Assignments from MTH373 Scientific Computing taken by Dr. Kaushik Kalyanaraman at IIIT Delhi in Monsoon 2018
This is an overview course in discretizations of continuous mathematics that is offered to 3rd and 4th year undergraduate, and postgraduate students. The course is structured to systematically build on and provide an overview of several ideas and topics that comprise the basics of discretizations of continuous mathematics. In this setup, we will concern ourselves with computational as well as stability analyses of both methods and algorithms.
We will begin with an introduction to scientific computing. Then we will analyze and study methods in numerical linear algebra: matrix factorizations, direct solution of linear systems, solutions of linear least square problems, and solutions to eigenvalue problems.
This will be followed by solutions of nonlinear equations in 1d and then more generally. We will apply this learning to unconstrained optimization in 1d and again more generally. We will also delve into some constrained optimization and nonlinear least squares problems.
The next part of the course will discuss polynomial interpolation (including using splines) of discrete data in 1d. This will be utilized in methods for numerical differentiation of sampled data, and for numerically carrying out integration in 1d (also known as quadrature).
- Python 3.5+
- Numpy
- Pandas
- matplotlib
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