Mathematical Models with Applications

Course Coordinator: Dr. Tony MT Chan, Grad Dip, MPhil (CUHK), PhD (CityU)

Course Developer: The Open University, UK, Course Team

This course is about the use of mathematics and mathematical models to solve real-life problems. It will be of particular interest to you if you use mathematics or mathematical reasoning in your work or study. Half of the course material deals with Newtonian mechanical modeling of the motion of moving objects. The other half of the course is concerned with non-mechanical models, such as the modelling of heat transfer and population dynamics. The methods that you will need are differential equations and calculus. The teaching is supported and enhanced by the computer algebra package MathCAD. This course is compulsory to the programmes of Electronics and Mathematics degrees.

This course is presented at 18-month intervals.

Advisory prerequisite(s)
You are advised to have already studied the foundation mathematics courses MATH S121 and MATH S122.

Aims
This course aims to:

• Teach mathematical modelling skills;
• Develop learners' concepts and skills in applying mathematical methods;
• Give learners an opportunity to explore mathematics using computer software;
• Enhance learners' abilities in analysis, exploration and manipulation of mathematical modelling techniques.

Contents
The course covers the following topics:

• Statics and dynamics
• Newton's laws of motion
• Oscillations and energy
• Modelling with non-linear differential equations
• Modelling motion in two and three dimensions
• Modelling heat transfer
• Interpretation of mathematical models
• Dampening, force and resonance
• Normal modes
• Systems of particles
• Circular motion
• Rotating bodies and angular momentum

Learning support
There will be about 12 tutorials and four regular surgeries during the presentation.

Assessment
There will be four assignments and a final examination. Students are required to submit assignments via the Online Learning Environment (OLE).

Online requirement
This course is supported by the Online Learning Environment (OLE). You can find the latest course information from the OLE. Through the OLE, you can communicate electronically with your tutor and the Course Coordinator as well as other students. To access the OLE, students will need to have access to the Internet. The use of the OLE is required for the study of this course and you can use it to submit assignments.

Equipment
Students will need access to a computer with a DVD drive, and a scientific calculator.

To ensure successful MathCAD installation, your computer needs to have the minimum requirements:

• English Windows XP or higher
• Pentium-compatible 32-bit (x86) or 64-bit (x86-64, EM64T) processor
• 256 MB RAM or more
• 550 MB of free hard disk space or more
• Internet Explorer 6.0 or later
• Adobe Reader 5.0 or later
• DVD drive
• SVGA or higher graphics card and monitor
• A printer (optional)

Software
For this course students will use the software MathCAD 14, which is supplied as part of the course material. The computing packages running in MathCAD will be supplied to students.

Set book(s)
There are no set books for this course.

Students with disabilities or special educational needs
If you have a physical disability, then you should consult with the Course Coordinator regarding the computing component.