DC23/DE23
MATHEMATICS - II
1. Complex
numbers 10 hours
1.1
Complex
numbers.
1.2
Representation
of complex numbers in two dimensions (Argand diagram).
1.3
Concept
of i and usual notation for complex number (z = a + ib, 
, a, b reals).
1.4
Real
and imaginary parts of a complex number.
1.5
Conjugate
of a complex number.
1.6
Integral
powers of complex number.
1.7
Representation
of complex number in Cartesian, polar and exponential form.
1.8
Conversion
of one form of complex numbers to another form.
1.9
Addition,
subtractions, multiplication and division of complex numbers.
1.10
Modulus
and argument of complex number.
1.11
De
Movire’s theorem and roots of complex number.
I [10] OR II [2]
2. Vector Algebra 10 hours
2.1
Concept
of a vector.
2.2
Representation
of a point by a vector.
2.3
Vectors
in Cartesian and polar form.
2.4
Arithmetic
operations on vectors : addition, subtractions, scalar multiplication.
2.5
Scalar
and vector product of two vectors.
2.6
Applications
of vectors in mechanics and electromagnetism.
I [1] OR II [4]
3. Matrices
and Determinants 16 hours
3.1
Determinants
(upto 3rd order only).
3.2
Sarus’
diagram.
3.3
Row
and Column expansion.
3.4
Properties
of determinant.
3.5
Application
of determinants to solutions of linear equations.
3.6
Cramer’s
rule.
3.7
Matrices.
3.8
Algebraic
structures on matrices.
3.9
Properties
of addition, multiplication and scalar multiplication of matrices.
3.10
Some
special matrices Symmetric, skew symmetric, hermitian and skew hermitian
matrices.
3.11
Solution
of linear equations by matrix method.
3.12
Elementary
matrices.
3.13
Reduction
of a matrix to triangular form.
3.14
Adjoints
and inverses.
3.15
Characteristic
equation.
3.16
Cayley
Hamilton Theorem (without proof).
3.17
Application
of Cayley Hamilton theorem in computing inverse of a square matrix.
I [2, 3] OR II [7]
4. Introduction
to Fourier Series 8 hours
4.1
Periodic
functions.
4.2
Convergence
of Fourier series.
4.3
Even
and Odd functions.
4.4
Equation
of waves.
4.5
Determination
of Fourier coefficients of periodic functions.
I [9]
5. Laplace
transform 8 hours
5.1
Introduction
to Laplace transform.
5.2
Elementary
Laplace transforms.
5.3
Inverse
Laplace transform.
I [8] OR II [11]
6. Differential
equations of Second order 8 hours
6.1
Solutions
of differential equations of second order having 
Sin ax, Cos ax on the
right hand side of the equation.
6.2
Homogeneous
linear equations with constant coefficients.
6.3
Applications
of Laplace transforms in solving second order differential equations.
I [7] OR II [9]
Text Book
I. H K Dass, ‘ Applied Mathematics for Polytechnics’, CBS Publishers & Distributors.
OR
II.
R S L Srivastava, ‘Engineering Mathematics’, Vol-I, Tata McGraw-Hill
Public Co.Ltd.,
Reference Book
1.
B
S Grewal, ‘Elementary Engineering Mathematics’ Khanna Publishers.