Mathematics III (BE-3001) - CS,IT,EC - B.E RGPV CBCS & CBGS Scheme Notes -->

## 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.

• 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.

## You May Also Like

#### Services

###### COMPLETELY FREE !!!

Yup, everything is free....

###### NO REGISTRATION REQUIRED

User doesn't have to register for accessing the files, all the files are free & universally accessible without any condition or restriction.

###### RESPONSIVE DESIGN & USER-FRIENDLY

Our webpages are responsive & user-friendly, which means it will automatically adjust according to your device screen size and you will find stuff without ant hustle.

All the files are uploaded on our super-fast servers so that they can be easily downloaded with high speed.

###### NEW PROJECTS

For providing a better experience to our users we are developing our Android application, the application will have a lot of awesome features so stay tuned ;).

###### AWESOME SUPPORT TEAM

Our AI-powered Chatbots are always here to help you so, feel free to ask any question or report if you face any problem. Our team also monitors all chatbots traffic & they will contact you if chatbot fails to help.

+91-8989595022

###### Email :

[email protected]