Math 309 B/C: Linear Analysis

Course Description

This class will focus on the tools and techniques used to study differential equations which arise in the study of many interacting objects. The textbook is Differential Equations with BVP by Boyce. We will apply methods learned in 307 and 308 to the solution and qualitative study of linear systems of ordinary differential equations (occupying us for the first 5 weeks), and to the analysis of classical partial differential equations (occupying us for the second 5 weeks). In the case of partial differential equations, separation of variables is used to obtain boundary value problems which are then solved and are used to generate the Fourier series solutions of the original partial differential equation.

Office Hours

Office Hours will be held weekly on Wednesdays and Thursdays from 3:00 to 4:20 in my office, Padelford (PDL) C–342. Depending on attendance, the times and location may change, at which time I will update this webpage to reflect the new information. Feel free to also ask questions via email: .

Midterm and Final

In this course there will be one midterm, and one final. The midterm will be held on Friday, February 15th in class and will cover the material from the first 5 weeks of the course. The final exam will be held on Thursday, March 21, from 8:30 to 10:20 for Math 309 B, and Monday, March 18, from 2:30 to 4:20 for Math 309 C in their respective classrooms. The final exam will be cumulative, but strongly weighted towards the material in the last 5 weeks of the course: approximately 1/8 from the first 5 weeks, and 7/8 from the second. A single page note sheet will be allowed for both exams, as well as a non-graphing calculator (although the exam will be designed to not require the use of the calculator). The note sheet must be hand-written, but you may use both sides of a standard sized piece of paper.

I’ve uploaded the Midterm Review Sheet here to help you as you study. Note that there are many more problems than there will be on the actual exam so that you have many to practice on. Additionally, now that the final is near, I’ve uploaded the Final Review Sheet to help you prepare. There are again many more problems than you would see on the exam, and several of them this time are a fair bit trickier than you would expect to see on the exam. Additonally, since it has been requested a couple of times, I’ve posted an answer key to the midterm.

Homework

The homework will be, in general, assigned after each class, collected on Fridays by the end of class, and returned the following Friday. Problems will be mostly drawn from the textbook. Due to the large class size, only a small subset of the problems from each week will be graded, but all will be checked to be present. Additionally, with so many students, stapling (or paper-clipping) is required to keep everything organized, so a two point penalty will be given for not stapling.

• Homework 1 (Due January 11th):
  • Lecture 1 Related Reading Section 7.1 Problems 7.1 - 3, 4, 5, 7, 10
  • Lecture 2 Related Reading Section 7.1, 7.2 Problems 7.1 - 15, 16; 7.2 - 4, 6, 7, 12
  • For the first week’s assignment, I’ll type the problems here.
• Homework 2 (Due January 18th):
  • Lecture 3 Related Reading 7.2, beginning 7.4 Problems 7.2 - 8, 9, 21, 23, 25
  • Lecture 4 Related Reading 7.3 Problems 7.3 - 1, 2, 6, 8
  • Lecture 5 Related Reading 7.3 Problems 7.3 - 12, 13, 14, 15
  • Since the book is still hard to come by, I’ll again type the problems.
• Homework 3 (Due January 30th):
  • Lecture 6 Related Reading 7.3, 7.4 Problems 7.3 - 16, 22, 32
  • Lecture 7 Related Reading 7.4, 7.5 Problems 7.4 - 6, 7; 7.5 - 1, 5
  • Lecture 8 Related Reading 7.5 Problems 7.5 - 9, 11, 24
  • Lecture 9 Related Reading 7.6 Problems 7.6 - 3, 10, 13, 28
• Homework 4 (Due February 8th):
  • Lecture 10 Related Reading 7.8 Problems 7.8 - 3, 6, 10
  • Lecture 11 Related Reading 9.1, 7.7 Problems 9.1 - 7 (without part (d)); 7.7 - 6, 12
  • Lecture 12 Related Reading 7.9 Problems 7.9 - 3, 7
  • Lecture 13 Related Reading 7.9 Problems 7.9 - 6, 12
• Homework 5 (Due February 22nd):
  • Lecture 14 Related Reading 9.2 Problems 9.2 - 27
  • Lecture 15 Related Reading 9.2, a tiny bit 9.3, a tiny bit 9.5 Problems 9.2 - 8, 24; 9.3 - 5
  • I’ve done part (b) of 8 for you, so it need not be included. This links also show you how to get phase portraits out of Wolfram|Alpha is you ever want to check things are correct. You can also use it to do problem 24, part (b), by using the command “contour plot…”. The study of non-linear things, throughout all levels of mathematics, is very computer heavy!
  • Lecture 16 Related Reading 10.1 Problems 10.1 - 3, 8
  • Lecture 17 Related Reading 10.1,10.2 Problems 10.1 - 16; 10.2 - 4, 8
• Homework 6 (Due March 1st):
  • Lecture 18 Related Reading 10.2 Problems 10.2 - 13, 15, 16
  • Lecture 19 Related Reading 10.3, 10.4 Problems 10.3 - 2; 10.4 - 5, 6, 16, 35
  • Lecture 20 Related Reading 10.5 Problems 10.5 - 1, 3, 5
• Homework 7 (Due March 8th):
  • Lecture 21 Related Reading 10.5, 10.6 Problems 10.5 - 7, 10, 22; 10.6 - 9(a)
  • Lecture 23 Related Reading 10.6 Problems 10.6 - 12(a&b), 14(a)
  • Lecture 24 Related Reading 10.7 Problems 10.7 - 1(a)
• Homework 8 (Not collected):
  • Note: This homework will not be collected or graded, it is to give you practice on the material from the last week of class.
  • Lecture 25 Related Reading 10.7 Problems 10.7 - 5(a), 16(c&d) (recall we did (a&b) in class),
  • Lecture 26 Related Reading 10.8 Problems 10.8 - 1(a&b), 3(a&b)
  • Lecture 27 Related Reading 10.8 Problems 10.8 - 6(a&b), 8(a&b )

Final Grades

Final grades in the course will be calculated by 30% homework, 30% midterm, and 40% final exam.