MATH2702 Linear Algebra and Differential Equations

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Overview

Linear algebra and differential equations underpin much of modern mathematics and are fundamental in both modelling and pure mathematics. This topic introduces key concepts from these two areas. While linear algebra is motivated by the study of simultaneous algebraic equations, the ideas generalise to many other settings. After reviewing the solution of systems of linear equations through row operations and matrix inverses, these concepts are used to motivate the introduction of abstract vector spaces, linear transformations and eigenvalues. The ideas developed are then utilised in the study of ordinary differential equations (ODEs), where several common classes of equations are introduced, analysed and solved, including systems of ODEs. The approaches introduced have wide applications across mathematical modelling while also motivating further mathematical questions and ideas.

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Aims

This topic aims to introduce key principles of linear algebra and differential equations. This includes the ability to understand essential definitions and techniques used in linear algebra, and to apply solution techniques for ordinary differential equations, together with applications to real-world phenomena.

Learning outcomes

On completion of this topic you will be expected to be able to:

Understand key definitions used in linear algebra

Apply fundamental techniques from linear algebra to theoretical problems

Solve ordinary differential equations using different solution techniques

Use linear algebra and ordinary differential equations to solve real-world problems

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Requisites information

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Handbook

Linear Algebra and Differential Equations

MATH2702