Description
First and second order ordinary differential equations with applications, Laplace transforms,
series solutions and qualitative behavior, Fourier series, partial differential equations,
boundary value problems, Sturm-Liouville theory.
Course Objectives
The goal of the course is for the student to learn not only the material, but also
a way of thinking. This course will introduce the classical and rich theory of differential equations.
It is a subject which can easily suffer from the perception that it is little more
than a collection of rules and procedures to be appropriately (and blindly)
applied to a handful of problem types. In reality, there are deep insights
to be gained from this material. These fundamental ideas will (hopefully)
influence the way you think and problem solve. Thus, our goal is to not
only teach you the content outlined in the course synopsis, but to also more
broadly impact the way you think about problems in your chosen discipline.
Prerequisites
A solid understanding of fundamentals from linear
algebra at the level of Math 216 is essential. This includes the concepts of linearity,
span, basis, eigenvalues and eigenvectors as well as the ability to use them in
argument and calculation. Thus, a review of linear algebra is a must (a review can be found in
ODE and PDE Notes I on Sakai). We will also make frequent use of
single variable (and on occasion, multi-variable) calculus as covered in Math 212.
Exam Schedule
- There will be two midterms and a final exam.
- The date of the Final Exam is set by the Registar and will not be changed.
- Exams are open notes and open book, but no other resources are allowed.
| Exams |
Date |
Location |
| Midterm 1 |
TBA |
In class |
| Midterm 2 |
TBA |
In class |
| Final Exam |
(listed on DukeHub) |
Grading
Grades will be assigned based on an assessment of your performance on homework, midterm exams, and a
final exam. The components will be weighted (roughly) as follows:
- Weekly homework (20%), lowest dropped
- Midterm exams (20% each)
- Final exam (40%)
Note that because this baseline score does not correspond directly to a letter grade; in a vacuum,
it does not provide much more information than a sense of how compontents are weighted. The interpretation
of all scores and course (letter) grade will depend on the final exam and an assessment of your performance
as a whole.
Homework
- Homework will typically be assigned weekly and is due one week after
assigned, collected at the start of class.
- No late homework will be accepted,
barring exceptional circumstances as per Duke policy.
- Working and studying in groups is encouraged
(you will get much more out of doing homework if you discuss it with others!).
However, you should write your own solutions to each problem in your own words.
- Solutions should be complete arguments; the process by which you
arrive at the solution is far more important than a correct answer.
When appropriate (which is often), use complete sentences to develop your arguments.
- Homework pages must be stapled together with clearly readable work.
Solutions should be in the same order as in the list of assigned problems.
- Some more conceptual problems will be drawn from the Additional homework
problems (on Sakai). These problems are also a good resource for testing
your understanding of the material (not just calculation).
Ethics
Students are expected to follow the Duke Community Standard.
If a student is found responsible for academic dishonesty
through the Office of Student Conduct, the student will receive a
core of zero for that assignment. If a student’s admitted academic
shonesty is resolved directly through a faculty-student resolution
agreement approved by the Office of Student Conduct, the terms of that
ent will dictate the grading response to the assignment at issue.