Essential Mathematics 2: Calculus

• • Graphs of equations and functions
  • Limits and continuity
  • Slope of a line and the derivative
  • Properties of derivatives; maximum and minimum problems
  • The chain rule; implicit differentiation and the sign of the derivative
  • Rectilinear motion; related rates and higher-order derivatives
  • Graph sketching and sine and cosine functions
  • Graphing sine and cosine & other trigonometric functions
  • Antiderivatives and the definite integral
  • The fundamental theorem and area and arc length
  • The natural logarithm and the exponential function
  • L'Hôpital's Rule; Exponential Growth and Decay and Trigonometric Substitutions

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Additional requirements

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Calculus concerns the rate of change of a function with respect to its variable, which is geometrically represented by the slope of a curvilinear trajectory. All of science and engineering, including economics and finance, use calculus as a main tool. Understanding the technical aspects of today's information technology is not possible without calculus, and calculus has and will continue to have a crucial role in the development of the technologies of the future.

The main devices in calculus are limits of real functions and their properties. The use of limits enables us to understand change simply and precisely. This is how areas of irregular shapes can be computed exactly, and how physical processes involving change can be fully understood.

UniSA Online’s 10-week short courses give you the flexibility to upskill in a certain area, stay current with developments in your field, diversify your knowledge, or even explore a new direction in your career – without having to commit to the time and cost of a full university degree. 

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This is a course from UniSA Online’s Associate Degree in Engineering.

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Current study term: 18 Sep 22 to 25 Nov 22