Algebra of Sets and Counting Methods
The algebra of sets and counting methods are useful in understanding the basic
concepts of probability. These concepts are briefly reviewed from the point of
view
MA 601 - MATHEMATICAL METHODS FOR ENGINEERS
Assignment #5
September 10, 2015
Question 1 Find the eigenvalues and eigenvectors of the following matrices.
Also diagonalize them.
2 2
1 1
(i)
(ii)
1 1
0 2
MA 601: Mathematical Methods for Engineers
Date: August 28, 2015
Time: 60 Minutes
Quiz # 1
Name . Roll No.
Tick the correct answer (only one choice) in each of the following questions.
Each correct an
MA 601 - MATHEMATICAL METHODS FOR ENGINEERS
Assignment #7
October 26, 2015
Question 1 Solve the following system of second order initial value problems.
(i)
d2 x dx
dx
d2 x dx
dx
+
2x = 1, x(0) = 1,
MA 601: Mathematical Methods for Engineers
TUTORIAL SHEET # 4
September 3 , 2015
Question 1 Find orthonormal bases for the following subspaces of <4 .
U = cfw_(x1 , x2 , x3 , x4 ) <4 : x1 + x3 = 0 = x
MA 601: Mathematical Methods of Engineers
Review Execises
Q1 Find out which of the following subsets are subspaces of the respective
spaces. Prove your assertion.
Z 1
p(x)dx = 0
(i) U = cfw_(x1 , x2 )
MA 601: Mathematical Methods of Engineers
TUTORIAL SHEET # 2
August 14, 2015
Question 1 Prove that the set of all real symmetric n n matrices forms a
vector sub-space of Mnn . Find its basis and dimen
MA 601: Mathematical Methods of Engineers
TUTORIAL SHEET # 3
August 23, 2015
Question 1 Let T : R3 R3 be given by its action on the basis vectors
(1, 1, 1), (1, 1, 1), (1, 0, 1) as under.
T (1, 1, 1)
2.7
Correlation coefficient and Bivariate Normal Distribution
Meaning of correlation:
In a bivariate distribution we may be interested to find out if there is any correlation
or covariance between the
2.6
Functions of Random Variables
The previous modules discussed basic properties of events defined in a given
sample space and the random variables used to represent those events. The
fundamental ass
1.2
Basic Concepts in Probability
Introduction to uncertainty
Every day we have been coming across statements like the ones mentioned
below:
1.
2.
3.
4.
Probably it will rain tonight.
It is quiet like
1.4
Theorems in Probability
In this module, we shall prove some theorems which help us to evaluate the
probabilities of some complicated events in a rather simple way. In proving these
theorems, we sh
1.3.
Definitions of Probability
The probability of a given event is an expression of likelihood or chance of
occurrence of an event. How the number is assigned would depend on the
interpretation of th
1.5
BayesTheorem and Its Applications
One of the important applications of the conditional probability is in the
computation of unknown probabilities on the basis of the information supplied by
the ex
Unit 2
Probability distributions
2.1
Random Variable
While performing a random experiment we are mainly concerned with the
assignment and computation of probabilities of events. In many experiments we
2.2
Bivariate random variable
In the real life situations more than one variable effects the outcome of a random
experiment. For example, consider an electronic system consisting of two
components. Su
2.3
Mathematical Expectation
The term expectation is used for the process of averaging when a random variable
is involved. It is the number used to locate the centre of the probability
distribution (p
2.4
Discrete Probability Distributions
Modules
and
deal with general properties of random variables. Random
variables with special probability distributions are encountered in different fields
of scie
2.5
Continuous Probability Distributions
The continuous probability distributions are used in a number of applications in
engineering. For example in error analysis, given a set of data or probability
MA 601: Mathematical Methods for Engineers
Tutorial Sheet # 8
November 3, 2015
Q1 Solve the wave equation
2u
u
2u
=
; u(0, t) = 0, u(1, t) = 0; u(x, 0) = f (x),
(x, 0) = g(x)
2
t
x2
t
f (x) and g(x) a