Stokes’ Theorem and the Divergence Theorem

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Section Stokes’ Theorem and the Divergence Theorem

Worksheet APP-4 Reading

Objectives

Things you should understand and know:
- Explain the meaning of Stokes’ Theorem
  
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- Explain the meaning of the Divergence Theorem
  
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Things you should be able to do:
- Use Stokes’ Theorem to evaluate a line integral
  
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- Use Stokes’ Theorem to calculate a surface integral
  
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- Use Stokes’ Theorem to calculate a curl
  
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- Use the Divergence Theorem to calculate the flux of a vector field
  
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You will be assessed on the following criteria:
- Problem structure: Solution should be organized and easy to follow, with clear, complete steps that follow progressively from one to the next.
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- Stokes’ Theorem: Be able to apply Stokes’ Theorem to evaluate line integrals, surface integrals, and curls.
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- Apply Stokes’ Theorem to find a given surface integral.
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- The Divergence Theorem: Understand the Divergence Theorem and apply it to find the flux of a vector field.
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All of the readings for this course come from the OpenStax Calculus Volume 3 textbook, which is available for free online at https://openstax.org/details/books/calculus-volume-3. You can read the textbook online or download a PDF version. The textbook is also available in print from various retailers if you prefer a physical copy.

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For this lesson, you should read sections 6.7 Stokes’ Theorem and 6.8 The Divergence Theorem. You should read through the sections carefully, making sure to understand the definitions, examples, and key ideas. You should also work through the exercises at the end of each section to test your understanding and practice applying the concepts. Some of the exercises at the end of the section are assigned in the WP assignments.

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Worksheet APP-4 Videos

Stokes’ Theorem

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The Divergence Theorem

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Worksheet APP-4 Written Practice

INFORMATION ABOUT ALL WRITTEN PRACTICE (WP) ASSIGNMENTS:

All of the WP problems come from our online textbook: https://openstax.org/details/books/calculus-volume-3

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Complete solutions to all WP assignments can be found in Canvas within the section Module.

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Links to the text and PDFs of the text can be found in the Canvas module under the Reading and Information.

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THE WP ASSIGNMENTS ARE DESIGNED TO PREPARE YOU FOR THE QUIZZES AND ASSESSMENTS

Work on every problem on every assignment.

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If you get stuck or do not understand a solution, ask questions.

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For each problem, try it once or twice before looking at solutions or asking for help.

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Mark the problems you did correctly on the first try.

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Highlight problems where you got help (using solutions, videos, a tutor, etc) -These are the problem types that you will need more practice on to be ready for the assessments.

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Understand that just copying the solutions instead of working through the problems will greatly reduce your chances of success in this class.

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