Mathematical Methods MA 575 (Elective Course for M. Sc 2^{nd} Yr. and B.Tech. 4th Yr. students)
Three one-hour lectures per week: 6 credits
Class Timing: 09:00-9:55, Wednesday; 10:00-10:55, Thursday; 11:00-11:55, Friday
Reserve Slot: 08:00-08:55, Tuesday.
Room Number: 1104
First Day of Instruction: Thursday, July 28, 2017
Last day of Instruction: Wednesday, November 22, 2017
Course Instructor: Swaroop Nandan Bora
Office: E-306 or HOD Chamber (SNB)
Phone: 2604 and 2601
Email: swaroop@iitg.ernet.in
Change of time-table:
Classes with Tuesday time-table |
17 August 2017, Thursday |
Classes with Thursday Time table |
17 October 2017, Tuesday |
NO Classes |
25 (Monday)-27 (Wednesday) September, 2017 |
Course Contents:
Total number of lectures: 42
Power series solutions, Bessel functions, Modified Bessel functions, Legendre polynomial, Laguerre polynomial, Chebyshev polynomial, Hermite polynomials: recurrence relations, orthogonality. (Tentative 14 lectures)
Concept and calculation of Green's function, Properties, Green's function method for ordinary and partial differential equations. (Tentative 6 lectures)
Fourier Series, Fourier Cosine series, Fourier Sine series, Fourier integrals. Fourier transform, Laplace transform, Hankel transform, finite Hankel transform, Mellin transform. Solution of differential equations by integral transform methods. (Tentative 14 lectures)
Construction of the kernels of integral transforms on a finite interval through Sturm-Liouville problem Occurrence of integral equations, Regular and singular integral equations: Volterra integral equations, Fredholm integral equations, Volterra and Fredholm equations with different types of kernels (Tentative 8 lectures)
Suggested Books:
Plan of the course:
Important Dates:
*Quiz I: Wednesday, August 29, 2017 (15 Marks)
Mid Semester Exam: 14:00-16:00 hrs, Friday, September 22, 2017
*Quiz II: Wednesday, November 1 (15 Marks) - Tentative
End Semester Exam: 14:00-17:00 hrs, Tuesday, November 28, 2017
*Total of quizzes will be scaled to 25 marks.