Program Overview

Programming Techniques in Applied Mathematics II

Course Description

The course covers a range of topics including review of programming and toolboxes, packages, modules, iterative linear algebra problems, root finding programs, recursive functions and algorithms, optimisation algorithms, data fitting and interpolation, extrapolation, numerical integration, and numerical solutions of differential equations.

Course Objectives

At the end of this course, the student will learn:

• how to solve linear algebra equations
• how to solve root finding problems in different fields
• recursive algorithms
• how to solve optimisation problems
• data analysis tools and data description
• numerical integration methods to calculate integrals involved in applied mathematics
• how to numerically solve initial as well as boundary value problems in differential equations

Course Learning Outcomes

Student, who passed the course satisfactorily will be able to:

• understand basic problems in applied mathematics
• be aware of possible ways to solve problems from different fields
• analyse and interpret data from measurements or observations
• numerically solve basic optimisation problems
• numerically solve basic differential equations

Tentative Weekly Outline

• Review of Programming and Toolboxes, Packages, Modules
• Iterative Linear Algebra Problems
• Root Finding Problems
• Recursive Functions and Algorithms
• Optimisation Algorithms
• Data Fitting and Interpolation (and Extrapolation)
• Numerical Integration
• Numerical Solutions of Differential Equations: IVPs and BVPs
• Selected Topics: algorithms and coding distinctively from
  • Actuarial Sciences
  • Cryptography
  • Financial Mathematics
  • Scientific Computing

Course Textbook(s)

• Tobin A. Driscoll, Learning MATLAB, SIAM, 2009
• Tobias Oetiker, Hubert Partl, Irene Hyna and Elisabeth Schlegl, The Not So Short Introduction to LaTeX 2e, 2016