Introduction to Undergraduate Mathematics
This course is aimed at students undertaking an undergraduate degree which will involve mathematics and, in particular, calculus. The focus is mainly on an introduction to trigonometry and calculus, both of which are central to all physical sciences and form the basis of most first year mathematics courses. The course is ideal as a refresher for students who may have studied mathematics at this level previously.
Competency in simple arithmetic and algebra is a prerequisite for this course. Students are expected to be able to manipulate fractions, surds and indices, and solve simple equations including simultaneous and quadratic equations. Students wishing to take the course, but without these competencies, are strongly advised to consider taking the preliminary course Foundation Mathematics beforehand.
Topics to be covered include:
- Review of algebra, including algebraic fractions
- Trigonometry: in right triangles, on the circle, sine and cosine rules, radians, graphing, identities
- Differentiation: definition, product rule, quotient rule, chain rule, common functions
- Exponential and Natural Logarithm
- Applications of calculus to dynamics, optimisation and graphing, exponential growth and decay
- Integration: definition and fundamental theorem of calculus, method of substitution
Note: Students will require a Scientific Calculator for the course.