Monash College Unit Guide

FUNCTIONS AND THEIR APPLICATIONS (MCD2130)

Purpose

The focus of this unit will be on the behaviour of functions and examining some of their applications to the real world. The way that functions will be introduced is by individually describing the characteristics of families of different function types (linear, polynomial, rational, exponential, logarithmic and trigonometric). The composition of functions through possible combination of different types of component functions will also be investigated. Computer algebra software will be introduced to investigate function patterns and determine appropriate models for real-life problems. Other operations on functions such as transformations via shifting, scaling and reflection will be presented, along with the existence and meaning of inverse functions.

This initial part of the course will then be used to provide a foundation for examining the rate of change of a function. Principally this involves defining the elementary principles of differential calculus and then utilising these with respect to the types of functions mentioned above. As a final topic an introduction to integral calculus is presented.

Prerequisites

Nil.

Learning outcomes

On completion of this subject, students will have acquired knowledge of:

1. The notions of function and their representation as tables, graphs or mathematical expressions;
2. Basic characteristics of linear, polynomial, rational, exponential, logarithmic and trigonometric functions;
3. The algebra of functions;
4. Methods of transformations of a function and finding inverse functions;
5. The notion of rate of change of a function;
6. Finding the anti-derivative of a function and using its main application: The Fundamental Theorem of Calculus.
7. And will have developed skills in:
8. Identifying different types of functions and mathematically analysing their behaviour;
9. Creating graphs illustrating important characteristics of a function (by hand or on a computer algebra system);
10. Being able to interpret transformations of a function and to be able to find the inverse of a function (with the notable exception of inverse trigonometric functions as they are not currently on the syllabus);
11. Basic techniques of The Calculus;
12. Forming a LOGICAL progression of thought.

Assessment

Assesment will consist of

• Three assignments, each worth 7%, 7% and 6 % respectively (a total of 20%).
• Tutorial work (a total of 10%).
• Diagnostic online quizzes to be completed weekly, beginning from week 3 of the Semester (a total of 10% ).
• Final exam (a total of 60% ). Students must pass the final exam in order to be granted a pass in the subject.

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