Abstract

This subject provides an introduction to calculus and linear algebra, with an emphasis on understanding and applications addressed in geometry, physics, economics and environmental modelling. A symbolic algebra package, Maple, is used to assist with computation. Every topic will be presented geometrically, numerically and algebraically. Formal definitions will be based … For more content click the Read More button below.

Syllabus

Functions and graphs; Limits and continuity; The derivative; Derivative rules; Applications of the derivative; The definite integral; Integration rules; Numerical methods of integration; Applications of the integration; Solving systems of linear equations; Matrices, determinants and eigenvalues.

Learning outcomes

Upon successful completion of this subject, students should:
1.
be able to graph and solve equations involving the most common functions including algebraic, exponential, logarithmic and trigonometric functions;
2.
be able to calculate limits;
3.
be able to differentiate simple functions, including implicit functions;
4.
be able to use derivatives in applications, including rates of change, graphing, optimisation and approximation;
5.
be able to integrate simple functions, analytically and numerically;
6.
be able to formulate and evaluate integrals for area, volume, arc length, and average;
7.
be able to describe the connections between a function, its derivative and its integral;
8.
be able to solve systems of linear equations;
9.
be able to perform addition, subtraction, scalar multiplication, matrix multiplication, transposition and inversion of matrices;
10.
be able to calculate a determinant of a matrix;
11.
be able to calculate eigenvalues and eigenvectors, and interpret these in linear transformations.
12.
be able to analyse complex problems, transform them into mathematical forms and solve them using appropriate methods; and
13.
be able to use mathematical software for solving and communicating complex mathematical problems.

Assumed knowledge

Assumed knowledge for this subject is the equivalent of MTH105 or MTH400 or HSC Mathematics Advanced.

HSC Mathematics Advanced includes the following topics:Working with FunctionsTrigonometry and Measure of AnglesTrigonometric Functions and IdentitiesIntroduction to DifferentiationLogarithms and ExponentialsGraphing TechniquesTrigonometric Functions and GraphsDifferential CalculusIntegral Calculus

Enrolment restrictions

Available to postgraduate students only.