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Online Session 2 Session 2

Unit Summary

Unit type

UG Coursework Unit

Credit points

12

AQF level

7

Level of learning

Intermediate

School/College

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.

GA1: Intellectual rigour, GA2: Creativity, GA3: Ethical practice, GA4: Knowledge of a discipline, GA5: Lifelong learning, GA6: Communication and social skills, GA7: Cultural competence
On completion of this unit, students should be able to: GA1 GA2 GA3 GA4 GA5 GA6 GA7
1 demonstrate a sound knowledge and understanding of the concepts of differentiation and integration Intellectual rigour Knowledge of a discipline
2 demonstrate a proficiency in applying differentiation and integration techniques Knowledge of a discipline
3 apply appropriate differentiation and integration techniques to 'real world' problems Knowledge of a discipline Communication and social skills
4 communicate mathematical ideas, processes and results effectively at different levels of formality. Communication and social skills

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: Intellectual rigour
    • GA4: Knowledge of a discipline
  2. demonstrate a proficiency in applying differentiation and integration techniques
    • GA4: Knowledge of a discipline
  3. apply appropriate differentiation and integration techniques to 'real world' problems
    • GA4: Knowledge of a discipline
    • GA6: Communication and social skills
  4. communicate mathematical ideas, processes and results effectively at different levels of formality.
    • GA6: Communication and social skills

Prescribed texts

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