof Part 1. Stokes' Theorem Proof Part 2. Stokes' Theorem Proof Part 3. Stokes' Theorem Proof Part 4. Stokes' Theorem Proof Part 5. Stokes' Theorem Proof Part 6. Stokes' Theorem Proof Part 7. Introduction to Parametrizing a Surface with Two Parameters. Determining a Position Vector-Valued Function for a Parametrization of Two Parameters. Partial Derivatives of Vector-Valued Functions. Introduction to the Surface Integral. Example of calculating a surface integral part 1. Example of calculating a surface integral part 2. Example of calculating a surface integral part 3. Surface Integral Example Part 1 - Parameterizing the Unit Sphere. Surface Integral Example Part 2 - Calculating the Surface Differential. Surface Integral Example Part 3 - The Home Stretch. Surface Integral Ex2 part 1 - Parameterizing the Surface. Surface Integral Ex2 part 2 - Evaluating Integral. Surface Integral Ex3 part 1 - Parameterizing the Outside Surface. Surface Integral Ex3 part 2 - Evaluating the Outside Surface. Surface Integral Ex3 part 3 - Top surface. Surface Integral Ex3 part 4 - Home Stretch. Conceptual Understanding of Flux in Three Dimensions. Constructing a unit normal vector to a surface. Vector representation of a Surface Integral. Stokes' Theorem Intuition. Green's and Stokes' Theorem Relationship. Orienting Boundary with Surface. Orientation and Stokes. Conditions for Stokes Theorem. Stokes Example Part 1. Part 2 Parameterizing the Surface. Stokes Example Part 3 - Surface to Double Integral. Stokes Example Part 4 - Curl and Final Answer. Evaluating Line Integral Directly - Part 1. Evaluating Line Integral Directly - Part 2. Stokes' Theorem Proof Part 1. Stokes' Theorem Proof Part 2. Stokes' Theorem Proof Part 3. Stokes' Theorem Proof Part 4. Stokes' Theorem Proof Part 5. Stokes' Theorem Proof Part 6. Stokes' Theorem Proof Part 7.

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