MA40002: Integral Equations And Variational Methods
| MA40002 | |||||||||||||||||||||||||||
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| Course name | Integral Equations And Variational Methods | ||||||||||||||||||||||||||
| Offered by | Mathematics | ||||||||||||||||||||||||||
| Credits | 4 | ||||||||||||||||||||||||||
| L-T-P | 3-1-0 | ||||||||||||||||||||||||||
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| Semester | Spring | ||||||||||||||||||||||||||
Syllabus
Syllabus mentioned in ERP
Prerequisite: voidIntegral Equations: Basic concepts, Volterra integral equations, relationship between linear differential equations and Volterra equations, resolvent kernel, method of successive approximations, convolution type equations, Volterra equation of the first kind. Abel s integral equation. Fredholm integral equations, Fredholm equations of the second kind, the method of Fredholm determinants, iterated kernels, integral equations with degenerate kernels, eigen values and eigen functions of a Fredholmalternative, construction of Green s function for BVP, singular integralequations.Calculus of Variations: Euler - Lagrange equations, degenerate Euler equations, Natural boundary conditions, transversality conditions, simple applications of variational principle, sufficient conditions for extremum. Variational formulation of BVP, minimum of quadratic functional. Approximate methods Galerkin s method, weighted-residual methods, Colloation methods. Variational methods for time dependent problems.