Instructor:   Andrej Cherkaev
Office: JWB 225   ph: 581-6822   email:cherk@math.utah.edu
Office hours: F, 10-12 and by appointment

About the subject: Partial differential equations (PDE) are a type of differential equation, i.e., a relation involving an unknown function (or functions) of several independent variables and their partial derivatives with respect to those variables. PDEs are used to formulate, and thus aid the solution of problems involving functions of several variables.

PDEs are for example used to describe the propagation of sound or heat, electrostatics, electrodynamics, Fuid flow, and elasticity. These seemingly dis- tinct physical phenomena can be formalized identically (in terms of PDEs), which shows that they are governed by the same underlying dynamic. PDEs fnd their generalization in stochastic partial dierential equations. Just as orinary differential equations often model dynamical systems, partial dierential equations often model multidimensional systems.
     Wikipedia: Partial differential equation

Student Solutions Manual  can be downloaded from the author's website:
http://www.math.missouri.edu/~nakhle/pdebvp/student-manual.pdf

Tutoring is available in T. Benny Rushing Mathematics Center

Syllabus is here

Home work
HW1. Section 1.2: Problems 5, 11, 16. Section 2.1: Problems 2, 9, 12, 14, 19.
HW2. Section 2.2: Problems 5, 11, 15. Section 2.3: Problems 4, 17. (You may use Maple)
HW3. Section 2.3: Problems 2, 9, 17. Section 2.4: Problems 4, 16.
HW4. Section 3.3: Problems 1, 9, 11. Section 3.4: Problem 2.
HW5. Section 3.5: Problems 2, 4, 12. Section 3.6: Problems 2, 5, Section 3.7: Problems 1, 2.

HW 6. Section 3.8: Problem 4. (Graph the solution). Section 3.9: Problems 3, 7 Example: Maple code for Fourier series calculations
# Example of computing Fourier series (Ch. 2)

# 1. Set the periodic function f and period p
f := x - exp(x);
p := 1;

# 2. Compute Fourier coefficients:
a0 := (int(f, x = -p .. p))/(2 p);
an := (int(f*cos(n*Pi*x/p), x = -p .. p))/p;
bn := (int(f*sin(n*Pi*x/p), x = -p .. p))/p;

# 3. Compute the partial sum fn (Here, n=15)
fn := a0+sum(an*cos(n*Pi*x/p)+bn*sin(n*Pi*x/p), n = 1 .. 15);

# 4. Plot the function, the partial sum, and their difference
plot({f, fn}, x = -p .. p);
plot(f-fn, x = -p .. p);

# 5. Repeat for any function and any period.