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Unit Summary
Unit type
UG Coursework Unit
Credit points
12
AQF level
Level of learning
Intermediate
Former School/College
Pre-requisites
have completed MAT71215 - Introductory Algebra and Calculus OR MAT10001 - Foundation Mathematics OR be admitted to course: 3507285 - Bachelor of Engineering (Honours) in Civil Engineering OR 3507328 - Bachelor of Engineering (Honours) in Mechanical Engineering OR 3507250 - Bachelor of Engineering (Honours) in Coastal Systems Engineering
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: | GA1 | GA2 | GA3 | GA4 | GA5 | GA6 | GA7 | |
|---|---|---|---|---|---|---|---|---|
| 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
- GA1:
- GA4:
-
demonstrate a proficiency in applying differentiation and integration techniques
- GA4:
-
apply appropriate differentiation and integration techniques to 'real world' problems
- GA4:
- GA6:
-
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.