The unit will develop the tools of calculus including multivariable calculus that will then be applied to real-world problems. Wherever possible the computer-algebra software system will be used to facilitate the applications. The emphasis will be on the development of powerful mathematical tools to analyse and solve problems from various scientific and engineering fields. The unit will cover: Introduction to multivariable calculus: functions of several variables, derivative maps, inverse function theorem, implicit function theorem, multiple integrals; Introduction to differential equations: systems of linear ordinary differential equations, nonlinear ordinary differential equations, dynamical systems; Applications may include: Lorenz model of the atmosphere, fluid dynamics and earth?s magnetic field, Lotka-Volterra model, chemical kinetics, predator-prey models in population biology, elementary theoretical mechanics, celestial mechanics, elementary quantum mechanics, Maxwell theory, problems in engineering and applied mathematics such as control theory. The unit provides students with a sound knowledge of mathematical principles and ideas in modern science. It also provides the students with the essential skills for mathematical modelling.

Learning outcomes

On successful completion of this unit, students will be able to:
1. Demonstrate understanding of powerful mathematical tools such as calculus of several variables, differential equations and elementary dynamical systems theory;
2. Compute with these tools, manually and with mathematical software;
3. Apply these tools to mathematically analyse and solve contemporary problems of both theoretical and practical importance;

4. Recognise the power of mathematical modelling and analysis and be able to apply their understanding to their further studies.

Graduate attributes

1. UC graduates are professional - employ up-to-date and relevant knowledge and skills
1. UC graduates are professional - use creativity, critical thinking, analysis and research skills to solve theoretical and real-world problems
3. UC graduates are lifelong learners - adapt to complexity, ambiguity and change by being flexible and keen to engage with new ideas

Prerequisites

Mathematical Methods.

Corequisites

None.

Equivalent units

None.

Assumed knowledge

None.