# Linear Algebra

with ODE's

**Course:** Math 213, Spring 2017

**Time & Place:**

- Section A: TR 11:50 am – 1:10 pm (RKC 102)
- Section B: TR 3:10 pm – 4:30 pm (RKC 102)

**Instructor:** Jim Belk (belk@bard.edu)

**Office Hours:**

- Monday 3–4 pm (3rd floor Albee)
- Monday 7–9 pm (RKC 100)

**Course Tutors:**

**Math Study Room:** Sun–Thurs, 7–10 pm (RKC 111)

## Announcements

#### Office Hours This Week

I will

**not** be having my usual hours tonight. However, I will be having office hours on Wednesday on Thursday night this week:

- Office Hours: Wednesday 7–9 pm (RKC 100)
- Office Hours: Thursday 7–9 pm (RKC 100)

#### Quiz 5

The fifth quiz will be this

**Thursday** in class. It will cover vectors, vector components, and vector geometry.

#### Homework 5

Here are the homework problems for this week:

Note that there are three pages of problems.

#### Tutor Office Hours

The course tutors will be holding office hours at the following times this Sunday and Monday:

- Sunday 2–4 pm (3rd floor Albee)
- Monday 11:40 am–1:30 pm (3rd floor Albee)

The times are tentative, and may be changed if no students show up. So if you like the times, please make sure to attend!

#### Notes (Updated)

Here are all of the notes for this week's material:

#### Extra Office Hours

I am having extra office hours this Friday (March 10) from 3 pm to 5 pm on the 3rd floor of Albee.

#### Midterm Postponed

I have decided to postpone the midterm exam until after spring break. It will be offered all day on Friday, March 31.

#### Quiz 4

The fourth quiz will be next Tuesday in class. It will cover applications of separation of variables and integrating factors, slope fields, and Euler's method.

#### Homework 4

Here are the homework problems for this week:

Note that there are three pages of problems.

#### Notes

Here are some notes on the material from this week:

#### Quiz 3

The third quiz was on Tuesday, February 28. It covered algebraic methods of solving differential equations, including separation of variables and integrating factors.

#### Homework 3

Here are the homework problems for this week:

Note that there are three pages of problems.

#### Notes

Here are some notes for this week's material:

For convenience, here is a single PDF that combines all of these notes together:

There are problems at the end of each set of notes. (An HTML version of the problems will be posted soon.)

#### Quiz 2

The second quiz will be next Tuesday in class. A few notes on the quiz:

- • The quiz will cover all of the material from last week, including exponential growth, exponential decay, oscillation, and applications of these.
- • You should bring a calculator to the quiz. (A scientific calculator app on your phone should suffice, as long as it has trigonometric functions, logarithms, and so forth.)
- • The quiz will be slightly longer than usual (30 min. or so), and will count 50% more than a typical quiz.

You can study for the quiz by reading the notes and working on the homework problems (see below).

#### Homework 2

Here are the homework problems for this week:

Note that there are four pages of problems.

#### Notes (Updated)

Here are all the notes for this week's material:

For convenience, here is a single PDF that combines all of these notes together:

#### No Quiz Tuesday

Because of the cancellation last Thursday, we will not be having a quiz on Tuesday.

#### Extra Problems

By request, here are a few more problems involving guess and check:

#### Notes

Here are the notes for everything that we covered this week:

For convenience, here is a single PDF that combines all of these notes together:

#### Quiz 1

The first quiz will be next Tuesday in class. It will cover all of the material from this week, including integrable equations, finding solutions via guess and check, initial-value problems, and second-order equations. You can study for the quiz by reading the notes and working on the homework problems (see below).

#### Homework 1

Here are the homework problems for this week:

Note that there are four pages of problems.

#### Derivatives & Integrals Practice Problems

We will be using basic derivatives and integrals quite a lot in this course. To help you with reviewing these topics, here are 30 practice questions on derivatives and integrals:

If you have trouble with any of these problems, you might want to try watching some of the review videos listed below.

#### Review Videos

You might find the following videos helpful for reviewing derivatives and integrals;

#### Welcome!

Welcome to Math 213. I will be using this course webpage to post all announcements and documents, including homework assignments, homework solutions, and practice exams.

## Course Policies

#### Introduction

This course is an introduction to two fields of mathematics, linear algebra and ordinary differential equations, that are of fundamental importance throughout mathematics and its applications, and that are related by the important use of linear algebra in the study of systems of linear differential equations. Topics in linear algebra include

*n*-dimensional Euclidean space, vectors, matrices, systems of linear equations, determinants, eigenvalues, and eigenvectors; topics in ordinary differential equations include graphical methods, separable differential equations, higher order linear differential equations, systems of linear differential equations, and applications.

#### Prerequisites

Math 213 is designed for students who have completed the standard two-semester calculus sequence (Math 141–142), or who have taken a calculus course in high school. We will be making heavy use of derivatives (including the product rule and chain rule) and integrals (including substitution and integration by parts).

#### Homework and Quizzes

There will be a homework assignment every week, consisting of several practice problems. You do not need to turn in solutions to these problems, but I highly recommend that you solve all of them.

In addition to the homework, there will be a short quiz every Tuesday, with questions on the material from the previous week.

#### Exams and Grading

The grade will be based on the weekly quizzes, the midterm exam, and the final exam:

Quizzes | 40% |

Midterm Exam | 30% |

Final Exam | 30% |

The midterm exam is two hours long, and will be offered on **Friday, March 31**. The final exam is two hours long, and will be on **Tuesday, May 23** (the last day of classes).

#### Calculator

You will need a calculator for the quizzes and the exams. Any calculator is permitted, and even a scientific calculator app on a smartphone would suffice.