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Unit of study_

MATH1931: Calculus Of One Variable (SSP)

The Mathematics Special Studies Program is for students with exceptional mathematical aptitude, and requires outstanding performance in past mathematical studies. Students will cover the material of MATH1921 Calculus of One Variable (Adv), and attend a weekly seminar covering special topics on available elsewhere in the Mathematics and Statistics program.

Code MATH1931
Academic unit Mathematics and Statistics Academic Operations
Credit points 3
Prerequisites:
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None
Corequisites:
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None
Prohibitions:
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MATH1001 or MATH1901 or ENVX1001 or MATH1906 or MATH1021 or MATH1921
Assumed knowledge:
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(HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent

At the completion of this unit, you should be able to:

  • LO1. apply mathematical logic and rigor to solving problems, and express mathematical ideas coherently using precise mathematical language.
  • LO2. understand new mathematical concepts beyond routine methods and calculations
  • LO3. demonstrate fluency in the mathematical manipulation of complex numbers and functions, including concepts of surjectivity, injectivity and inverse functions
  • LO4. understand and be able to use fundamental properties of continuous and differentiable functions including limits, limit laws, intermediate and extreme value theorems as well as mean value theorems and applications
  • LO5. work with Taylor polynomial approximations and Taylor series representations of functions including dealing with remainder estimates
  • LO6. demonstrate an understanding of the definition and computation or estimation of definite, indefinite and improper Riemann integrals including proficiency in using integration methods without too much guidance
  • LO7. understand and be able to use the relationships between integral and differential calculus via the Fundamental Theorem of Calculus
  • LO8. apply concepts of calculus to a variety of contexts and applications
  • LO9. gain an appreciation of a diverse range of mathematical problems and applications through participating in class discussions and the completion of assignments

Unit outlines

Unit outlines will be available 2 weeks before the first day of teaching for the relevant session.