MATH 18.152 SYLLABUS - FALL 2011
1. Practical Information
Professor:
Office:
Office hours:
Email:
Class times:
Meeting room:
Grader:
Grader’s email:
Grader’s office:
Grader’s office hours:
Jared Speck
2-163
Tuesday 1:30 - 2:30
jspeck@math.mit.edu
Tuesdays and Thursdays 2:30 - 4:00
2-142
Nikhil Savale
nikhilas@mit.edu
2-486
Wednesday 4:00 - 5:00
Course website: http://math.mit.edu/~jspeck/18.152_Fall2011/18152_CourseWebsite.htm
Required Text: Partial Differential Equations in Action by Sandro Salsa
2. Course Description
The two primary goals of many pure and applied scientific disciplines can be summarized as
follows: i) formulate/devise a collection of mathematical laws (i.e., equations) that model the
phenomena of interest; ii) analyze solutions to these equations in order to extract information and
make predictions. The end result of i) is often a system of partial differential equations (PDEs).
Thus, ii) often entails the analysis of a system of PDEs. This course will provide an applicationmotivated introduction to some fundamental aspects of both i) and ii).
In order to provide a broad overview of PDEs, our introduction to i) will touch upon a diverse
array of equations including a) the Laplace and Poisson equations of electrostatics; b) the diffusion
equation, which models e.g. the spreading out of heat energy and chemical diffusion processes;
c) the Schrödinger equation, which governs the evolution of quantum-mechanical wave functions;
d) the wave equation, which models e.g. the propagation of sound waves in the linear acoustical
approximation; e) the Maxwell equations of electrodynamics; and other topics as time permits.
In our introduction to ii), we will study three important classes of PDEs that differ markedly
in their quantitative and qualitative properties: elliptic, diffusive, and hyperbolic. In each case,
we will discuss some fundamental analytical tools that will allow us to probe the nature of the
corresponding solutions.
3. Homework
Homework is perhaps the most important component of this course: it provides you with regular
feedback on whether or not you are keeping up with the material, and it challenges you to creatively
apply what you have already learned. There will be an assignment almost every week. Homework
assignments will typically be posted on the course website on Thursday and due at the start of
class on the following Thursday. No late assignments will be accepted. Your lowest homework
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MATH 18.152 SYLLABUS - FALL 2011
score will not factor into your grade. For your own benefit, I encourage you to learn how to use
the typesetting program LaTeX to type up your homework. However, you can turn in neatly
handwritten assignments if you prefer. Your homework will be graded both on correctness and on
the quality of your written arguments.
Policy on collaboration: Collaboration is an important component of your mathematical and
personal development, and I encourage you to work with your classmates. By “work with,” I mean
that every member of a collaborative effort is expected to be an active contributor. The version of
the homework that you turn in must be written in your own words and your own writing style, and
you must fully understand the written arguments; copying someone else’s homework line by line
is plagiarism. Also, at the top of every homework assignment in which you collaborate, write the
names of the people you worked with.
Policy on citations: It is natural to consult resources when you get stuck on a problem. If you
use a resource (e.g. Wikipedia, a textbook, a journal article, etc.), you must cite it using one of the
standard citation styles. Indicate the title, author, volume number, year, and page number (or web
address if appropriate) of your references.
4. Exams
There will be a single 90 minute midterm exam held in class on Thursday, October 27th. There
will be no homework due that week. The final exam date has not been scheduled yet, but I will
notify you when it has been. Both the midterm and the final will be closed book, closed note. The
final exam will be cumulative with a slight emphasis on the material covered after the midterm.
5. Grading
The breakdown of your final grade is as follows:
• Homework: 30 %
• Midterm Exam: 30 %
• Final Exam: 40 %
6. Course Plan
An approximate outline for the course will be posted on the course website. Since our class
meetings will be interactive, I cannot precisely predict the pace of the course.
Feedback: Please do not hesitate to provide me with feedback on the pace or on any other aspect
of the course.