MODULE 8: THE FOURIER TRANSFORM METHDOS FOR PDES
Lecture 4
15
Vibration of an Innite String
In this lecture we shall learn how Fourier Transforms can be used to solve one dimensional
wave equations in
Module 8: The Fourier Transform Methdos for PDEs
In the previous modules (Modules 5-7), the method of separation of variables was used
to obtain solutions of initial and boundary value problems for pa
Module 7: The Laplace Equation
In this module, we shall study one of the most important partial dierential equations in
physics known as the Laplace equation
2 u = 0 in Rn ,
where 2 u :=
n
2u
i=1 x2
i
MODULE 7: THE LAPLACE EQUATION
17
Lecture 4
The Mixed BVP for a Rectangle
In this lecture we shall consider solving the mixed BVP for the Laplace equation. To
begin with, let us consider the following
13
MODULE 6: THE WAVE EQUATION
Lecture 4
The Finite Vibrating String Problem
In this lecture, we shall study the transverse vibrations of a nite string. If u(x, t) represents the displacement (deectio
10
MODULE 6: THE WAVE EQUATION
Lecture 3
The Semi-Innite String Problem
Before we introduce the semi-innite string problem, let us look at some special cases of
DAlemberts formula derived in the previ
Module 3: Second-Order Partial Dierential
Equations
In Module 3, we shall discuss some general concepts associated with second-order linear
PDEs. These types of PDEs arise in connection with various p
16
MODULE 5: HEAT EQUATION
Lecture 4
Time-Independent Homogeneous BC
The boundary conditions in previous lecture are assumed to be homogeneous, where we
are able to use the superposition principle in
MODULE 2: FIRST-ORDER PARTIAL DIFFERENTIAL EQUATIONS
Lecture 3
16
Quasilinear First-Order PDEs
A rst order quasilinear PDE is of the form
a(x, y, z )
z
z
+ b(x, y, z )
= c(x, y, z ).
x
y
(1)
Such equa
Module 6: The Wave Equation
In this module we shall study the one-dimensional wave equation which describes transverse vibrations of an elastic string. This module is organized as follows. In the rst
MODULE 5: HEAT EQUATION
5
Lecture 2
The Maximum and Minimum Principle
In this lecture, we shall prove the maximum and minimum properties of the heat equation.
These properties can be used to prove uni
Module 2: First-Order Partial Dierential Equations
The mathematical formulations of many problems in science and engineering reduce to
study of rst-order PDEs. For instance, the study of rst-order PDE
Steven R. Dunbar
Department of Mathematics
203 Avery Hall
University of Nebraska-Lincoln
Lincoln, NE 68588-0130
http:/www.math.unl.edu
Voice: 402-472-3731
Fax: 402-472-8466
Stochastic Processes and
Ad
An Introduction to Hill Ciphers
Using Linear Algebra
Brian Worthington
University of North Texas
MATH 2700.002
5/10/2010
Hill Ciphers
Created
by Lester S. Hill in 1929
Polygraphic
Uses
Substitution Ci
Mathematical Database
PIGEONHOLE PRINCIPLE
Pigeonhole principle is a fundamental but powerful tool in combinatorics. Unlike many other
strong theorems, the principle itself is exceptionally simple. Un
Homework 1
Math 375
Spring 2007
Discrete Structure
Remark 1: This work covers the following topics.
1) Addition Principle.
2) Multiplication Principle.
3) Inclusion-Exclusion Principle.
Remark 2: The
Free to photocopy and distribute
August 19, 2007 Version
David A. SANTOS
[email protected]
Contents
Preface
ii
Legal Notice
iii
To the Student
iv
1 Preliminaries
1.1 Sets . . . . . . . . . . . .
1.2
DEPARTMENT OF MATHEMATICS
Indian Institute of Technology Guwahati
MA501: Discrete Mathematics
Mid Semester Exam
September 23, 2012
Instructor: Bikash Bhattacharjya
Time: 2 hours
Maximum Marks: 30
Mode
MAL 705: DISCRETE MATHEMATICAL STRUCTURES
ABSTRACT ALGEBRA CLASS NOTE-I
Rupam Barman
DEPARTMENT OF MATHEMATICS
INDIAN INSTITUTE OF TECHNOLOGY DELHI
Octover, 2013
Contents
1 Introduction to Groups
1
1.