# Linear Algebra and Differential Equations

Queensland University of Technology

## Course Description

• ### Course Name

Linear Algebra and Differential Equations

• ### Host University

Queensland University of Technology

• ### Location

Brisbane, Australia

Algebra

• ### Language Level

Taught In English

• ### 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 linear algebra and ordinary differential equations. Linear algebra, assumed knowledge for this unit, is extended with you investigating non-square linear systems of equations and the Eigenvalue problem. Differential equations, also assumed knowledge for the unit, are investigated in more detail including exposure to second order equations. This unit builds fundamental skills for you to transition to second year units and the Majors of the Bachelor of Mathematics, including applications of interest in each major area of study.

Learning Outcomes
On successful completion of this unit you should be able to:

1. Competently communicate elementary mathematical arguments and results, both orally and in written form.
2. Recognise, interpret and solve problems using linear systems, vectors and differential equations.
3. Demonstrate your ability to reduce complex problems to smaller elements and mathematical models.
4. Work effectively as a member of a group to resolve mathematical problems.

Content
The mathematical content in this unit includes:
Matrix methods, with a focus upon the solution of large systems of linear equations, including the interpretation of system stability on the basis of eigenvalues of the coefficient matrix.
Various classes of differential equations will be discussed and appropriate solution methods described. Differential equations that may be classified as 1st order linear or non-linear, and 2nd order linear with constant coefficients will be the principal focus here. The use of Taylor and Fourier series for approximating functions, as well as advanced techniques such as solution by Laplace Transforms may be introduced.

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

Strategies for working in groups to solve relevant problems will also be explored to prepare you for the peer review assessment activity. The standards for presentation and communication (both oral and written) of mathematical and statistical information will be discussed and demonstrated by example.

### 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.