This course explores how calculus and linear algebra problems can be solved, at least in an approximated form, using numerical methods. As such, the subject has very broad applications in applied mathematics, physics, engineering, social and life sciences. Topics covered in this course include algorithms for solving linear and nonlinear equations, least squares problems, interpolation, numerical quadrature, ordinary and partial differential equations. Theory and practical examples are combined to study these topics.
Python will be used as a tool for implementing the numerical methods and is necessary for all the weekly homework assignments and for the final project. Though students do not need to possess any previous skills in Python, they are expected to familiarize themselves on the basics of this language. For these purpose, students are required to install the Jupyter Notebook application on their computers so that they might be able to use computations (most of which will be already coded and provided by the professor). In the first three weeks of the course, students will be guided through the use of Python, as well as the required installation and use of Jupyter Notebooks.
Course textbook: Sauer, T., Numerical Analysis, 2nd Edition, Pearson, 2014.
https://nyuad.nyu.edu/en/academics/divisions/science/faculty/moses-boudourides.html