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

Texts: We will be following 2 linear algebra texts at the beginning of the semester and then will start using a differential equations text as a supplement to the lectures. The bookstore should have Curtis' Abstract Linear Algebra in stock. I can get you copies of the other 2 texts for $5.50 each.

• Abstract Linear Algebra by Morton L. Curtis ISBN 13: 978-0387-97263-3 AddAll.com (New from Amazon for $42)
  
• Linear Algebra (2^nd or 3^rd Edition) by S. Friedberg, A. Insel, & L. Spence ISBN 13: 978-0132-33859-2 AddAll.com (Used approx. $12)
  
• Elementary differential equations with linear algebra (2^nd or 3^rd Edition) by Albert L Rabenstein ISBN 13: 978-0125-73945-0 AddAll.com (Used approx. $9)
  

Web Page: My webpage is located here: https://mathsci.appstate.edu/~cookwj and
                    our course webpage is located here: https://mathsci.appstate.edu/~cookwj/courses/math3510-spring2013.

Meeting times: Tuesday & Thursday from 9:30am – 10:45am in Walker Hall room 308.

Final Exam: We will have final project presentations on during our final exam time on Wednesday, May 8^th from 9:00am – 11:30am.

Lecturer:

	Name:	Dr. William (Bill) Cook
	Office:	Walker Hall 347
	Office Hours:	Monday from 10:00am – 11:45am Tuesday & Thursday from 9:00 – 9:30am & 11:00am – 11:45am Wednesday from 9:00am – 11:45am Other times by appointment
	Phone:	(828) 262-2367
	Email:	cookwj@appstate.edu
	Webpage:	https://mathsci.appstate.edu/~cookwj

Technology: You are welcome to use any technology at your disposal to complete out of class assignments. We will use Maple occasionally to help with some big calculations and possibly to explore how Maple uses symmetries to solve differential equations. Maple should be available on all campus lab computers. If you would like a personal copy, one can be obtained for about $75. Calculators and other computer technology will not be allowed on exams or quizzes. This includes cell phones. Your cell phone should never be out during an exam or quiz.

Course topics: We will spend approximately half of the semester exploring topics from advanced linear algebra. Then the remainder of the semester will be devoted to methods for solving differential equations and systems of differential equations. Although I will assume familiarity with the basics from 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.

We will cover the following topics (in more or less detail according to interest):

• Linear Algebra: 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, homework, term project/presentation, 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 15% of your final grade. The first test will focus on linear algebra and the second exam on differential equations. The dates of the tests listed in the tentative course schedule may change. The actual dates will be announced in class.

Homework & Quizzes: I will post homework problems (some suggested and some to be turned in) in class and on our course webpage. We might have a few short quizzes as well. 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 quizzes and homeworks will make up 30% of your term grade.

Participation & Final Project: After the second test, everyone will pick out a topic for further study and make a (brief) proposal. I will look over and approve proposals for projects and then suggest some problems/issues for you to consider. You will type up your project (minimum 5 pages). This should include some background, proofs of some basic facts, and several worked out representative homework problems. Your paper will be due toward the end of the semester. We will then use the final class periods (as well as the final exam period itself) for presentations. Your proposal, paper, presentation, and overall class participation will make up 40% of your term grade.

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

Component Weight Tests 15% x 2 = 30% Quizzes & Homeworks 30% Project, Presentation, & Participation 40%

Attendance: Don't miss class.

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/syllabi.