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Title OPERATIONAL RESEARCH-I  (Code-09050506)

S.No. Content of the topics Learning        Objectives Teaching Guidelines Methodology Time                         (Hours)
1 1.Linear integral equations, Some basic Identities Student will understand the IEs and its types Lecture should be effective so that student will be able to grasp the topics easily Assignments/Seminars/ Class Tests/ Presentations 10
2.IVP reduced to Volterra IEs
3.Method of successiveapproximation to solve Volterra IEs of second kind
4.Iterated kernels and Neumann series for Volterra equation
5.Resolvent kernel as a series in □
6.Laplace transform method for a difference kernel
7.Solution of a Volterra IE of the first kind
2 1.Boundary value problem reduced to Fredholm IEs Student will be able to understand boundary value problems, resolvent kernel and Fredholm kernel Lecture should be effective so that student will be able to grasp the topics easily Assignments/Seminars/ Class Tests/ Presentations 15
2.Method of successiveapproximation to solve Fredholm equation of second kind
3.Iterated kernels and Neumann series for Fredholm equations
4.Resolvent kernel as a sum of series
5.Ferdholm resolvent kernel as a ratio of two series
6.Fredholm equations with degenerate kernel
7.Approximation of a kernel by a degenerate kernel
8.Fredholm Alternative
3 1.Green’s functions Student will be able to understand Green’s function and its application in solving non-homogeneous BVP Lecture should be effective so that student will be able to grasp the topics easily Assignments/Seminars/ Class Tests/ Presentations 15
2.Use of method of variation of parameters to construct the Green’s function for a non-homogeneous linear second degree BVP
3.Basic four properties of the Green’s function
4.Alternate procedure for construction of the Green’s function by using its basic four properties
5.Method of series representation of the Green’s function in terms of the solutions of the associated homogeneous BVP
6.Reduction of a BVP to a Fredholm IE with kernel as a Green’s function
4 1.Homogeneous Fredholm equations with symmetric kernels Student will be able to understand the applications of Fredholm IEs Lecture should be effective so that student will be able to grasp the topics easily Assignments/Seminars/ Class Tests/ Presentations 13
2.Solution of Fredholm equations of the second kind with symmetric kernel
3.Method of Fredholm Resolvent Kernel
4.Method of iterated kernels
5.Fredholm Equations of the first kind with symmetric Kernels

Books Recommended:

  1. Sharma, J. K., Mathematics Model in Operations Research, Tata McGraw Hill.
  2. H.A. Operations Research – An Introduction.
  3. Kanti Swarup,  Gupta,  K. And Manmohan. Operations Research.
  4. Gupta,  K. And Hira, D. S.  Operation  Research, S. Chand & Co.
  5. D Sharma Imtroduction to Operations Research.
  6. Mokhtar S. Bazaeaa, John J. Jarvis and Hanif D. Sherali ,Linear Programming and Network Flows, 2nd, John Wiley and Sons, India 2004,
  7.      S. Hillier and G.J. Lieberman, Introduction to Operations Research, 9th Ed., Tata McGraw Hill Singapore, 2009.
  8. Hamdy A. Taha, Operations Research, Introduction, 8th Prentice-Hall India, 2002.
  9. G Hadley Linear Programming, Narosa Publishing House, New Delhi, 2002.

 

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