### 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 on pages 1–30. Work through the examples 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 on pages 101–109. Then, work through the examples and try the odd-numbered exercises 1–13 at the end of section 3.1 on page 104, and the 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 on pages 110–112. Work through the examples 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 on pages 47–50. Work through the examples 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 (that is, cylindrical or spherical). This section 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 121–123 of section 3.5. Work through the examples and try exercises 1 and 3 at the end of the 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 on pages 135–142. Work through the examples 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. Gauss' and Faraday's laws of electromagnetism involve the flux of electric and magnetic field, respectively.

Read section 4.4 on pages 156–164. Work through the examples and try the odd-numbered exercises 1–9 at the end of the section. The answers are on 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.