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.
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
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|
|2||demonstrate a proficiency in applying differentiation and integration techniques|
|3||apply appropriate differentiation and integration techniques to 'real world' problems|
|4||communicate mathematical ideas, processes and results effectively at different levels of formality.|
On completion of this unit, students should be able to:
- demonstrate a sound knowledge and understanding of the concepts of differentiation and integration
- demonstrate a proficiency in applying differentiation and integration techniques
- apply appropriate differentiation and integration techniques to 'real world' problems
- communicate mathematical ideas, processes and results effectively at different levels of formality.
- Hughes-Hallett, D, 2008, Calculus: Single and multivariate, 5th edn (or 6th edn), Wiley, Hoboken, NJ.
Teaching and assessment
Commonwealth Supported courses
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