University of Mumbai

Class: S.E. Branch:Instrumentation Semester: IV
Subject: Engineering Mathematics-IV (Abbreviated as EM-IV)
Periods per Week(60 min. each)

Lecture

05
Practical
Tutorial
Hours Marks
Evaluation System

Theory

05 100
Practical and Oral

Oral

Term Work

Total

05 100

 

Module

Contents

Hours
1 Vector Analysis:Scalar    and   Vector   point    functions,   Curl,    gradient   and

Divergence, Conservative, Irrotational and Solenoidal fields. Line   Integral,   Greens   Theorem   for   plane   regions   and properties     of     line    integral,    Stoke’s    theorem,     Gauss’s Divergence  theorem   (without  proof)  related  identities  and deductions.

22
2 Matrices :Types of matrices, adjoint of a matrix inverse of a matrix,

rank of a matrix, linear dependence and independence of rows and columns of a matrix over a real field, reduction to normal form and partitioning of a matrix.

Systems of homogeneous and non-homogeneous equations, their consistency and solutions.

Brief revision of vectors over real fields, inner product, norm, linear independence and orthogonality of vectors.

 

Characteristic       Polynomial,       characteristic       equation, characteristic roots, and characteristic vectors of square matrix, properties of characteristic roots and vectors of different types of  matrices  such  as   orthogonal  matrix,  Hermitian  matrix, Skew-Hermitian  matrix,  Diagonal  matrix,  Cayley-Hamilton theorem (without proof), functions of square matrix , minimal polynomial and derogatory matrix.

Quadratic  forms,  Congruent  and  orthogonal  reduction  of quadratic  form,  rank,  index,  signature  and  class  value  of quadratic form.

30

 

 

3.                    Probability and Statistics :                                                             23

Concept    of    probability,    conditional    probability.    Baye’s

theorem (without proof).

Random variable

Probability distribution  for  discrete  and  continuous  random

variables. Density function and distribution function. Expected value,       variance,             moments,   moment      generating                    function, binomial, Poission, normal distributions for detailed study with proof,

Curve fitting

Correlation,  Karl  Pearson  coefficient  &  Spearman’s  rank

correlation  coefficient  (without  proof),  regression,  lines  of regression.

 

Theory Examination:

1.         Question paper will consist of total 7 questions, of 20 marks each.

2.         Only 5 questions need to be attempted.

3.         Q.1 will be compulsory covering entire syllabus.

4.         Remaining questions will be of mixed nature.

5.         In  question  paper  weightage  of  each  module  will  be  proportional  to  the number of respective lecture hours as mentioned in the syllabus.

 

Books Recommended:

1. Wartikar P.N. / Wartikar J. N., Textbook of Applied Mathematics, Pune Vidyarthi

Griha Prakashan, 1981.

2. Shastri S.S., Engineering Mathematics, Prentice Hall.

3. Shantinarayan, Matrices, S. Chand & co.

4. Gupta Kapoor, Mathematical Statistics.