ESE 502
Homework 1
Due date: Wednesday, January 23, 2013
Problems (you do not need to do the sketches!):
14, 20 (section 11.1);
2,4,16,26 (section 11.2)
Spring 2013

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ESE 502 Mathematics of Modern Engineering II
Lecture 6
Wave equation continued. DAlemberts method.
We have solved the wave equation with specified boundary/initial conditions using the method of separation of variables.
It is useful to notice that the o

ESE 502 Mathematics of Modern Engineering II
Lecture 8
Heat equation on unbounded intervals: solution through Fourier transform.
The wave equation and heat equation considered previously were solved
under some specied boundary conditions. In other words,

ESE 502 Mathematics of Modern Engineering II
Instructor: Vladimir Kurenok
OUTLINE EXAM 1:
Please note: You can use during Exam 1 One one-sided sheet of paper with your own formulas/notes.
1. An orthogonal system of functions cfw_cos nx, sin nx, n = 0, 1,

ESE 502 Mathematics of Modern Engineering II
Lecture 9
Heat equation: an application to nance. Black-Scholes-Merton formula.
We focus ourselves on a particular stock with price St , t 0. The price
is changing randomly so that, for any xed t, the value St

ESE 502 Mathematics of Modern Engineering II
Lecture 3
Extending the Fourier series: Fourier integral.
What we know: Any function f dened on a finite interval, without loss
of generality we can assume it to be [L, L], and satisfying the Existence
conditio

ESE 502 Mathematics of Modern Engineering II
Lecture 1
Some general remarks about the course. Fourier series of a periodic function.
The course consists of two parts:
Part I: Fourier series and Fourier transformations and their applications
to solution of

ESE 502 Mathematics of Modern Engineering II
Lecture 2
Fourier series of a periodic function with period 2L.
It should be clear that any function defined on a finite interval and satisfying the Existence conditions of Fourier series from Lecture 1, should

ESE 502 Mathematics of Modern Engineering II
Lecture 5
Some general facts about PDEs. The wave equation.
Let u(t, x) : [0, ) S IR be a given real-valued function where t
[0, ) and S IRn is a subset of IRn . The variable t is interpreted here
as a time pa

ESE 502 Mathematics of Modern Engineering II
Lecture 10
Laplace equation. The potential
Let P0 = (x0 , y0 , z0 ) and P = (x, y, z) be two arbitrary points from IR3
where P0 is considered to be fixed and P is variable. The distance between
P0 and P is defi

ESE 502
Homework 5
Spring 2013
Due date: Wednesday, February 20, 2013
Problems:
#18 (section 12.6);
Problem 2. Find the solution of heat equation as a model for long bars if the initial
condition is given in the form u(0,x)=f(x) with f(x)=x for |x|<1;
# 1