# Lecture 32: Stokes' theorem continued and exam review

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Lesson Summary:

In this wrap-up lecture on Stokes' Theorem, the instructor reviews the past 7 weeks and provides an exam review. Stokes' Theorem states that a line integral along a closed curve in space bounding some surface S can be computed as a surface integral for flux of a different vector field, namely curl f dot NDS, given compatible orientations. The lecture also covers the concept of simply connected regions and how it applies to path independence and gradient fields. Additionally, examples of non-orientable surfaces and surface independence in Stokes' Theorem are discussed.

Lesson Description:

Learn more about Stokes' Theorem in a wrap-up lecture of the past 7 weeks as we review for the upcoming exam.

Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (Accessed March 21, 2009). License: Creative Commons Attribution-Noncommercial-Share Alike.

Questions answered by this video:
• What is Stokes' Theorem?
• How is Stokes' Theorem related to path independence?
• What is the proof that if F is defined in a simply-connected region and curl F = 0, then F is a gradient and the line integral of F is path-independent?
• What is orientability?
• Why does Stokes' Theorem have surface independence?
• Where can I find review problems for Calculus 3 topics?
• #### Staff Review

• Currently 4.0/5 Stars.
This lesson wraps up an explanation of Stokesâ Theorem that was started last lecture. A proof of a theorem derived from Stokesâ Theorem is explained and proved. Orientability and some more ideas about topology are discussed in the beginning of this lesson. The last twenty minutes are devoted to reviewing topics from the last 7 weeks, including three-dimensional topics, triple integrals, spherical and cylindrical coordinates, and other topics.