Math 213 Bard College

Linear Algebra
with ODE's

Course:  Math 213, Spring 2017

Time & Place:

Instructor:  Jim Belk (belk@bard.edu)

Course Tutors:

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

Announcements

Office Hours

Here are my office hours for today (Monday):

Final Exam Times & Rooms

The final exam will be from 10 am to 6 pm tomorrow (Tuesday) in the following rooms: Any students working on the exam at 11:45 am will need to move from RKC 200 to RKC 102.

Final Exam Tuesday

The final exam is tomorrow (Tuesday), May 23rd. Here is the formula sheet for the final: The final will only cover the material from the second half of the semester. Here's roughly what to expect: Of course, many of these topics also require knowledge of vectors, dot product, cross product, determinants, and so forth. Here are a few more notes on the final:

Quiz and Midterm Solutions

Here are the solutions to all of the quizzes on vectors: Also, here are the solutions to the midterm exam:

All Homework and Notes for the Final

Here are all of the homework assignments and notes that may be relevant to the final: Note that Homeworks 5 and 6 were from before the midterm, but I'm including them since they were on vectors.

Notes and Homework on Matrices

Here are some notes on row reduction: There are problems at the end of each set of notes. Here as an HTML version of these problems:

Notes and Homework on Row Reduction

Here are some notes on row reduction: There are problems at the end of each set of notes. Here as an HTML version of these problems:

Notes and Homework on Subspaces

Here are some notes on subspaces and linear dependence: There are problems at the end of each set of notes. Here as an HTML version of these problems:

No Quiz Tuesday

There will be no quiz next Tuesday, May 9th. We lost a few days earlier in the semester due to snow, so I want to make sure we have enough class time to cover the remaining material. Notes and homework on the recent material will be posted soon.

Quiz 7 Tuesday

The seventh quiz will be this Tuesday, April 25th. The quiz will cover all of the material on Homework 8 and Homework 9 below. This quiz will be slightly longer than usual and will be worth 50% more than a typical quiz.

Homework 9

Here are the homework problems for this week:

Notes

Here are some notes for the material this week:

Homework 8

Here are the homework problems for this week:

Notes

Here are some notes for the material this week:

No Quiz Tuesday

We will not be having a quiz next Tuesday. The next quiz will be the following Tuesday, April 25th. There will still be notes and homework for this week, which will be posted soon.

Homework 7

Here are the homework problems for this week: Note that there are three pages of problems.

Quiz 6

The sixth quiz will be this Tuesday, April 11th. The quiz will cover all of the material we discussed this week, including using dot product to find components, determinants, and cross products. Because we covered more than the usual amount of material this week, the quiz will be slightly longer than usual and will be worth 50% more than a typical quiz.

Notes

Here the notes on the material we covered this week:

Formula Sheet

The following sheet of formulas will be available during the exam.

Midterm Exam

The midterm exam is this Friday, 10 am – 6 pm in the 3rd floor of Albee. Remember:

Quiz Solutions

Here are the solutions to the first four quizzes:

Midterm Review Questions

Here are some review questions for the midterm. These cover the material on quizzes 1 through 5, but not the new material.

Notes and Practice Problems

Here are some notes on the new material that will be covered on the midterm: Here is an HTML version of the associated practice problems:

Office Hours This Week

I will be having extra office hours on Wednesday on Thursday night this week:

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: 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: 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.