Mathematics III (BE-3001) - CS,IT,EC
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RGPV notes CBGS Bachelor of engineering
COURSE OBJECTIVE-
The objective of this course is to fulfill the needs of Engineers to understand the Applications of Fourier Series, Fourier & Laplace Transforms and Statistical Techniques in order to acquire Mathematical knowledge and to Solving a wide range of Practical Problems Appearing in the CS/IT/EC discipline of Engineering.
Syllabus
UNIT 1:
Fourier Series: Fourier Series for Continuous & Discontinuous Functions, Expansion of odd and even
periodic functions, Half-range Fourier series, Complex form of Fourier Series.
UNIT 2:
Integral Transforms:
Fourier Transform: Complex Fourier Transform, Fourier Sine and Cosine Transforms, Applications of
Fourier Transform in Solving the Ordinary Differential Equation.
UNIT 3:
Laplace Transform: Introduction of Laplace Transform, Laplace Transform of elementary Functions,
Properties of Laplace Transform, Change of Scale Property, First and Second Shifting Properties,
Laplace Transform of Derivatives and Integrals. Inverse Laplace Transform & its Properties,
Convolution theorem, Applications of Laplace Transform in solving the Ordinary Differential
Equations.
UNIT 4:
Random Variables: Discrete and Continuous Random Variables, Probability Function, Distribution
Function, Density Function, Probability Distributions, Mean and Variance of Random Variables.
UNIT 5:
Distribution: Discrete Distributions- Binomial & Poisson Distributions with their Constants, Moment
Generating Functions, Continuous Distribution- Normal Distribution, Properties, Constants, Moments.
Curve Fitting using Least Square Method.
NOTES
- Unit 1
- Unit 2
- Unit 3
- Unit 4
- Unit 5
EVALUATION-
Evaluation will be continuous, an integral part of the class as well as through external assessment.
COURSE OUTCOMES-
The curriculum of the Department is designed to satisfy the diverse needs of students. Coursework is designed to provide students the opportunity to learn key concept of Applications of Fourier Series, Fourier & Laplace Transforms and Statistical Techniques.
Books Recommended
1. Probability & Statistics by G Shanker Rao, University Press.
2. Mathematical Statistics by George R., Springer
3. Erwin Kreyszig: Advanced Engineering Mathematics, Wiley India.
4. H C Taneja: Advanced Engineering Mathematics, I.K. International Publishing House Pvt. Ltd.
5. S S Sastri: Engineering Mathematics, PHI
6. Ramana, B.V.: Advance Engg. Mathematics, TMH New Delhi
7. Engineering Mathematics By Samnta Pal and Bhutia, Oxford Publication
8. Probability and Statistics in Engineering, W.W. Hines et. al., Wiley India PVT Ltd.
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