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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:

  1. Jerri, A.J., Introduction to Integral Equations with Applications.
  2. Polyanin, A. D., Manzhirov, A.V., Handbook of Integral Equations, CRC Press.
  3. Kondo, J., Integral Equations, Oxford Applied Mathematics and Computing Scinnce Series.
Admissions Open 2019-20