Course Description:


Math 54 is a one term course in second-year Calculus at Berkeley. It's a bit of two different subjects glued together: Linear Algebra and Differential Equations. Each subject is really interesting in its own right---I'll attempt to do just enough of each to convince you that this is true, and to also get you to wonder about taking more.

We start out in the course by studying some fundamental facts about matrices; in their most accessible form, a matrix is a short-hand notation for a system of linear equations. We will discuss how to solve these systems, what it means when you can, and special solutions of those systems. We will do this by introducing the notation of Linear Algebra, and that will lead us into new topics about vector spaces, linear transformations, eigenvalues, etc. It's a remarkably appealing subject, and probably, for many of you, your first trip into "abstraction."

We then take a turn toward the "very" applied, and develop some machinery to solve differential equations. This is truly useful--- everything from analyze circuits to population dynamics to the spread of infectious diseases. We end with Fourier Series; at its most fundamental level, Fourier Series explain how one can get a note out of guitar, piano, violin, you name it.

Honestly, this course is *great fun*. Yeah, I know you are saying "sure, but he's a math professor". Well true, but take a leap of faith and believe me. You are going to find out how your CD player works, how Google works, how electronic music is made, why changing the design of the Golden Gate Bridge by just a little could really be dangerous, and why tsunamis are so powerful.


How This Course Works:
My job is to help you to figure out this subject. Your job is to ask questions if you are lost. That means you are supposed to ask questions, no matter how supposedly dumb. You can be assured that any question you think up, there are at least 20 people out there who are desperately glad that you asked.
Important Details:

1. Class starts at 11:10AM. Show up. I can be very rough on people who stumble in at 8:25.
2. Office Hours: My office is 725 Evans Hall, which is the Mathematics Building. My office hours are Tuesday and Thursday : 10:30-11:00, and 12:30-1PM. Please try to come see me during those hours. If you need to see me, but can't make those hours, come talk to me after class.
3. Grades/Exams There will be two midterms and one final, as well as tons of homework and an occasional quiz in section. The grade breakdown is: Homework/Quizzes: 10%, Each Midterm: 25%, Final: 40%
4. I am not big on incompletes. University regulations require that you have must have a compelling reason for an incomplete, plus at least a C- at the time the incomplete is granted. The C- requirement can be waived in *exceptional circumtances*, such as "Martians landed in my dorm room and I had to choose between studying math and defending Earth."