AV Mathematics-III for EC Engineering (BMATEC301)

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:

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