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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.

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:GA1GA2GA3GA4GA5GA6GA7
1demonstrate a sound knowledge and understanding of the concepts of differentiation and integrationIntellectual rigourKnowledge of a discipline
2demonstrate a proficiency in applying differentiation and integration techniquesKnowledge of a discipline
3apply appropriate differentiation and integration techniques to 'real world' problemsKnowledge of a disciplineCommunication and social skills
4communicate 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

Teaching and assessment

Notice

Intensive offerings may or may not be scheduled in every session. Please refer to the timetable for further details.

Southern Cross University employs different teaching methods within units to provide students with the flexibility to choose the mode of learning that best suits them. SCU academics strive to use the latest approaches and, as a result, the learning modes and materials may change. The most current information regarding a unit will be provided to enrolled students at the beginning of the study session.

Fee information

Domestic

Commonwealth Supported courses
For information regarding Student Contribution Amounts please visit the Student Contribution Amounts.

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.

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