Text: Applied Partial Differential Equations by J. David Logan Second Edition

Info about the course: Following ordinary differential equations, Intro to PDEs is a first incursion into the systematic

study of differential equations that involve functions and derivatives with respect to more than one variable. Obviously,

the course relies heavily on a good understanding of ordinary differential equations and calculus in higher dimensions

(differentiation, integration for functions of more than one variable). We will often follow a modeling approach in

deriving PDEs (e.g. for the heat equation), so some basic concepts from physics will be needed. Besides deriving PDEs

we will also be interested in solving them, sometimes by imposing additional conditions (initial or boundary conditions).

As with any other mathematics course, rigour in writing arguments and proofs is a must. Clear notation, good use of

mathematical quantifiers, correct arguments should be always on your mind when taking notes, solving homework or

exam problems. What you write someone will read! - so do make sure that your ideas are transparent to the reader

(be it you or someone else).

Computer Lab / Calculators: Students can use the computers from the Mathematics Department Computer Laboratory

in Avery 18 with their university account (go to http://activedir.unl.edu to activate your account). There will be a very

short introduction to Maple for gaining more insight into the material. Student versions of Maple or Mathematica are

available for purchase in the campus computer shop. During the semester at least two or three lectures will be held in

the Computer Laboratory (Avery 18), so students will get familiarized with simple programming in Maple and also with

using the computer to solve partial differential equations. The use of calculators will not be allowed during exams.

The use of any other electronic device (cell phones, ear pieces etc.) is not permitted during class time or during exams.

Assessment: Your final grade will be computed based on the following scheme.

20 % Homework

25 % Exam 1

25 % Exam 2

30 % Final Exam

The final letter grade will be computed based on the following table:

Final average |
98-100 |
92-98 |
88-92 |
85-88 |
80-85 |
77-80 |
74-77 |
70-74 |
67-70 |
64-67 |
60-64 |
55-60 |
<55 |

Letter grade |
A+ |
A |
A- |
B+ |
B |
B- |
C+ |
C |
C- |
D+ |
D |
D- |
F |

Honor Code: Some of your work during the course will be done individually, while some will be collaborative.

I expect you to acknowledge the help you have received from your colleagues, outside friends, or me on homework

assignments. I will assume that you will adhere to the UNL Policy on Academic Honesty.

Course Policy: Class attendance is expected. If you miss a class it is your responsibility to get the material from your

colleagues. Extensions for homework assignments will not be allowed. Make-up exams will be administered only in

extreme cases. Cheating will be penalized by at best giving a lower letter for the course grade.

Scheduling: A tentative schedule for the first few weeks of classes is listed below. These details are presented as a

guide, the instructor may add or delete topics from this list, may change the dates for the exams. It is your responsibility

to keep track of the course details and the schedule.

Week 08/21 -- 08/25: Review on Ordinary Differential Equations

Modeling with PDEs

Conservation Laws. The Method of Characteristics

Week 08/28 -- 09/01: Diffusion

PDEs in Biology

Vibrations and Acoustics

Week 09/04 -- 09/08: Labor Day - No class

Heat Flow in Three Dimensions

Laplace's Equation

Week 09/11 -- 09/15: Classification of PDEs

Cauchy Problem for the Heat Equation

Cauchy Problem for the Wave Equation

If you have any questions or suggestions, please feel free to bring them up!