Download APPLIED_MATHEMATICS_II.pdf

The Maharaja Sayajirao University of Baroda
Polytechnic,
Department of Electrical Engineering,
ACADEMIC YEAR
2015-2016
Near Shastri Bridge, Fatehgunj, Vadodara-390001, <<e-mail ID>>
Computer Engineering : (Higher Payment Program)
YEAR
Semester
I
II
CORE/Elective/Foundation 1:
AMT3202 : Applied Mathematics-II
CREDIT
-
HOURS
-
OBJECTIVES:
COURSE CONTENT / SYLLABUS
UNIT-I
UNIT-II
UNIT-III
UNIT-IV
Complex numbers
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, i2 = -1, 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 comlex 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’ stheorem and roots of complex number.
Vector Algebra
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, substractions, scalar multiplication.
2.5
Scalar and vector product of two vectors.
2.6
Applications of vectors in mechanics and electromagnetism.
Matrices and Determinants
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
Algebratic 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 eqaations 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.
Introduction to Fourier Series
4.1
Periodic functions.
4.2
Convergence of Fouries series.
4.3
Even and Odd functions.
4.4
Equation of waves.
3
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8
3
UNIT-V
UNIT-VI
4.5
Determination of Fourier coefficients of periodic functions.
Laplace transform
5.1
Introduction to Laplace transform.
5.2
Elementary Laploce transforms.
5.3
Inverse Laplace transform.
Differential equations of Second order
6.1
Solutions of differential equations of second orde having cax, Sin ax, Cos ax on the
right hand side of the equation.
6.2
Homogeneous linear equations with constant coefficient.
6.3
Applications of Laplace transforms in solving second order differential equations.
REFERENCES
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