### Optional Review: Topics in Vector Calculus

This unit is a review of the mathematical background necessary to solve many problems in the study of electromagnetism. You may wish to refer to it as necessary as you work through the rest of the course.

If you already feel comfortable with these topics, you may skip this unit. This unit is **not** required to complete this course.

### Vector Algebra

Read the first four sections of "Chapter 1: Vectors in Euclidian Space" on pages 1 through 30. Work through examples in the text and try the odd-numbered exercises after each section. You can find the answers on page 189.

### Multivariable Calculus

### Double and Triple Integrals in Cartesian Coordinates

Watch this lecture series. Double integrals are typically used to calculate volumes.

Read the first two sections of "Chapter 3: Multiple Integrals" on pages 101 through 109. Then, work through examples in the text and try the odd-numbered exercises 1-13 at the end of section 3.1 on page 104 and odd-numbered exercises 1-11 at the end of section 3.2 on page 109. You can find the answers on page 191.

Watch these videos, which demonstrate how triple integrals could be used to calculate mass and find the center of mass of three-dimensional objects.

Read "Section 3.3: Triple Integrals" on pages 110 through 112. Work through examples in the text and try the odd-numbered exercises 1-9 at the end of the section on page 112. You can find the answers on page 191.

### Integrals in Curvilinear Coordinates

Read "Section 1.7: Curvilinear Coordinates" on pages 47 through 50. Work through examples in the text and try the odd-numbered exercises 1-9 on page 50. You can find the answers on page 189. Some integrals are much easier to take when they are expressed in terms of coordinates that are not Cartesian – cylindrical or spherical. This reading explains how to convert curvilinear coordinates to Cartesian and vice versa.

Watch these two videos on using triple integrals in cylindrical coordinate systems.

Read pages 121 through 123 of "Section 3.5: Change of Variables". Work through examples in the text and try the exercises 1 and 3 at the end of this section. The answers are on page 191.

### Line and Surface Integrals

Watch these videos, which introduce line integrals. Line integrals are needed to calculate the physical quantities of work and circulation.

Read "Section 4.1: Line Integrals" on pages 135 through 142. Work through examples in the text and try the odd-numbered exercises 1-13 at the end of the section on page 142. The answers are on page 191.

Watch this lecture series, which introduces and gives examples of surface integrals.

Watch this lecture series, which covers surface integrals in detail.

Watch this lecture series. The flux of a field, electric or magnetic, is used to determine how strong the field is. The Gauss Law and Faraday Law of electromagnetism both involve the flux of electric and magnetic field, respectively.

Read "Section 4.4: Surface Integrals and Divergence Theorem" on pages 156 through 164. Work through examples in the text and try the odd-numbered exercises 1-9 at the end of the section. The answers are on the page 191.

### Differential Equations

Watch this lecture series, which introduces differential equations.

Watch this lecture series, which introduces separable differential equations.

Work through the six examples on the page. Be sure to solve them on your own before looking at the solutions.