Math 348
MONDAY
Techniques of Applied Mathematics Fall 2015
WEDNESDAY
FRIDAY
August
24
26
28
Course Introduction: The Heat equation, an initial value
The linear, nonhomogeneous
and a boundary value problem.
first order problem.
31 September
2
4
The homogeneous
Linear independence, unique solution to the IVP
second order problem
and the constant coefficient case.
7
9
11
Labor Day
Pathway Holiday
Use of a known solution
Holiday
Road to glory.
find a second solution.
14
16
18
Non-homogeneous
Review
Test I
case.
21
23
25
A first order linear problem
Some common power series and
made hard (a series solution).
the calculus of power series.
28
30 October
2
Power series solution of
A case of
y 00 (x) − 2xy 0 (x) + 2y(x) = 0
failure.
5
7
9
Mild failure and a fix: The Frobenius method.
The roots satisfy
The indicial equation and indicial roots r1 ≥ r2 .
r1 − r2 6= nonnegative integer.
12
14
16
Bessel’s differential equation.
Test II
r1 − r2 is arbitrary.
Review
19
21
23
A first order partial
Introduction to the
Periodic functions.
differential equation. 1.1.
Wave equation. 1.2
Orthogonality 2.1
26
28
30
Continuous and piecewise continuous functions.
Fourier series and a convergence theorem. 2.2
November
2
4
6
Fourier series with arbitrary
Test III
periods. 2.3
Review
9
11
13
Even-Odd
Veteran’s Day.
Half-range
functions. 2.3
Thank a Veteran.
expansions. 2.4
16
18
20
Connection with the
Mean-square error
even-odd parts of f (x).
of approximation. 2.5
23
25
27
Parseval’s
Turkey Day Holiday.
Identity. 2.5
Think of the story of William Bradford.
30 December
2
4
“Interesting” sums:
Review
Test IV
∞
X
1
π2
e.g,
=
2
n
6
n=1
Finals week, December 7-11.