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Unit of study_

MATH1111: Introduction to Calculus

This unit is an introduction to the calculus of one variable. Topics covered include elementary functions, differentiation, basic integration techniques and coordinate geometry in three dimensions. Applications in science and engineering are emphasised.

Code MATH1111
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
MATH1011 or MATH1901 or MATH1906 or MATH1001 or HSC Mathematics Extension 1 or HSC Mathematics Extension 2 or ENVX1001 or MATH1021 or MATH1921 or MATH1931
Assumed knowledge:
Knowledge of algebra and trigonometry equivalent to NSW Year 10

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

  • LO1. Apply mathematical logic and rigour to solving problems, and express mathematical ideas coherently in written and oral form;
  • LO2. Demonstrate fluency in manipulating real numbers, their symbolic representations, operations, and solve associated algebraic equations and inequalities;
  • LO3. Develop fluency with lines, coordinate geometry in two dimensions, the notion of a function, its natural domain, range and graph;
  • LO4. Become conversant with elementary functions, including trigonometric, exponential, logarithmic and hyperbolic functions and be able to apply them to real phenomena and to yield solutions of associated equations;
  • LO5. Perform operations on functions and be able to invert functions where appropriate;
  • LO6. Understand the definitions of a derivative, definite and indefinite integral and be able to apply the definitions to elementary functions;
  • LO7. Develop fluency in rules of differentiation, such as the product, quotient and chain rules, and use them to differentiate complicated functions;
  • LO8. Understand and apply the Fundamental Theorem of Calculus; and develop fluency in techniques of integration, such as integration by substitution, the method of partial fractions and integration by parts;
  • LO9. Develop some fluency with coordinate geometry in three dimensions, planes, surfaces, ellipsoids, paraboloids, level curves and qualitative features such as peaks, troughs and saddle points.