Topics to be covered before mid sem
Complex analysis
(21st-25th July, 28th July-1st August; 1 extra class)
Complex functions,
Derivative of complex valued functions,
Analytic function,
Cauchy- Riemann equations,
Harmonic functions, Harmonic conjugates
Conformal mapping
Linear fractional Transformations
Complex Integration
(4th August-8th August, 11th August-14th August; 1 extra class)
Line integral in the Complex plane,
Cauchy’s integral theorem,
Cauchy’s integral formula,
Taylor series, Maclaurin series, Laurent series,
Singularities and Zeros,
Residue theorem,
Evaluation of real Integrals.
Vector spaces
(18th August-22nd August, 25th August-29th August)
Vector spaces,
Subspaces,
Basis and Dimension,
Linear transformations,
Kernels and images,
Matrix representation of linear transformation,
No classes in 1st week of September
2nd and 3rd weeks of September are for
mid sem exams
Topics to be covered after mid sem
Inner product spaces
(22nd September-26th September; 1 extra class)
Inner product spaces,
Norm (and Normed spaces),
Orthonormal bases,
Gram Schmidt orthogonalization.
No classes in 4th week of September/1st Week of October
Solution of algebraic and transcendental equations
(6th October-10th October)
Fixed point iteration method,
Regula-Falsi method,
Newton Raphson method.
Iterative methods to solve linear system (13th October-17th October; only 2 classes)
Gauss Jacobi method,
Gauss Seidel method.
No classes in 4th week of October
(Tatthva break)
Numerical integration
(27th October-31st October; only 2 classes)
Trapezoidal method
Simpson’s method
Numerical solution of ODEs
(3rd November-7th November; only 2 classes)
Euler's method,
modified Euler's method,
Runge-Kutta methods.
No classes on 2nd Week on November
3rd and 4th weeks of November are for
End sem exams