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