The syllabus is here. Note that in the syllabus I handed out in class there was a small error. The final exam is on Wednesday December 11th and not Monday December 11th. This has been corrected.

The book we will be using is Introduction to the Foundations of Applied Mathematics, Mark H. Holmes, Springer, 2019 (2nd edition).

Important: There is a first edition from 2009 but I strongly recommend you get the 2nd edition so that we are all looking at exactly the same thing. In any case the first edition had quite a few mistakes and typos in it which have mostly been fixed in the second edition.

ANNOUNCEMENTS: 12/04/2024 The homework questions for the last class on Monday are 9.3a, 9.5 and 9.8acd. I will be having extra office hours this Friday from 11.30-12.30.

11/19/2024 In class yesterday we went through the homework questions and covered Section 4.6 as far as equation (4.55). The 4th test on Monday will cover what we have done from Sections 4.4-4.6. The test will be in the Math Testing Centre again and I will send out the usual email in a day or two. The homework exercise for tomorrow if 4.19.

11/14/2024 In class yesterday we finished Section 4.5. The homework exercises for next week are 4.10, 4.11, 4.13abe and 4.14.

11/11/2024 We briefly talked about the solution to the step function initial condition in Section 4.4.2 and then the firsttwo pages of Section 4.5 on Fourier Transforms.

10/31/2024 In class yesterday we continued the anaylsis of random walks and Brownian motion and got as far as deriving the heat equation (4.13). IMPORTANT: The third test on Wednesday will be in the Math Testing Centre -- the same as the first test. I will send out a confirmatory email in the next day or two. The test will cover what we have done starting from the stability of steady states. The homework exercises for Monday are 4.1 and 4.6.

10/28/2024 In class I covered Section 3.8 and talked about a few examples of Brownian motions and random walks.

10/24/2024 In class yesterday we did the Examples in Section 3.5.3 and Section 3.6 (skipping over the details of the inner solution and matching), and we just started Section 3.8. The exercises for Monday are 3.16abc, 3.19a-f and 3.20abc.

10/19/2024 I have posted midterm grades based upon the first two tests.

10/10/2024 IMPORTANT: The second test is next Wednesday and will focus on the material we have covered since the first test starting with finding asymptotic expansions for various kinds of equations right upto the general method for finding conserved quantities (Section 3.4) that we covered yesterday. The exam will most likely take place in the lecture room and NOT in the math testing centre like last time but I will confirm this by email over the weekend. Remember the University is closed on Monday and there are no classes. Enjoy your long weekend.

10/07/2024 In class today we continued until the end of Section 3.3.1. The homework Exercises for Wednesday are 3.1c, 3.2, 3.4, 3.8, 3.9.

10/03/2024 In class yesterday we completed the two timing example and got asfar as the start of Section 3.2.1. The only homework question for Monday Exercise 2.32 a,b. For part c) just set up the two-timing and ansatz.

09/30/2024 In class I went through the homework questions and we started the two-timing pendulum example.

09/26/2024 We finished the examples in Sections 2.4 and 2.5. Please attempt the three questions below by Monday.

09/24/2024 The homework questions for next week will be 2.9, 2.12, 2.24 and maybe 2.32 if we get far enough tomorrow.

09/23/2024 I went through the test solutions. Please read the examples in Section 2.2.2. We covered the first example in Section 2.2.3 and started Section 2.4.

09/11/2024 In class today we covered Section 2.1 as well as reviewing Taylor series and introducing the little Oh and big Oh notation. The homework questions for Monday are Exercises 1.17, 1.19, 1.28 and 2.1ad and 2.6. I will be sending details of the location of the first test next Wednesday to your GMU email in the next day or two and will need you to reply to it.

09/09/2024 In class today we almost finished Sections 1.5.1 and 1.5.2.

09/05/2024 In class yesterday we covered Section 1.4. The homework exercise for Monday is Exercise 1.13.

09/03/2024 The Math Department is having a Meet and Greet tomorrow Wednesday September 4th from 2-3.30 in Exploratory Hall (2nd floor, open collaboration area). All are welcome. I will be there from 2-2.30 so my office hours will be shortened to 2.30-3 just for tomorrow.

08/28/2024 The homework questions for next week (to be attempted but not handed in) are 1.3, 1.4 and 1.6.