## Availabilities:

Location Domestic International
Online Session 2 N/A

## Unit Summary

### Unit type

UG Coursework Unit

12

7

Intermediate

### Former School/College

Former School of Education

## Unit aim

Consolidates and expands a student's knowledge of the calculus of a single variable. Topics include functions and limits, techniques of differentiation, methods of integration and infinite series. Applications to a wide range of fields will be considered.

## Unit content

Functions and limits (Topic 1) - Exponential and logarithmic functions. Inequalities. Functions. Limits and their evaluation. Continuity

Differentiation (Topics 2 to 5) - The first derivative and rates of change. Formal definition of the derivative. Rules of differentiation. Second and higher order derivatives. Implicit differentiation. L'Hopital's rule. Mean Value theorem. Rolle's Theorem - Applications of differentiation

Integration (Topics 6 to 8) - Antidifferentiation and indefinite integrals. The definite integral. Fundamental Theorem of Integral Calculus. Rules and methods of integration. Numerical methods for evaluating definite integrals. Improper integrals - Applications of definite integrals

Sequences and series (Topics 9 and 10) - Sequences. Series. Convergence of series. Tests of convergence. Power series. Taylor and Maclaurin series

## Learning outcomes

Unit Learning Outcomes express learning achievement in terms of what a student should know, understand and be able to do on completion of a unit. These outcomes are aligned with the graduate attributes. The unit learning outcomes and graduate attributes are also the basis of evaluating prior learning.

On completion of this unit, students should be able to:

1. demonstrate a sound knowledge and understanding of the concepts of differentiation and integration
• GA1:
• GA4:
2. demonstrate a proficiency in applying differentiation and integration techniques
• GA4:
3. apply appropriate differentiation and integration techniques to 'real world' problems
• GA4:
• GA6:
4. communicate mathematical ideas, processes and results effectively at different levels of formality.
• GA6:

## Prescribed texts

• Hughes-Hallett, D, 2008, Calculus: Single and multivariate, 5th edn (or 6th edn), Wiley, Hoboken, NJ.
Prescribed texts may change in future teaching periods.