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 use integrals in applications, including area, volume, arclength 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 of a matrix;
12.
be able to use differentiation, integration and linear algebra to solve a wide range of applied problems; and
13.
be able to use Maple to help solve mathematical problems.

Assumed knowledge

It is assumed that students have completed the equivalent of HSC Mathematics Advanced (formerly known as 2-Unit Mathematics).

Students who have not completed HSC Mathematics Advanced or an equivalent subject in their state or country are advised to complete MTH105 Introductory Mathematics before attempting MTH101.

It is important to note that HSC Mathematics General, Mathematics Standard, Maths in Society and other subjects at a similar level that do not include calculus are not sufficient preparation for MTH101.

HSC Mathematics Advanced includes the following topics:

Working with FunctionsTrigonometry and Measure of AnglesTrigonometric Functions and IdentitiesIntroduction to DifferentiationLogarithms and ExponentialsProbability and Discrete Probability DistributionsGraphing TechniquesTrigonometric Functions and GraphsDifferential CalculusThe Second DerivativeIntegral CalculusModelling Financial SituationsDescriptive Statistics and Bivariate Data AnalysisRandom Variables

Enrolment restrictions

Available to undergraduate students only. Not available to students who have completed MTH401.