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Unit of study_

MATH1011: Applications of Calculus

This unit is designed for science students who do not intend to undertake higher year mathematics and statistics. It establishes and reinforces the fundamentals of calculus, illustrated where possible with context and applications. Specifically, it demonstrates the use of (differential) calculus in solving optimisation problems and of (integral) calculus in measuring how a system accumulates over time. Topics studied include the fitting of data to various functions, the interpretation and manipulation of periodic functions and the evaluation of commonly occurring summations. Differential calculus is extended to functions of two variables and integration techniques include integration by substitution and the evaluation of integrals of infinite type.

Code MATH1011
Academic unit Mathematics and Statistics Academic Operations
Credit points 3
MATH1001 or MATH1901 or MATH1906 or BIOM1003 or ENVX1001 or MATH1021 or MATH1921 or MATH1931
Assumed knowledge:
HSC Mathematics. Students who have not completed HSC Mathematics (or equivalent) are strongly advised to take the Mathematics Bridging Course (offered in February). Please note: this unit does not normally lead to a major in Mathematics or Statistics or Financial Mathematics and Statistics

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

  • LO1. analyse practical problems using techniques from differential and integral calculus;
  • LO2. fit as appropriate a linear, polynomial, exponential or a periodic function to a set of experimental data;
  • LO3. sketch the generalised sinusoidal functions;
  • LO4. use differential calculus to solve optimisation problems in one independent variable;
  • LO5. calculate the partial derivatives of functions of two variables, and hence to solve optimisation problems in two independent variables;
  • LO6. calculate finite sums and use the sigma notation where appropriate;
  • LO7. evaluate definite integrals and use definite integrals in applications;
  • LO8. determine when improper integrals of infinite type exist.