Integral Equations (Optional Paper)
Paper Code:
MAT 425
Credits:
5
Contact Hours:
75.00
Max. Marks:
100.00
Unit I:
I
15.00
Linear integral equations– Definition and classification. Conversion of initial and boundary value problems to an integral equation. Eigen values and Eigen functions. Solution of homogeneous and general Fredholm integral equations of second kind with separable kernels.
Unit II:
II
15.00
Solution of Fredholm and Volterra integral equations of second kind by methods of successive substitutions and successive approximations. Resolvent kernel and its results. Conditions of uniform convergence and uniqueness of series solution.
Unit III:
III
15.00
Solution of Volterra integral equations of second kind with convolution type kernels by Laplace transform. Solution of singular integral equations by Fourier transform.
Unit IV:
IV
15.00
Integral equations with symmetric kernels– Orthogonal system of functions. Fundamental properties of eigen values and eigen functions for symmetric kernels. Expansion in eigen functions and bilinear form.
Unit V:
V
15.00
Hilbert-Schmidt theorem. Solution of Fredholm integral equations of second kind by using Hilbert-Schmidt theorem.Classical Fredholm theory– Fredholm theorems. Solution of Fredholm integral equation of second kind by using Fredholm first theorem.
Essential Readings:
- Shanti Swaroop Integral Equations ( Krishna Publication Meerut)
- William Vernon Lovitt., Linear Integral Equations, Dover Publication.
- A. D. Polyanin and A. V. Manzhirov, Handbook of Integral Equations, Second Edition,Chapman & Hall/CRC Press, Boca Raton,
Academic Year:
