# Mathematics 1B

** 20 **

** MA12001 **

### 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 1 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.

### Prerequisites

Students taking this module must have taken the module MA11001, or equivalent.

### Indicative Content

#### Calculus Component

#### Integral Calculus

Idea of integral, including elementary treatment of the definite integral as a limit using rectangles. Fundamental theorem of calculus. Methods of integration including integration by substitution, by parts and with partial fractions. Relation of integrals with areas. Trapezium and Simpson′s rules for numerical integration.

#### Differential Equations

First order ordinary differential equations by (a) separation and (b) integrating factor. Second order ordinary differential equations with constant coefficients and simple right- hand sides. (Complex roots included, but no resonance problems.)

#### Algebra Component

#### Vectors

Vector geometry in

**R**² and**R**³ vector properties and manipulation. Unit vectors, position vectors, Cartesian coordinates. Scalar product and vector product.#### Matrices and linear equations

Matrix properties, addition, multiplication. Inverse matrices, determinants. Linear mappings in

**R**² (rotation, reflection). Systems of linear equations, Gaussian elimination and row operations.#### (Further) complex numbers

Polar form, exponential notation. Multiplication, de Moivre′s Theorem, powers and roots.

#### Lines, planes and spheres

Implicit and parametric equations of lines. Implicit equations of planes. Intersections, distances between points, lines and planes. Equations of spheres, tangent planes. Linear dependence and independence, colinear and coplanar vectors.

### Delivery and Assessment

This module is delivered in the form of lectures and workshops/tutorials and assessed via an exam (50%) and coursework (50%) consisting of homeworks and tests and project work.

### Credit Rating

This module is a Scottish Higher Education Level 1 or SCQF level 7 module and is rated as 20 SCOTCAT credits or 10 ECTS credits.