Unit description
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.
Learning outcomes and graduate attributes
| 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 | ||||||
Prescribed texts
Session 2
- Hughes-Hallett, D, 2008, Calculus: Single and multivariate, 5th edn (or 6th edn), Wiley, Hoboken, NJ.
Session 3
- Hughes-Hallett, D, 2008, Calculus: Single and multivariate, 5th edn (or 6th edn), Wiley, Hoboken, NJ.
Teaching and assessment
Lismore
| Teaching method |
| Lecture on-site 2 hours (12 Weeks) |
| Tutorial on-site 2 hours (12 Weeks) |
| Assessment | |
| Quiz | SR |
| Calculations | 25% |
| Calculations | 25% |
| Exam: closed book | 50% |
Online
| Teaching method |
| Tutorial online 1 hour (8) |
| Assessment | |
| Quiz | SR |
| Calculations | 25% |
| Calculations | 25% |
| Exam: closed book | 50% |
Fee information
Domestic
Commonwealth Supported courses
For information regarding Student Contribution Amounts please visit the Student Contribution Amounts.
Commencing 2015 Commonwealth Supported only. Student contribution band: 2
Fee paying courses
For POSTGRADUATE or UNDERGRADUATE full fee paying courses please check Domestic Postgraduate Fees OR Domestic Undergraduate Fees
International
Please check the international course and fee list to determine the relevant fees.