Syllabus for MA 561 Methods of Applied Mathematics I

Syllabus for MA 561 Methods of Applied Mathematics I, Fall 2024

Course Information

Lecturer: Ryan Goh

Email: rgoh@bu.edu
Office: CDS 423
Office Hours:
Monday 1:00-2:30pm
Thursday, 12:30-2pm
or by appointment (please provide your availability when requesting an appointment).
Web page: http://math.bu.edu/people/rgoh/

Lectures:

Time: Tuesday, Thursday 11:00 am-12:15pm;
Location: SOC B59

Textbook:

I've listed both of these in the BU bookstore website, but note that these are both available for download on the BU library website.
Required:
"Introduction to Partial Differential Equations" by Peter Olver; 3rd Edition. The PDF of the text book can be downloaded through the BU library website here . Corrections for the manuscript can be found here The latest version of the text can be downloaded (while on the BU network) here

Supplementary: "Applied Partial Differential Equations" by David J. Logan; 3rd Edition. The PDF of the text book can be downloaded through the BU library website here .

Course Webpage:

math.bu.edu/people/rgoh/teaching/ma561-fs24/course-page.html

Course Description:

This course will focus on the study of partial differential equations (PDEs), a key part of an applied mathematicians toolbox. Such equations model phenomena in virtually every area of science ranging across time/length scales ranging from nuclear physics, chemical reactions, fluid interactions, and galaxy formation. We will highlight how to solve (both numerically and analytically) and characterize the behavior of fundamental PDE examples. An solid understanding of ordinary differential equations (at the level of MA 226) and calculus (at the level of our Calc I, II, and III courses) is required. Some experience with basic linear algebra will be helpful. There will also be a numerical component (see below) which will require writing basic codes to numerically solve various equations.

Roughly our course schedule, subject to student interests and class pace, will be as follows

Week 1: Ch. 1 - 2.1,2.2: Introduction to PDE, linear waves and characteristics
Week 2: Ch 2.2, 2.3: more on 1st order equations, method of characteristics, nonlinear waves, shocks
Week 3: Ch 2.4, 3.1: Wave equation, Fourier Series for the heat equation
Week 4: Ch 3.1 - 3.4: Fourier Series: derivation, computaiton, some theory
Week 5: Ch 4.1, 4.2: Heat and wave equations on bounded domain, separation of variables
Week 6: Ch. 4.3 Planar Laplace and Poisson equation
Week 7: Midterm 1
Week 8: Ch 5.1, 5.2: Finite differences and PDE
Week 9: Ch 5.3 - 5.5: Finite differences and PDE
Week 10: Ch. 6.1, 6.2: Generalized functions and Green's functions
Week 11: Ch. 6.2, 6.3 More on Green's Functions
Week 12: Ch. 7: Fourier transforms
Week 13: Ch. 7: Fourier transforms
Week 14: Ch. 8: linear/nonlinear evolution equations, other fun examples
Week 15: more fun examples

Numerical exploration

We will also utilize computer/numerical simulations to help us explore and analyze differential equations throughout the course. In my examples, I will mainly use MATLAB, which can be downloaded here for free by any BU student. See this quick tutorial on how to get started with the software if you haven't used it, and here for a tutorial on solving differential equations with it. I will also use Mathematica from time to time (mostly for plotting). See download instructions here and a tutorial to get started. You are of course welcome to use another software (such as Python, Julia, etc...) and while I may be familiar with the specific language you are using, I cannot guarentee I will be able to help debug/troubleshoot code written in all languages.

Applications

Additional References

More references and links to specific papers relevant to lectures will be posted on the course webpage.

Homework

Homework will be posted on the course webpage and gradescope. Please neatly write out or type your solutions, turn them into one PDF (scanning if you write them on paper), and submit them through the course Gradescope page. This can also be found on the course blackboard page. They will be due at 9am on Fridays. No late work will be accepted. Please start problems and get help early! Your lowest two scores will be dropped.

Doing exercises and problems is the best way to learn mathematics. As such we will have homework assignments every 1-2 weeks. You are welcome (and encouraged!) to work together, but please make sure to write up solutions by yourself and in your own words. You must understand how to solve the problems yourself. If it is suspected that you copied down your answers from another source of any kind, you may be asked to come to my office and explain your solution(s), without any books or notes.

In your solution sets, explain your work clearly, concisely, and using complete sentences. Homework should be legible and organized. If you are worried about the legibility of your handwriting, please contact me about using the mathematical typesetting software LaTeX. The homework problems will be graded using the following 6-point system adapted from Prof. Chad Topaz, of Williams College:

Mathematical content (4 points)
- 4 points - The solution is 100% correct.
- 3 points - The solution shows a good understanding of the problem but there are some minor mistakes and/or typos present.
- 2 points - The solution is incorrect but has some good ideas in it.
- 1 points - A serious effort has been made on the problem
- 0 points - Only a trivial, or no effort has been made
Communication (2 points) These will only be assigned if you get 2 points or higher on the mathematical content portion.
- 2 points - The solution is clearly written, well-organized, and justified with sufficient detail.
- 1 point - The solution is readable, but is missing details or is hard to follow in places.
- 0 points - The solution is unreadable, or has is missing many details.

Solution sets will be emailed out along with your graded solutions one to two weeks after the due date.

Midterm

There will be one in-class written midterm on Thursday, October 17th during the regular lecture time. It will consist of problems simular to homework problems and examples discussed in class. The specific material covered on the exam will be outlined a week or two before the exam.

Final Exam

The final will be a take home exam. The problems will be roughly similar to examples done in class and in homework. Material covered will be outlined at the week before the exam. You will have at least 48 hours to complete the exam. The exam will be open book and open note. The use of the internet or other resources, unless explicitly mentioned, will not be allowed. You must do the exam on your own and will not be allowed to communicate with others about it.

Grades

Your course grade will assigned as follows

Homework scores (55% - two lowest scores dropped)

Midterm (20% each )

Final project (25%)

Records for assignment grades will be kept on the course blackboard website.

Classroom policies

Questions are always welcome during lecture. Please raise your hand or interupt me if I'm facing the board. Sometimes, due to time restraints or flow of the lecture, I may have to delay a question till another section, or after class.

The use of cellphones, laptops, or the internet, when not part of class activities (i.e. to take notes, or share the result of a computer simulation), is forbidden. Such activities can be very disruptive, distracting, and disrespectful to those around you and are not conducive to a productive learning environment.

Attendance Policy : Students are expected to attend each class. We will follow the BU attendance policy . The class periods will be a key component of the course. While math is mostly learned by doing, I view lectures as a guide which helps one more efficiently and effectively learn a topic.

Excused absenses and make-up exams

Please let me know about all religious observances at the beginning of the semester. As mentioned above, there will be no make-ups for homeworks. In extreme circumstances (religious observance, death in the family, emergency) there can be make-ups for exams. Please tell me during the first week of school if you will need a make-up exam.

Students with disabilities

Please contact me as soon as possible. I am happy to work with you and the BU office of Dissability and Access Services.

Academic code of conduct

Please do not cheat. Furthermore, copying of answers from a friend, solution manual, or online solution set is detrimental to your learning. You will be held to the BU academic code of conduct.

How to Succeed

Math is learned by doing! Try to read the corresponding sections of the textbook before and/or after they are covered in class and work out the examples for yourself as you go along. The text is quite readable and will help you absorb the material. Start the homework early and discuss with others. Stop by office hours often!

Extra Help

If you feel you are falling behind in the course please do not hesitate to contact me! It is always easier to address misunderstandings sooner than later. In addition to working with me, I can also put you in touch with TAs in the tutoring room who are knowledgeable in partial differential equations.

Last Modified

The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by Boston University.