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MODULE 5: HEAT EQUATION
Lecture 5
Time-Dependent BC
In this lecture we shall learn how to solve the inhomogeneous heat equation
ut 2 uxx = h(x, t)
with time-dependent BC. To begin with, let us consider the following IBVP problem with
time-dependent BC:
MAL 705: DISCRETE MATHEMATICAL STRUCTURES
ABSTRACT ALGEBRA CLASS NOTE-II
Rupam Barman
DEPARTMENT OF MATHEMATICS
INDIAN INSTITUTE OF TECHNOLOGY DELHI
Octover, 2013
Contents
1 Cyclic Groups and Lagranges Theorem
1
1.1 Introduction . . . . . . . . . . . . .
1
Spaces
1.1
Linear Spaces and Linear Operators
As we have said in the preface, the concept of a norm is dened on
linear spaces, and one of the important class of functions between
normed linear spaces is the class of all linear operators.
1.1.1
Linear sp
2
Operators
2.1
Bounded Linear Operators
Recall from real analysis that if J is a subset of R and if f is a real
valued function dened on J , then
(i) f continuous at a point t0 J does not imply that it is
continuous at another point t1 J ;
(ii) f continu