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Unit Summary
Unit type
UG Coursework Unit
Credit points
12
AQF level
Level of learning
Intermediate
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 | 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:
- demonstrate a sound knowledge and understanding of the concepts of differentiation
and integration
- GA1: Intellectual rigour
- GA4: Knowledge of a discipline
- demonstrate a proficiency in applying differentiation and integration techniques
- GA4: Knowledge of a discipline
- apply appropriate differentiation and integration techniques to 'real world' problems
- GA4: Knowledge of a discipline
- GA6: Communication and social skills
- 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.