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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.