Mathematics 2B module (MA22001)

About the module

This module consists of a Calculus and Algebra component. It is part of a series of four modules, Mathematics 1A, 1B, 2A, 2B, which are the core Mathematics modules in years 1 and 2, and provide the foundations in Calculus, Algebra and Geometry for all mathematics modules in higher levels. This module is mandatory for all Level 2 students on Mathematics (including Mathematics combined) degrees. The module is also suitable for students on non-mathematics degrees and recommended for students on physics and computing degrees. If you have questions about this module please contact our Undergraduate Admissions Tutor or your Advisor of Studies.

Prerequisites

Students taking this module must have achieved a pass mark in each of the modules MA11001 and MA12001, and have taken MA21001, or equivalents.

Indicative Content

Calculus Component

• Multivariable Calculus

  Limits and continuity of functions of two variables. Partial Derivatives. Method of Lagrange Multipliers. Taylor series in two variables. Stationary points for functions of two variables. Double integrals, Jacobian of a change of variables.

• Series

  Tests for convergence of series of numbers. Convergence of power series, radius of convergence. Application to Taylor and Maclaurin series (mention of Taylor's Theorem).

Algebra Component

• General vector spaces and subspaces

  P_n, Cⁿ and other vector spaces. Span, linear dependence/independence, bases. Reduction to row-ecehelon form, relation to linear independence Intersections, unions and direct sums of subspaces. Range and nullspace of a matrix.

• Inner products

  Definition of inner products and inner product spaces. Gram-Schmidt orthogonalisation.

• Eigenvalues and eigenvectors

  Definitions and examples. Complex and repeated eigenvalues, algebraic and geometric multiplicity. Diagonalization of matrices. The Cayley-Hamilton theorem.

• Linear mappings

  Definitions and matrix representations. Composition of linear mappings. Kernel and image.

Delivery and Assessment

The module is delivered in the form of lectures and workshops/tutorials and assessed via an exam (60%) and coursework (40%).

Credit Rating

This module is a Scottish Higher Education Level 2 or SCQF level 8 module and is rated as 20 SCOTCAT credits or 10 ECTS credits.