# Calculus of One and Two Variables

Queensland University of Technology

## Course Description

• ### Course Name

Calculus of One and Two Variables

• ### Host University

Queensland University of Technology

• ### Location

Brisbane, Australia

Calculus

• ### Language Level

Taught In English

• ### Prerequisites

Completion one of MXB100, MXB101 or MZB125 is required

• ### Course Level Recommendations

Lower

ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

### Hours & Credits

• Credit Points

12
• Recommended U.S. Semester Credits
3 - 4
• Recommended U.S. Quarter Units
4 - 6
• ### Overview

This unit introduces you to university level single variable calculus and simple multivariable calculus, building on prior assumed knowledge equivalent to high school differential and integral calculus. Topics include continuity and differentiability of functions, differential calculus (single and multi variable), Taylor series, integral calculus (single and multi variable). Multivariable and vector-valued functions are introduced and explored and natural extensions of the concepts of differentiation and integration to such functions are developed and investigated. This unit builds fundamental skills for you to transition to second year units and the majors, including applications of interest in each Major area of study.

Learning Outcomes
On successful completion of this unit you will provide evidence that you can:
Interpret mathematical notation and use it in communicating your work.

Recognise, construct and solve problems, in both abstract and real world contexts, using single and two variable functions and calculus, incorporating relevant mathematical software where appropriate.

Demonstrate your ability to reduce complex problems to smaller elements.

Apply principles of teamwork including demonstration of roles within a team.

Content
The mathematical content of the unit includes:
Continuity and differentiability of functions of a single variable will be considered in greater depth than covered in previous studies.

Techniques for integrating such as by parts and trigonometric substitution will be covered as well as simple approximations for integrals based on the Riemann sum. Applications of using integrals may include the calculation of volumes of revolution and centres of mass.

Simple vector calculus is introduced in this unit by considering vector equations of lines, planes and curves. Applications may include the determination of arc length, projectile motion problems, and the use of polar coordinates.

Multivariable calculus is introduced in this unit leading to the exploration of such ideas as level curves, partial derivatives, directional derivatives and the integration of multivariable functions. Applications may include the determination of extrema, the use of differentials for estimating functions and calculating volumes and other properties of 3 dimensional bodies.

Where appropriate relevant mathematical software and related technologies will be introduced to support and illustrate concepts covered in the content of this unit.

### Course Disclaimer

Courses and course hours of instruction are subject to change.

Eligibility for courses may be subject to a placement exam and/or pre-requisites.

Some courses may require additional fees.

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.