The current and official versions of the course specifications are available on the web at https://www.usq.edu.au/course/specification/current.
Please consult the web for updates that may occur during the year.

# MAT1102 Algebra and Calculus I

 Semester 1, 2022 Toowoomba On-campus Units : 1 Faculty or Section : Faculty of Health, Engineering and Sciences School or Department : School of Mathematics, Physics & Computing Student contribution band : Band 1 Grading basis : Graded Version produced : 17 May 2022

## Staffing

Examiner: Nathan Downs

## Overview

Mathematical concepts and processes provide powerful descriptive and investigative tools for science, engineering, business and other fields. In particular, the techniques of calculus, matrices, vectors and complex numbers are fundamental for modelling and analysis in a wide range of applications. This course provides opportunity for students to advance their mastery of these topics, and explore their applications in many contexts.

It is assumed that students entering this course have up-to-date Qld Maths B competencies, that is, well-established algebra, function, graphing and trigonometry competencies, and introductory level skills in matrices, vectors and calculus. This course advances conceptual and technical competencies in these fields by investigating limits, continuity, inverse functions, compositions, rational functions and implicit functions. Calculus concepts, differentiation and integration are advanced and used in problem-solving applications. Vector algebra is extended and applied to the description of lines and planes in space. Matrix algebra is extended to determinants, and used for modelling and to solve systems of linear equations in a range of settings. Euler notation is used to represent complex numbers and functions.

## Course learning outcomes

On successful completion of this course students should be able to:

1. Examine and apply mathematical techniques and skills to solve problems essential to further study in mathematics, applied mathematics and engineering
2. Interpret and solve a range of authentic problems involving mathematical concepts relevant to this course
3. Effectively communicate mathematical concepts and arguments using appropriate notation
4. Use computational aids for graphing, matrix manipulation, concept development and problem solving in algebra and calculus

## Topics

Description Weighting(%)
1. Mathematical writing and communication. 10.00
2. The library of common types of functions of one variable and their graphs; function concepts, and their applications. 20.00
3. Calculus: techniques of differentiation, higher derivatives and their applications; definite, indefinite and improper integrals, integration techniques; applications of calculus to engineering and science. 30.00
4. Vector algebra and cross product, and application to describing lines and planes in space. 15.00
5. Matrix algebra, inverse and determinants; applications to solving systems of linear equations in engineering and other contexts. 15.00
6. Complex number applications, Euler form and complex functions. 10.00

## Text and materials required to be purchased or accessed

James, G. et al 2020, Modern engineering mathematics, 6th edn, Pearson (Prentice Hall).
Study Book (current year), Course MAT1102 algebra and calculus I, USQ Distance Education Centre, Toowoomba.
(Available on the course StudyDesk.)
Matlab (any recent version) Matlab is freely accessible in the USQ computer laboratories.
Scientific calculator.

## Student workload expectations

To do well in this subject, students are expected to commit approximately 10 hours per week including class contact hours, independent study, and all assessment tasks. If you are undertaking additional activities, which may include placements and residential schools, the weekly workload hours may vary.

## Assessment details

Description Group
Assessment
Weighting (%) Course learning outcomes
Quiz No 10 1
Problem Solving 1 No 30 1,2,3
Problem Solving 2 No 30 1,2,3
Problem Solving 3 No 30 1,2,3,4
Date printed 17 May 2022