Mathematics-II for Electrical & Electronics Engineering Stream
Course Code: BMATE201
CIE Marks:50
Course Type(Theory/Practical/Integrated)
Integrated SEE Marks:50
Total Marks:100
Teaching Hours/Week (L:T:P: S) 2:2:2:0
Exam Hours:03
Total Hours of Pedagogy 40 hours Theory + 10 to 12 Lab slots Credits:04
Module-1
Vector Calculus: Introduction to Vector Calculus in EC & EE engineering applications.Vector Differentiation: Scalar and vector fields. Gradient, directional derivative, curl and divergence - physical interpretation, solenoidal and irrotational vector fields. Problems. Vector Integration: Line integrals, Surface integrals. Applications to work done by a force and flux. Statement of Green’s theorem and Stoke’s theorem. Problems.
Self-Study: Volume integral and Gauss divergence theorem.
Applications: Conservation of laws, Electrostatics, Analysis of streamlines and electric potentials.
Click here to download Module-1
Module-2
Vector Space and Linear Transformations: Importance of Vector Space and Linear Transformations in the field of EC & EE engineering applications. Vector spaces: Definition and examples, subspace, linear span, Linearly independent and dependent sets, Basis and dimension. Linear transformations: Definition and examples, Algebra of transformations, Matrix of a linear transformation. Change of coordinates, Rank and nullity of a linear operator, Rank-Nullity theorem.Inner product spaces and orthogonality.
Self-study: Angles and Projections.Rotation, reflection, contraction and expansion.
Applications: Image processing, AI & ML, Graphs and networks, Computer graphics.
Click here to download Module-2
Module-3
Laplace Transform: Importance of Laplace Transform for EC & EE engineering applications. Existence and Uniqueness of Laplace transform (LT), transform of elementary functions, region of convergence. Properties–Linearity, Scaling, t-shift property, s-domain shift, differentiation in the sdomain, division by t, differentiation and integration in the time domain. LT of special functionsperiodic functions (square wave, saw-tooth wave, triangular wave, full & half wave rectifier), Heaviside Unit step function, Unit impulse function.Inverse Laplace Transforms:Definition, properties, evaluation using different methods, convolution theorem (without proof),problems, and applications to solve ordinary differential equations.
Self-Study: Verification of convolution theorem.
Applications: Signals and systems, Control systems, LR, CR & LCR circuits.
Click here to download Module-3
Module-4
Numerical Methods -1: Importance of numerical methods for discrete data in the field of EC & EE engineering applications. Solution of algebraic and transcendental equations: Regula-Falsi method and Newton-Raphson method (only formulae). Problems. Finite differences, Interpolation using Newton’s forward and backward difference formulae, Newton’s divided difference formula and Lagrange’s interpolation formula (All formulae without proof). Problems.Numerical integration: Trapezoidal, Simpson's (1/3)rd and (3/8)th rules(without proof). Problems.
Self-Study: Bisection method, Lagrange’s inverse Interpolation, Weddle's rule.
Applications: Estimating the approximate roots, extremum values, area, volume, and surface area.
Click here to download Module-4
Module-5
Numerical Methods -2:Introduction to various numerical techniques for handling EC & EE applications. Numerical Solution of Ordinary Differential Equations (ODEs): Numerical solution of ordinary differential equations of first order and first degree - Taylor’s series method, Modified Euler’s method, Runge-Kutta method of fourth order and Milne’s predictorcorrector formula (No derivations of formulae). Problems.
Self-Study: Adam-Bashforth method.
Applications: Estimating the approximate solutions of ODE for electric circuits.
Click here to download Module-5
Important Links:
1. Click here to download MQP with Solutions (To be Updated Soon)
2. Click here to download Star Making Questions-With Solutions(To be Updated Soon)
List of Laboratory experiments (2 hours/week per batch/ batch strength 15)
10 lab sessions + 1 repetition class + 1 Lab Assessment
1 Finding gradient, divergent, curl and their geometrical interpretation and Verification of Green’s theorem
2 Computation of basis and dimension for a vector space and Graphical representation of linear transformation
3 Visualization in time and frequency domain of standard functions
4 Computing inverse Laplace transform of standard functions
5 Laplace transform of convolution of two functions
6 Solution of algebraic and transcendental equations by Regula-Falsi and Newton-Raphson method
7 Interpolation/Extrapolation using Newton’s forward and backward difference formula
8 Computation of area under the curve using Trapezoidal, Simpson’s (1/3)rd and (3/8)th rule
9 Solution of ODE of first order and first degree by Taylor’s series and Modified Euler’s method
10 Solution of ODE of first order and first degree by Runge-Kutta 4th order and Milne’s predictor-corrector 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,3rdEd., 2016.
3. N.P Bali and Manish Goyal: “A Textbook of Engineering Mathematics” LaxmiPublications, 10thEd., 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 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.
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)
http://academicearth.org/
VTU e-Shikshana Program
VTU EDUSAT Program
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