__AV Mathematics-III for EC Engineering__

#### Course Code BMATEC301

CIE Marks 50

Teaching Hours/Week (L:T:P: S) 3:0:0:0

SEE Marks 50

Total Hours of Pedagogy 40

Total Marks 100

Credits 03

Exam Hours 03

Examination type (SEE) Theory

__Module-1:__

Fourier series and practical harmonic analysis
Periodic functions, Dirichlet’s condition. Fourier series expansion of functions with period 2𝜋
and with arbitrary period: periodic rectangular wave, Half-wave rectifier, rectangular pulse,
Saw tooth wave. Half-range Fourier series. Triangle and half range expansions, Practical
harmonic analysis, variation of periodic current.(8 hours)
(RBT Levels: L1, L2 and L3)

__Module-2:__

Infinite Fourier Transforms
Infinite Fourier transforms, Fourier cosine and sine transforms, Inverse Fourier transforms,
Inverse Fourier cosine and sine transforms, discrete Fourier transform (DFT), Fast Fourier
transform (FFT). (8 hours)
(RBT Levels: L1, L2 and L3)

__Module-3:__

Z Transforms
Definition, Z-transforms of basic sequences and standard functions. Properties: Linearity,
scaling, first and second shifting, multiplication by n. Initial and final value theorem. Inverse
Z- transforms. Application to difference equations. (8 hours)
(RBT Levels: L1, L2 and L3)

__Module-4__:

Ordinary Differential Equations of Higher Order
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. Application of linear differential equations to L-C circuit and
L-C-R circuit.(8 hours)
(RBT Levels: L1, L2 and L3)

Module-5:

Module-5:

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, Coefficient of correlation, Lines
of regression, Angle between regression lines, standard error of estimate, rank correlation.
(RBT Levels: L1, L2 and L3)(8 hours)

__Suggested Learning Resources:
Books __

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

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

__Reference Books: __

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

2. Srimanta Pal & Subodh C.Bhunia: “Engineering Mathematics” Oxford University Press,
3
rdEd., 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, 6thEd., 2017.

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

6. H.K. Dass and Er. Rajnish Verma: “Higher Engineering Mathematics” S.Chand
Publication, 3rdEd.,2014.

7. James Stewart: “Calculus” Cengage Publications, 7
th
Ed., 2019

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