2. Math Review, Fields

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Learning Objectives

  • To be able to describe the three coordinate systems we use in describing fields: Cartesian, cylindrical, and spherical.
  • To be able to manipulate vectors and perform common operations with them: decomposition, addition, subtraction, dot products, and cross products.
  • To be able to describe the fundamental meaning of integration in one, two, and three dimensions as a summation process.
  • To be able to describe the fundamental meaning of differentiation.
  • To be able to recognize situations where Taylor series should be used, and to be able to demonstrate that you can carry out a Taylor series expansion to first order.


Course Notes

Read through the course notes. The course note files may also contain links to associated animations or interactive simulations.

Math Review (PDF)

Learning Activities

Guided Activities

Read through the class slides. They explain all of the concepts from the module.

Slides (PDF - 2.6MB)


Once you have reviewed all the materials, try the Challenge Problems.

Challenge Problems

Math Review Challenge Problems (PDF)
Solutions (PDF)

Fields Challenge Problems (PDF)
Solutions (PDF)

Related Visualizations

The visualizations linked below are related to the concepts covered in this module.


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