Laplace Transform:
Definition and Laplace transforms of elementary functions (statements only). Laplace transforms of Periodic functions (statement only) and unit-step function – problems.
Inverse Laplace Transform:
Definition and problems, Convolution theorem to find the inverse Laplace transforms (without Proof) and problems. Solution of linear differential equations using Laplace transforms.
Fourier Series:
Periodic functions, Dirichlet’s condition. Fourier series of periodic functions period 2π and arbitrary period. Half range Fourier series. Practical harmonic analysis.
Fourier Transforms:
Infinite Fourier transforms, Fourier sine and cosine transforms. Inverse Fourier transforms. Problems.
Difference Equations and Z-Transforms:
Difference equations, basic definition, z-transform-definition, Standard z-transforms, Damping and shifting rules, initial value and final value theorems (without proof) and problems, Inverse z-transform and applications to solve difference equations.
Numerical Solutions of Ordinary Differential Equations(ODE’s):
Numerical solution of ODE’s of first order and first degree- Taylor’s series method, Modified Euler’s method. Runge -Kutta method of fourth order, Milne’s and Adam-Bash forth predictor and corrector method (No derivations of formulae)-Problems.
Numerical Solution of Second Order ODE’s:
Runge-Kutta method and Milne’s predictor and corrector method. (No derivations of formulae).
Calculus of Variations:
Variation of function and functional, variational problems, Euler’s equation, Geodesics, hanging chain, problems.
Course outcomes:
At the end of the course the student will be able to:
• CO1: Use Laplace transform and inverse Laplace transform in solving differential/ integral equation arising in network analysis, control systems and other fields of engineering.
• CO2: Demonstrate Fourier series to study the behaviour of periodic functions and their applications in system communications, digital signal processing and field theory.
• CO3: Make use of Fourier transform and Z-transform to illustrate discrete/continuous function arising in wave and heat propagation, signals and systems.
• CO4: Solve first and second order ordinary differential equations arising in engineering problems using single step and multistep numerical methods.
• CO5:Determine the externals of functionals using calculus of variations and solve problems arising in dynamics of rigid bodies and vibrational analysis.
Question paper pattern:
• The question paper will have ten full questions carrying equal marks.
• Each full question will be for 20 marks.
• There will be two full questions (with a maximum of four sub- questions) from each module.
• Each full question will have sub- question covering all the topics under a module.
• The students will have to answer five full questions, selecting one full question from each module.
Textbooks
1 Advanced Engineering Mathematics E. Kreyszig John Wiley & Sons 10th Edition, 2016
2 Higher Engineering Mathematics B. S. Grewal Khanna Publishers 44th Edition, 2017
3 Engineering Mathematics Srimanta Pal et al Oxford University Press 3 rd Edition, 2016
Reference Books
1 Advanced Engineering Mathematics C. Ray Wylie, Louis C. Barrett McGraw-Hill Book Co 6 th Edition, 1995
2 Introductory Methods of Numerical Analysis S.S.Sastry Prentice Hall of India 4 th Edition 2010
3 Higher Engineering Mathematics B.V. Ramana McGraw-Hill 11th Edition,2010
4 A Textbook of Engineering Mathematics N.P.Bali and Manish Goyal Laxmi Publications 6 th Edition, 2014
5 Advanced Engineering Mathematics Chandrika Prasad and Reena Garg Khanna Publishing, 2018
Web links and Video Lectures:
1. http://nptel.ac.in/courses.php?disciplineID=111
2. http://www.class-central.com/subject/math(MOOCs)
3. http://academicearth.org/
4. VTU EDUSAT PROGRAMME - 20