MTH101 Computer Aided Mathematics 1 with Applications (8)

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 on investigation and practical problems.

Availability

Session 1 (30)
On Campus
Bathurst Campus
Wagga Wagga Campus
Online
Wagga Wagga Campus
Session 2 (60)
Online
Wagga Wagga Campus

Continuing students should consult the SAL for current offering details: MTH101. Where differences exist between the Handbook and the SAL, the SAL should be taken as containing the correct subject offering details.

Subject Information

HD/FL

One session

School

School of Computing and Mathematics

Assumed Knowledge

This subject assumes that students have some knowledge of HSC Mathematics (previously called 2 Unit Mathematics).

Learning Outcomes

Upon successful completion of this subject, students should:
• Be able to graph and solve equations involving the most common functions including algebraic, exponential, logarithmic and trigonometric functions;
• Be able to calculate limits;
• Be able to differentiate simple functions, including implicit functions;
• Be able to use derivatives in applications, including rates of change, graphing, optimisation and approximation;
• Be able to integrate simple functions, analytically and numerically;
• Be able to use integrals in applications, including area, volume, arclength and average;
• Be able to describe the connections between a function, its derivative and its integral;
• Be able to solve systems of linear equations;
• Be able to perform addition, subtraction, scalar multiplication, matrix multiplication, transposition and inversion of matrices;
• Be able to calculate a determinant of a matrix;
• Be able to calculate eigenvalues and eigenvectors of a matrix;
• Be able to use differentiation, integration and linear algebra to solve a wide range of applied problems;
• Be able to use Maple to help solve mathematical problems.

Syllabus

This subject will cover the following topics:

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.