Mathematics 2B module (MA22001)

Mathematics 2B includes content on matrix algebra and multi-variable calculus.

This module is part of a series of four modules which include Mathematics 1A, 1B, 2A, and 2B. These are the core Mathematics modules in years 1 and 2.

Matrix algebra encountered in earlier modules includes using matrices and vectors to solve systems of equations.

In this module the focus is on the theory showing how many solutions there can be. Previously seen concepts such as linear independence, basis and null spaces are explored in the context of matrix algebra. New concepts such as determinants and eigenvalues are introduced. These new concepts are useful in understanding properties of matrices.

One of the fundamental mathematical operations in calculus is finding derivatives of functions. Derivatives give the rate of change of a function. If functions have more than one input variable then this gives partial derivatives.

In this module you will learn about partial derivatives and their properties. For a function of one variable, integrals find the area under the graph. You extend this to functions of two variables by studying integrals over a 2D domain.

What you will learn

In this module, you will:

• learn how linear independence, basis and null spaces are explored in the context of matrix algebra. Learn new concepts such as determinants and eigenvalues
• learn how differentiation can be extended to apply to a function of two variables. You will learn how the chain rule for differentiation applies in this situation
• learn how to integrate a function of two variables and how a change of variables can be used to help calculate integrals over 2 variables

By the end of this module, you will be able to:

• do basis and null space calculations and interpret the results in the context of matrix algebra
• apply the rules for evaluating determinants and find the eigenvalues and eigenvectors for a matrix
• calculate partial derivatives and to apply the chain rule
• find maximum and minimum values of functions of several variables
• evaluate integrals of functions of two variables. You will be able to do this by changing the order of integration and by change of variables if necessary

Assignments / assessment

• coursework (40%)
• final exam (60%)

Teaching methods / timetable

• four hours of lectures weekly
  • key points of the week's content will be discussed
  • lecture notes covering the full module content will be available before classes
  • in-class time will be prioritised for interactive discussion
• two hours of tutorials weekly
  • solve problems individually and in groups
  • support with difficulties will be provided by your lecturers and peers