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Integral equations (4
weeks): Relations between differential
and integral equations, Fredholm and Volterra
equations: classification, Fredholm equations
with separable kernels, Neumann series,
Hilbert- Schmidt theory
1st
Midterm exam
Series
and Integral transforms (2 weeks) :
Fourier series, Fourier and Laplace
transforms.
The
Green's function (3 weeks) : Relation
between integral equations and Green’s
function, Alternative definition of Green’s
function, Illustrative examples.
2nd
Midterm exam
Calculus
of variations ( 4 weeks) : A dependent
and independent variable, Applications of
Euler equation,
Several dependent variables, Several
independent variables, Several dependent and
independent variables, Lagrange multipliers,
Variation with constraints.
3th
Midterm exam
Introduction to
group theory (1 week)
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