## Mathematics-I for Electrical & Electronics Engineering Stream

### Module-1

Calculus: Introduction to polar coordinates and curvature relating to EC & EE Engineering applications.Polar coordinates, Polar curves, angle between the radius vector and the tangent, angle between two curves. Pedal equations. Curvature and Radius of curvature - Cartesian, Parametric, Polar and Pedal forms. Problems.

Self-study: Center and circle of curvature, evolutes and involutes.

Applications: Communication signals, Manufacturing of microphones, and Image processing.

### Module-2

Series Expansion and Multivariable Calculus: Introduction of series expansion and partial differentiation in EC & EE Engineering applications.Taylor’s and Maclaurin’s series expansion for one variable (Statement only) – problems.Indeterminate forms - L’Hospital’s rule - Problems.Partial differentiation, total derivative - differentiation of composite functions. Jacobian and problems. Maxima and minima for a function of two variables. Problems.

Self-study: Euler’s Theorem and problems. Method of Lagrange’s undetermined multipliers with single constraint.

Applications: Series expansion in communication signals, Errors and approximations, and vector calculus.

### Module-3

Ordinary Differential Equations (ODEs) of First Order :Introduction to first-order ordinary differential equations pertaining to the applications for EC & EE engineering. Linear and Bernoulli’s differential equations. Exact and reducible to exact differential equations Integrating factors on 1/𝑁(𝜕𝑀/𝜕𝑦 −𝜕𝑁/𝜕𝑥) 𝑎𝑛𝑑 1/𝑀(𝜕𝑁/𝜕𝑥 −𝜕𝑀/𝜕𝑦). Orthogonal trajectories, L-R and C-R circuits.Problems.Non-linear differential equations: Introduction to general and singular solutions, Solvable for p only, Clairaut’s equations,reducible to Clairaut’s equations.Problems.

Self-Study: Applications of ODEs, Solvable for x and y.

Applications of ordinary differential equations: Rate of Growth or Decay, Conduction of heat.

### Module-4

Integral Calculus:Introduction to Integral Calculus in EC & EE Engineering applications. Multiple Integrals: Evaluation of double and triple integrals, evaluation of double integrals by change of order of integration, changing into polar coordinates. Applications to find Area and Volume by double integral.Problems. Beta and Gamma functions: Definitions, properties, relation between Beta and Gamma functions. Problems.

Self-Study: Volume by triple integration, Center of gravity.

Applications: Antenna and wave propagation, Calculation of optimum power in electrical circuits,field theory.

### Module-5

Linear Algebra: Introduction of linear algebra related to EC & EE engineering applications.Elementary row transformationofa matrix, Rank of a matrix. Consistency and Solution of system of linear equations - Gauss-elimination method, Gauss-Jordan method and approximate solution by Gauss-Seidel method. Eigenvalues and Eigenvectors, Rayleigh’s power method to find the dominant Eigenvalue and Eigenvector.

Self-Study: Solution of system of equations by Gauss-Jacobi iterative method. Inverse of a square matrix by Cayley- Hamilton theorem

Applications of Linear Algebra: Network Analysis, Markov Analysis, Critical point of a network system. Optimum solution.

List of Laboratory experiments

10 lab sessions + 1 repetition class + 1 Lab Assessment

1 2D plots for Cartesian and polar curves

2 Finding angle between polar curves, curvature and radius of curvature of a given curve

3 Finding partial derivatives and Jacobian

4 Applications to Maxima and Minima of two variables

5 Solution of first-order ordinary differential equation and plotting the solution curves

6 Program to compute area, volume and centre of gravity

7 Evaluation of improper integrals

8 Numerical solution of system of linear equations, test for consistency and graphical representation

9 Solution of system of linear equations using Gauss-Seidel iteration

10 Compute eigenvalues and eigenvectors and find the largest and smallest eigenvalue by Rayleigh power method.

Suggested software’s: Mathematica/MatLab/Python/Scilab

Suggested Learning Resources:

Books (Title of the Book/Name of the author/Name of the publisher/Edition and Year)

Text 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,3rd Ed., 2016.

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

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

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

6. H. K. Dass and Er. Rajnish Verma: “Higher Engineering Mathematics” S. ChandPublication, 3rd Ed., 2014.

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

8. David C Lay: “Linear Algebra and its Applications”, Pearson Publishers, 4th Ed., 2018.

9. Gareth Williams: “Linear Algebra with Applications”, Jones Bartlett Publishers Inc., 6th Ed., 2017.

10. Gilbert Strang: “Linear Algebra and its Applications”, Cengage Publications, 4th Ed. 2022.

Web links and Video Lectures (e-Resources):

 http://nptel.ac.in/courses.php?disciplineID=111

 http://www.class-central.com/subject/math(MOOCs)