Mathematics-III for EE Engineering (BMATE 301)

Mathematics-III for EE Engineering

Course Code BMATE 301 
CIE Marks 50
Teaching Hours/Week (L:T:P: S) 3:1:0:0 
SEE Marks 50
Total Hours of Pedagogy 40 
Total Marks 100
Credits 03 
Exam Hours 03
Examination type (SEE) Theory 

Module-1 :

Ordinary Differential Equations of Higher Order (8 hours) Importance of higher-order ordinary differential equations in Electrical & Electronics Engineering applications. Higher-order linear ODEs with constant coefficients - Inverse differential operator, problems.Linear differential equations with variable Coefficients-Cauchy’s and Legendre’s differential equations - Problems. Applications:Application of linear differential equations to L-C circuit and L-C-R circuit. Self-Study: Finding the solution by the method of undetermined coefficients and method of variation of parameters. (RBT Levels: L1, L2 and L3) 

Module-2:

Curve fitting, Correlation and regressions Principles of least squares, Curve fitting by the method of least squares in the form 𝑦 = 𝑎 + 𝑏𝑥 , 𝑦 = 𝑎 + 𝑏𝑥 + 𝑐𝑥2 , and 𝑦 = 𝑎𝑥 𝑏 . Correlation, Co-efficient of correlation, Lines of regression, Angle between regression lines, standard error of estimate, rank correlation Self-study: Fitting of curves in the form 𝑦 = 𝑎 𝑒 𝑏𝑥 14.08.2023 14.08.2023 2 

Module-3

Fourier series. Periodic functions, Dirchlet’s condition, conditions for a Fourier series expansion, Fourier series of functions with period 2𝜋 and with arbitrary period. Half rang Fourier series. Practical harmonic analysis. Application to variation of periodic current. Self-study: Typical waveforms, complex form of Fourier series 

Module-4

Fourier transforms and Z -transforms Infinite Fourier transforms: Definition, Fourier sine, and cosine transform. Inverse Fourier transforms Inverse Fourier cosine and sine transforms. Problems. Z-transforms: Definition, Standard z-transforms, Damping, and shifting rules, Problems. Inverse z-transform and applications to solve difference equations Self-study: Convolution theorems of Fourier and z-transforms 

Module-5

Probability distributions Review of basic probability theory, Random variables-discrete and continuous Probability distribution function, cumulative distribution function, Mathematical Expectation, mean and variance, Binomial, Poisson,Exponential and Normal distribution (without proofs for mean and SD) – Problems. Sampling Theory: Introduction to sampling distributions, standard error, Type-I and Type-II errors.Student’s t-distribution, Chi-square distribution as a test of goodness of fit. Self-study: Test of hypothesis for means, single proportions only.

Suggested Learning Resources: Books

1. B. S. Grewal: “Higher Engineering Mathematics”, Khanna Publishers, 44thEd., 2021. 

2. E. Kreyszig: “Advanced Engineering Mathematics”, John Wiley & Sons, 10thEd., 2018. 

Reference Books 

1. V. Ramana: “Higher Engineering Mathematics” McGraw-Hill Education, 11th Ed., 2017 

2. Srimanta Pal & Subodh C.Bhunia: “Engineering Mathematics” Oxford University Press, 3rdEd., 2016. 

3. N.P Bali and Manish Goyal: “A Textbook of Engineering Mathematics” Laxmi Publications, 10thEd., 2022. 

4. C. Ray Wylie, Louis C. Barrett: “Advanced Engineering Mathematics” McGraw – Hill Book Co., New York, 6th Ed., 2017. 14.08.2023 14.08.2023 4 

5. Gupta C.B, Sing S.R and Mukesh Kumar: “Engineering Mathematic for Semester I and II”, Mc-Graw Hill Education(India) Pvt. Ltd 2015. 

6. H.K. Dass and Er. Rajnish Verma: “Higher Engineering Mathematics” S.Chand Publication, 3rd Ed.,2014. 7. James Stewart: “Calculus” Cengage Publications, 7thEd., 2019