Prerequisite: Math 1120 (Calculus II), Math 2240 (Linear Algebra), & Math 2110 (Intro. to Proofs)

Texts: We will be relying on a linear algebra text at the beginning of the semester and then will start using a differential equations text as a supplement during the latter portion of the class.

• Linear Algebra (4^th Edition) by S. Friedberg, A. Insel, & L. Spence ISBN 13: 9780130084514 AddAll.com or Bookfinder.com (Used/International Edition approx. $15-$20)
  
• Elementary differential equations with linear algebra (3^rd Edition) by Albert L Rabenstein ISBN 13: 9780125739450 AddAll.com or Bookfinder.com (Used approx. $9)
  

• Abstract Linear Algebra by Morton L. Curtis ISBN 13: 9780387972633 AddAll.com or Bookfinder.com (Used approx. $10)
  

Web Page: My webpage is located here: https://BillCookMath.com and
our course webpage is located here: https://BillCookMath.com/courses/math4010-spring2022.

Meeting times: Monday, Wednesday, and Friday 11:00am – 11:50am in Walker Hall room 304 (unless otherwise announced).

Final Exam: Our final exam will be held on Friday, April 29^th, 11:00am – 1:30pm.
Tentatively, this is to be held in our regular classroom (WA 304).

Lecturer:

Name:	Dr. William (Bill) Cook
Office:	Walker Hall 347 or via Zoom [Please call my office for the Zoom password and to make sure I have joined the meeting.]
Office hours:	Monday, Wednesday, & Friday before and after class In particular, Monday, Wednesday, & Friday at 8:30am to 9:00am, 10:00am to 11:00am, & 12:00pm to 12:30pm Other times by appointment.
Phone:	(828) 262-2367
Email:	cookwj@appstate.edu
Webpage:	https://BillCookMath.com

Technology: You are welcome to use any technology at your disposal to complete out of class assignments. We will use Maple and/or other mathematical software such as SAGE to help with some big calculations. Maple should be available on all campus lab computers. I will post (in AsULearn) information about obtaining a free student copy. Computing technology such as cell phones and calculators are not allowed on in class exams or quizzes unless otherwise specified.

Course Topics: I plan to spend approximately half of the semester exploring topics from "abstract" linear algebra. Then the remainder of the semester will be devoted to using algebraic methods to solve differential equations and systems of differential equations.

Although I will assume familiarity with introductory linear algebra, I will not assume any background from differential equations. Some topics may intersect with group or ring theory (modern algebra), but any background will be covered as needed.

Possible topics (in more or less detail according to interest):

• Linear Algebra: vector spaces over different fields, infinite dimensional spaces, dual spaces, quotient spaces, Jordan canonical form, the matrix exponential, tensor products, and exterior algebras.
• Differential Equations: solving DEs by factoring linear operators, the methods of undetermined coefficients, variation of parameters, and a partial fraction decomposition technique for solving non-homogeneous linear DEs, using the matrix exponential and variation of parameters for solving systems of DEs, symmetry methods for solving DEs (finding integrating factors and very basic, very applied Lie theory), and (if there is interest), some differential algebra which would including a touch of differential Galois theory which attempts to answer the question, "When can we solve a differential equation?"

Your term grade will be based on the results of your tests and final presentation as well as your scores on quizzes and homework and class participation. Here is more information about the individual components of your grade:

Tests: There will be two tests. Each test will make up 20% of your term grade. I have not attempted to fix dates for these tests presently. The actual dates will be negotiated/announced in class. Each test will likely have a take home portion.

Homework & Quizzes: I will regularly assign sets of homework problems to be turned in for a grade. We may have a few quizzes (if needed).

I encourage you to work on your homework with your classmates. However, you must write up your solutions yourself. Do NOT copy your collaborators work and turn it in as your own. The homeworks and quizzes will make up 40% of your term grade.

Participation & Final Presentations: Instead of having a final exam we will have final presentations. Everyone will pick a topic to present (this topic will have to be approved and should be something related to what we covered in class). I will require that you create a nice handout to go with your presentation. We will have presentations during the final exam period.

Also, I except you to come to class and participate in discussions.

Participation as well as your final presentation and handout will make up 20% of your term grade.

Here are the components of the term grade with their weights:

Component Weight Tests 20% x 2 = 40% Homework 40% Participation & Presentaion 20%

Attendance: Don't miss class. If you miss class, you are responsible for the material covered during your absence. If you miss a quiz, test/exam, or workshop, you must bring in documentation proving that your absence is excusable or otherwise receive a zero. If a make-up quiz/test/exam is granted, it must be made up before the next quiz/test/exam.

Help! If you need help, please come to my office hours. If you are in Walker Hall and my office door is open, please feel free to stop by and ask questions – even if it's not during my posted office hours.

Fine Print: Copies of the academic integrity code, disability services information, religious observance policies can be found at https://academicaffairs.appstate.edu/resources/syllabi-policy-and-statement-information.