Lecture 24: Simply connected regions and exam review

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Taught by OCW
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Lesson Summary:

In this lesson, the instructor wraps up the topic of simply connected regions and then moves on to a review for the third exam. They go over the validity of the gradient sphere and how the vector field needs to be defined everywhere inside a region for it to work. The instructor also discusses the extended version of the Green's sphere, which can be used for regions with holes. They then introduce the concept of simply connected regions and how they relate to topology. The main focus of the exam review is on setting up and evaluating double integrals and line integrals. The instructor uses an example to illustrate how to exchange the order of integration and the importance of drawing a picture of the region.

Lesson Description:

A wrap-up lesson on simply connected regions and review for the third 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.

Additional Resources:
Questions answered by this video:
  • What is a simply connected region?
  • What does it mean for a region in the plane to be simply connected?
  • How do you set up and evaluate double integrals and line integrals?
  • Where can I find review problems for Calculus 3?
  • What is a list of important topics in Calculus 3?
  • Staff Review

    • Currently 4.0/5 Stars.
    This video wraps up this part of the Calculus 3 semester by clarifying some ideas about curl, vector fields, line integrals, Green’s Theorem, and gradient fields. Simply connected regions as an introduction to topology are discussed. Double integrals in rectangular and polar coordinates are discussed along with moment of inertia, easy trigonometric integrals, u substitution, and other topics covered in the past 7 weeks.