Math 20580

Introduction to Linear Algebra and Differential Equations
Fall '10

Homework Assignments


Contact Information

(office, phone, email)

Office Hours


Jeffrey Diller

126 Hayes-Healy



Tues 6-8 PM

MWF 11:45-12:35

Hayes-Healy 127

Michael Gekhtman

128 Hayes-Healy



Mon 4-6 PM

MWF 3-3:50

Hayes-Healy 117

Brian Smyth

110 Hayes-Healy



Mon 3-5 PM

MWF 10:40-11:30

DeBartolo 140

Zhiliang Xu

226 Hayes-Healy



Mon, Wed 2-3 PM

MWF 8:30-9:20

Hayes-Healy 129

Teaching Assistant

Contact Information

Office Hours


Tiancong Chen

215 Hayes-Healy


Tues 7-9 PM

2-2:50 HH 129

3:30-4:20 HH 117

Xiaoyang He

215 Hayes-Healy


Tue 3-4 PM

Wed 3-4 PM

12:55-1:45 HH 129

3:30-4:20 Earth Sciences 101

Gun Sunyeekhan

253B Hayes-Healy


11-11:50 HH231

2-2:50 Earth Sciences 101

Textbooks: Linear algebra and its applications (3rd ed) by David Lay. Elementary Differential Equations and Boundary Value Problems (9th ed) by William Boyce and Richard DiPrima. Incidentally, you should be able to get by fairly well with the 8th ed of Boyce and DiPrima, provided you have a look at the 9th edition to see what's changed (e.g. homework problem #'s, and occasionally a section #).

What is linear algebra? Functions and equations that arise in the `real world' often involve many tens or hundreds or thousands of variables, and one can only deal with such things by being much more organized than one typically is when treating equations and functions of a single variable. Linear algebra is essentially a `language for accounting' that's been developed just for this purpose. We will learn methods for solving equations and ways of understanding their solutions that are very effective when the equations are what is called (of course) `linear'. In a kind of analogical way, we will even learn to `visualize' many-dimensional situations.

What are differential equations? Many functions that come up in applications do so only in an indirect fashion. That is, rather than being told what the formula is for a function, one is given some (differential) equation relating the function to one or more of it's derivatives. For instance, a bank does not advertise a formula for the amount of money in a hypothetical account. Instead it advertises an interest rate, which is a way of saying how the amount of money in an account will change with time. The main goal in studying a differential equation is to glean information about the function it applies to. In simple situations one can actually use the equation to determine a formula for the function. In more complicated ones, one does not find a formula for the function but rather tries to answer a specific question about it, like `What happens to the function when the independent variable becomes large?'

What we'll cover: we'll spend roughly 2/3 of the semester on linear algebra, covering chapters 1 through 6 in Lay's book. The limited time frame will likely force us to stick to mathematics proper and prevent us from looking at sections dealing with applications of linear algebra. Nevertheless, when you find yourself wondering to yourself what all this is good for, I'd highly encourage you to look at some of the application sections. Linear algebra shows up nearly everywhere that math is used to model real world situations. The remaining 1/3 of the semester (and the entirety of math 325, should you take it) will be spent on differential equations. In this semester, we'll cover chapters 1 through 3 of Boyce and DiPrima.

How you will be evaluated:

  1. Thursday, February 12; (last year's version)

  2. Tuesday, March 17; (last year's version)

  3. Thursday, April 16. (last year's version)

    Each midterm will count for 20% of your grade. Diller's section takes all midterms in (tentatively) Jordan 101.