#### 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:**

- 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,*2^{nd}, John Wiley and Sons, India 2004, - S. Hillier and G.J. Lieberman
*, Introduction to**Operations Research*, 9^{th}Ed., Tata McGraw Hill Singapore, 2009. - Hamdy A. Taha,
*Operations Research,*Introduction, 8^{th}Prentice-Hall India, 2002. - G Hadley
*Linear Programming*, Narosa Publishing House, New Delhi, 2002.