# Introduction to Linear Algebra and Differential Equations Fall '10

Instructor:
Jeffrey Diller (click for contact info)

Lectures:
Both sections meet MWF in Hayes-Healy 129, the first from 8:30-9:20 and the second from 9:35-10:25.

Teaching Assistants:
• Katelyn Grayshan (tutorials Thursday 11-11:50 and 2-2:50, both in HH229)
• Han Liu (tutorials 12:55-1:35 in Nieuw 184 and 3:30-4:20 in HH229)

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.

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 understand the function it applies to.  In simple situations one can use the equation to determine a formula for the function. In more complicated ones, when formulas are impractical or impossible, one can still try to answer specific question, like `what happens to the function when the independent variable becomes large?  does the function also become large?  small? ' etc.

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 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. Time is short, and we won't have much time to discuss applications of the math we're learning, particularly the linear algebra.  So I would highly encourage you to look at the chapter intros and some of the 'application' sections (e.g. 1.6) in Lay's book.  One can plausibly argue that linear algebra is *the* fundamental tool in modern applications of mathematics, used to determine airline schedules, rank webpages in search engines, compress electronic data, model the flow of oil underground, and so on and on and on.

How you will be evaluated:

• Homework: 5% of your final grade, collected each Friday except during exam weeks.  If I get ambitious, I'll also give two or three 'project' assignments separate from textbook homework.  Should that happen, I might weight homework higher (e.g. 10%) in your final grade, borrowing from the weight I assign to the final.

• Quizzes: 5% of your final grade.  These will be short straightforward checks to make sure you're staying engaged and up to date.  They'll take place each week at the beginning of tutorial, excepting exam weeks.
• Midterm exams: there will be three of these, each worth 20% of your final grade and each lasting from 8-9:15 AM:
• Tuesday, September 21 in 101 Jordan;
• Tuesday, October 26 in 101 Jordan;
• Tuesday, November 16 in 101 Jordan.
• Final exam:  Friday, December 17 from 1:45-3:45 PM in Hesburgh 107. The final will be comprehensive and count for 30% of your grade.