BIPH 6102  - NUMERICAL METHODS FOR BIOMEDICAL APPLICATIONS

Course Description

The development of powerful digital computers with fast processing speeds has encouraged the use of numerical methods and simulation in problem-solving by vastly increasing the range of mathematical calculations which can be conveniently performed. Numerical methods are techniques by which a variety of real-life problems are formulated so that they can be solved using arithmetic operations. The choice of the particular formula or algorithm or model has a marked influence not only on the computer programming but also on how the final results obtained are understood. As such, this course will give the student a thorough grounding in the use of computers, and the variety of computational tools and routines used in Medical Physics research and problem solving.

Course Aims

The primary aims of the course are to enable students to develop a thorough understanding of the computational tools and routines required for advanced studies in Pure and Applied Physics. In addition, students will concentrate on the programming of specific physical problems rather than learning abstract techniques so as to engender an environment of learning by doing. These techniques when acquired by students will produce graduates with good critical thinking and problem-solving skills who will be able to effectively select the appropriate computational technique, develop algorithms in order to analyse or simulate problems in Medical Radiation Science and interpret the results generated. Lastly, we aim to develop an overview of various commercial software packages and libraries to enable students to make intelligent use of these products.

Course Learning Outcomes

At the end of the course the students will be able to:

1. Explain the concepts and principles involved in the use of various computational techniques.
2. Demonstrate the use of a particular formula or algorithm for the simulation of a problem.
3. Explain how formulae determine the programming process in understanding final results.
4. Develop algorithms to efficiently and effectively solve problems drawn from different areas of medical physics.

Course Content

Introduction to MATLAB, Mathematica and/or Maple, Complex variables, Matrices and matrix manipulation, Vectors, Roots of polynomials and curve fitting, Error analysis, Interpolation: liner and cubic splines etc., Methods for solving differential equations: Euler’s method, Runge-Kutta method.

Assessment

Coursework                                    100%