__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

## 0 Comments