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Courses » Mathematical methods and its applications

Mathematical methods and its applications


ABOUT THE COURSE

This course is a basic course offered to UG student of Engineering/Science background. It contains ODE,PDE, Laplace transforms, Z-transforms, Fourier series and Fourier transforms. It plays an important role for solving various engineering sciences problems.Therefore, it has tremendous applications in diverse fields in engineering sciences. 

INTENDED AUDIENCE 

UG students of technical universities/colleges.

It is a core course for UG.

PRE-REQUISITES

Nil

INDUSTRIES THAT WILL RECOGNIZE THIS COURSE

Nil

COURSE INSTRUCTORS

           

Dr. P. N. Agrawal is a Professor in the Department of Mathematics, IIT Roorkee. His area of research includes approximation Theory and Complex Analysis. He delivered 13 video lectures on Engineering Mathematics in NPTEL Phase I and recently completed Pedagogy project on Engineering Mathematics jointly with Dr. Uaday Singh in the same Department. He has taught Engineering Mathematics II course many times and also worked as the course co-coordinator. He has supervised nine Ph.D. theses and has published 143 research papers in reputed international journals of the world.


 

Dr. S. K. Gupta is an Associate Professor in the Department of Mathematics, IIT Roorkee. His area of expertise includes nonlinear and non-convex optimization. He has taught Engineering Mathematics-II  many times and also acted as a coordinator of the course. He has guided two PhD theses and has published more than 30 papers in various international journals of repute.


COURSE PLAN 

Week 1: 
Introduction to linear differential equations ,Linear dependence, independence and Wronskian of functions,Solution of second-order homogeneous linear differential equations with constant coefficients-I,Solution of second-order homogeneous linear differential equations with constant coefficients-II,Method of undetermined coefficients 

Week 2:Methods for finding Particular Integral for second-order linear differential equations with constant coefficients-I,Methods for finding Particular Integral for second-order linear differential equations with constant coefficients-IIMethods for finding Particular Integral for second-order linear differential equations with constant coefficients-III,Euler-Cauchy equations,Method of reduction for second-order, linear differential equations

Week 3: Method of variation of parameters , Solution of second order differential equations by changing dependent variable, Solution of second order differential equations by changing independent variable,Solution of higher-order homogenous linear differential equations with constant coefficients, Methods for finding Particular Integral for higher-order linear differential equations

Week 4: Formulation of Partial differential equations, Solution of Lagrange’s equation-I, Solution of Lagrange’s equation-II,Solution of first order nonlinear equations-I,Solution of first order nonlinear equations--II

Week 5: Solution of first order nonlinear equations-III,Solution of first order nonlinear equations-IV,Introduction to Laplace transforms,Laplace transforms of some standard functions,Existence theorem for Laplace transforms

Week 6: Properties of Laplace transforms--I, Properties of Laplace transforms--II, Properties of Laplace transforms--III, Properties of Laplace transforms--IV, Convolution theorem for Laplace transforms--I

Week 7: Convolution theorem for Laplace transforms--II,Initial and final value theorems for Laplace transformsLaplace transforms of periodic functions, Laplace transforms of Heaviside unit step function,Laplace transforms of Dirac delta function

Week 8: Applications of Laplace transforms-I, Applications of Laplace transforms-II, Applications of Laplace transforms-III,   Z – transform and inverse Z-transform of elementary functions, Properties of Z-transforms-I

Week 9: Properties of Z-transforms-II, Initial and final value theorem for Z-transforms, Convolution theorem for Z- transforms, Applications of Z- transforms--I,Applications of Z- transforms-II

Week 10: Applications of Z- transforms--III, Fourier series and its convergence--I, Fourier series and its convergence--II, Fourier series of even and odd functions,Fourier half-range series

Week 11: Parsevel’s Identity, Complex form of Fourier series, Fourier integrals, Fourier sine and cosine integralsFourier transforms

Week 12: Fourier sine and cosine transforms,Convolution theorem for Fourier transforms,Applications of Fourier transforms to BVP-I,Applications of Fourier transforms to BVP-II,Applications of Fourier transforms to BVP-III

CERTIFICATION EXAM

The exam is optional for a fee. Exams will be on 23 April 2017.

Time: Shift 1: 9am - 12 noon 
          Shift 2: 2pm - 5pm

Any one shift can be chosen to write the exam for a course.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published.

CERTIFICATE

Final score will be calculated as : 25% assignment score + 75% final exam score
25% assignment score is calculated as 25% of average of Best 8 out of 12 assignments
E-Certificate will be given to those who register and write the exam and score greater than or equal to 40% final score. Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Roorkee. It will be e-verifiable at nptel.ac.in/noc.