Welcome to spring, block 8, and Vector Analysis! In this course we will discuss in some detail the bread and butter vector operations you will use over and over in any course that talks about fields--gravitational, electromagnetic, strain, resistivity, etc. In addition, we will spend some time on Fourier Analysis, which shows how to write almost any periodic function as the sum of sines and cosines or complex exponentials. Fourier Analysis is enormously useful in electronics (AC circuits) and digital signal analysis, and the Fourier Transform is the core of the indeterminancy principle in quantum mechanics. By the end of the course you should be able to use the divergence, curl, and gradient operators in cartesian, cylindrical and spherical polar coordinates, and to use the theorems of Gauss and Stokes. You should also know the conditions under which you can expand periodic functions as an infinite series of sinusoidal functions, and have derived the expansion coefficients for many such functions. You will also work out the properties of the Fourier Transform and work with some of its applications.

We will spend the second week of the block at Baca, where email, the internet, and other vital distractions of life can be found only in Crestone, a short walk away. The CC Lodge is pictured below.

Instructor
Dick Hilt
e-mail: dhilt@coloradocollege.edu
Phone: (719) 389-6581 (office), (719) 447-7966 (cell)

Textbooks
The first required textbook for this course is div, grad, curl and all that, 4 edition, by H. M. Schey. It's readable, with lots of applications, and thin! We should whip through it in a couple of weeks, leaving time for a week and a half of Fourier Series and Integral Transforms, by Allan Pinkus and Samy Zafrany.

Homework
Tentative reading and homework assignments are listed on the course schedule. We will spend most of each class discussing the text and problems assigned the previous day. Read the text with a pencil and paper handy to fill in steps in derivations and jot down questions to ask in class. Working problems is essential to understanding the material. I encourage you to work together on the homework. However, each of you should write up your own version of the problems. In physics, you learn by doing.

Problems are due every day. You will present problems at the board (which will count toward your class participation), and we will discuss them to make sure everyone understands them completely. On Friday morning, one randomly chosen assignment from the week will be turned in, and I will grade it that day. Exams are to be entirely your own work, and I will ask you to sign the honor pledge on each exam.

Quizzes and Exams
We will have two exams. See the schedule for the dates. The first exam will cover Schey; the second will cover everything else.

Grades

Class Participation	20%
Weekly Problems	20%
First Exam	30%
Second Exam	30%

(last modified 16:41, April 17, 2008)