MA3105 is an 4-credit elective offered to third year students by the Department of Mathematics and Statistics(DMS) at IISER Kolkata. It focuses on computational numerical analysis which has immense applications in various fields.
It encompasses the following aspects-
-
Interpolation: Newtons forward, backward and divided difference formulae; Lagranges method; Gauss, Stirling and Bessels formulae; spline interpolation.
-
Solution of Systems of Linear Equations: Gauss elimination method, Thomas algorithm, Gauss-Jacobi and Gauss-Seidel methods.
-
Eigenvalues and Eigenvectors: Power method, Jacobis method, Givens method, Householders method.
-
Solution of Non-linear Equations: Bisection method, fixed point iteration, Newton-Raphson, secant and regula-falsi methods.
-
Solution of System of Non-linear equations: Fixed-point method and Newtons method.
-
Numerical Differentiation: Formulae based on Newtons forward, backward, divided difference, and Lagranges formulae.
-
Numerical Integration: Trapezoidal rule, Simpsons 1/3rd and 3/8th rules, Weddles rule, quadrature formulae based on Stirlings and Bessels interpolation formulae.
-
Solution of Differential Equations: Taylors series method, Picards method and Runge-Kutta methods (1st, 2nd and 4th orders) for solving ODEs.
The course assumes a background in Linear Algebra and Analysis. Find out more about the course here
These are my submissions for the same.