# Mathematics 2A

** 20 **

** MA21001 **

### 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, or equivalents.

### Indicative Content

#### Calculus Component

#### Differential Equations

Revision of linear differential equations of second order with constant coefficients using undetermined coefficients. General solutions and solutions satisfying initial conditions. Resonance. Equations of higher order.

#### Hyperbolic Functions

Hyperbolic Functions; Solution of simple equations, inverse functions. Revision of standard methods of definite integration, including hyperbolic substitutions.

#### Fundamentals of Calculus

Limits, Continuity and Differentiability. Rolle′s Theorem, Mean Value Theorem. Definition and properties of the Riemann integral, Fundamental Theorem of Calculus. L′Hôpital′s Rule and Indeterminate Forms. Infinite and improper integrals. Taylor & Maclaurin series.

#### Algebra Component

#### Vectors and vector spaces

Definition of a vector space,

**R**^{n}. Vectors, lines and planes in**R**^{n}. Span, linear independence. Basis and dimension. Subspaces.#### Inner product

Scalar product, length. Projection. Normal form of hyperplanes in

**R**^{n}. Orthogonality.#### Linear equations and matrices

Systems of linear equations. Gaussian elimination. Matrices and matrix operations, transposes and inverses. Matrix equations. LU factorisation. Determinants.

### Delivery and Assessment

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

### 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.