Chapter 1 · Topic 6 of 7
1.6 How to use these notes
Chapter 2 collects the mathematics: vectors, the three coordinate systems, the gradient, divergence and curl, and the integral theorems. Chapter 3 builds electrostatics on it in four steps: Coulomb's law and the electric field, Gauss's law, the electrostatic potential, and fields in material media. Each section starts with a short list of what you will learn and ends with a recap, so that you always know where you are going and what you should take away.
Throughout the text, a few kinds of boxes help you read. They look like this:
A precise definition of a new quantity.
What the previous result means, said without equations.
A short question to test your understanding before you read on. Try it first!
The answer, one click away under "Show answer", so that you can check yourself immediately.
An error that students often make, and how to avoid it.
- Step-by-step instructions for a calculation you will do many times.
- …
Harder material: a proof or a side topic. You may skip it on a first reading without losing the thread, and come back to it later.
Engineering applications of the theory appear as soon as the theory needed for them has been developed. They are marked Application.
Each section of Chapter 3 ends with problems, always in the same order:
- Problems: model problems that show the methods,
- Home exercises: exercises to try on your own after the problems,
- Further exercises: additional exercises in the same spirit,
- Worked examples: numerical problems connected with the applications.
Each statement is followed immediately by its complete solution, which begins with the strategy (which law to use and why) and ends with a check (units, limiting cases, symmetry). The best way to use them is to try each problem first and to read the solution afterwards: the methods matter more than the answers. Chapter 2 contains its worked examples within the text.