#### Integral Equations (Code-09050504)

S.No. |
Topic |
Domain |
Hours as per UGC |

1 | · Linear integral equations, Some basic Identities | Must know | 10 |

· IVP reduced to Volterra IEs | |||

· Method of successive approximation to solve Volterra IEs of second kind | |||

· Iterated kernels and Neumann series for Volterra equation | |||

· Resolvent kernel as a series in □ | |||

· Laplace transform method for a difference kernel | |||

· Solution of a Volterra IE of the first kind | |||

2 | · Boundary value problem reduced to Fredholm IEs | Must know | 15 |

· Method of successive approximation to solve Fredholm equation of second kind | |||

· Iterated kernels and Neumann series for Fredholm equations | |||

· Resolvent kernel as a sum of series | |||

· Ferdholm resolvent kernel as a ratio of two series | |||

· Fredholm equations with degenerate kernel | |||

· Approximation of a kernel by a degenerate kernel | |||

· Fredholm Alternative | |||

3 | · Green’s functions | Must know | 15 |

· Use of method of variation of parameters to construct the Green’s function for a non-homogeneous linear second degree BVP | |||

· Basic four properties of the Green’s function | |||

· Alternate procedure for construction of the Green’s function by using its basic four properties | |||

· Method of series representation of the Green’s function in terms of the solutions of the associated homogeneous BVP | |||

· Reduction of a BVP to a Fredholm IE with kernel as a Green’s function | |||

4 | · Homogeneous Fredholm equations with symmetric kernels | Must know | 13 |

· Solution of Fredholm equations of the second kind with symmetric kernel | |||

· Method of Fredholm Resolvent Kernel | |||

· Method of iterated kernels | |||

· Fredholm Equations of the first kind with symmetric Kernels |

Books Recommended:

- Jerri, A.J., Introduction to Integral Equations with Applications.
- Polyanin, A. D., Manzhirov, A.V., Handbook of Integral Equations, CRC Press.
- Kondo, J., Integral Equations, Oxford Applied Mathematics and Computing Scinnce Series.