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GUJARAT UNIVERSITY
B.E. SEM III (COMPUTER ENGINEERING)
CE 301 Advanced Mathematics
Subject
Code
Teaching
Scheme
Examination Scheme
Theory
Lab/
Pract
Exam
Theory
Paper
Theory
Marks
Pract/
Oral
TW Total
Sessional
1.5 Hrs
50
Advanced
Mathematics
CE
301
4
-
University
3 Hrs
100
-
-
150
1. Fourier series :
Periodic functions, Drichlet's conditions, Fourier series, Euler's formula. Fourier
expansion of periodic functions with periodic functions with period 2π, Fourier series of
even and odd functions. Fourier series of periodic functions with arbitrary periods, Half
range Fourier series. Harmonic analysis.
2. Higher Order differential equations :
Linear differential equations of higher order with constant coefficients, Method of
variation of parameters, Higher order linear differential equations with variable
coefficients (Cauchy's and legendre forms), Series solution, Simultaneous linear
differential equations, Models for the real world problems and their solutions.
3. Partial Differential equations :
Formation of partial differential equations, Directly integrable equations, Lagrange's
equation, Solutions of special type of non-linear partial differential equations of the first
order, Homogeneous linear equations with constant coefficients, Method of separation of
variables, solution of one dimensional wave equation, heat equation and Laplace
equation.
4. Matrices:
Caley-Hamilton's theorem, Special matrices like Hermitian, Skew-Hermitian and
Unitary. Reduction to diagonal form, Quadratic forms.
5. Functions of complex variables :
Reorientation, Analytic function, Cauchy- Riemann equations (Cartesian and polar
forms), Harmonic functions, orthogonal property, conformal mappings, some standard
conformal transformation. Complex integration, Cauchy's integral theorem and Cauchy’s
integral formula.
Reference Books :
1.
Erwin Kreyszig
:
Advanced Engineering Mathematics
(8th Edition) Wiley Eastern Ltd., New Delh