# Mathematics and Statistics Group

## MAT912: Mathematics and its Applications II

**SCQF Level: **8

**Availability: **Semester module, Spring

**Course Prerequisite: **MAT911 and either Higher or `A'
level Mathematics

**Credit Value: **22 (1 module)

### Aims

To develop skills in solving linear simultaneous equations, to use
matrix theory to understand the nature of their solutions, to apply
vector and matrix techniques in studying the geometry of lines and
planes.

To review, consolidate and develop understanding of the differential and
integral calculus; to use the calculus to solve a range of "real-world"
problems.

Complex numbers will also be studied, and used to provide a link between
the exponential and trigonometric functions.

### Learning Outcomes

Students should be able to solve a system of linear equations, solve
geometrical problems of lines and planes, describe a discrete dynamical
system; carry out calculations with complex numbers; differentiate
elementary functions involving algebraic, trigonometric, exponential and
logarithmic functions; integrate using standard techniques such as
partial fractions, parts and substitution; and apply calculus methods to
optimization problems.

### Content

A1: Linear simultaneous equations: row echelon form, applications

A2: The geometry of lines and planes

A3: A matrix treatment of linear simultaneous equations: determinants,
eigenvalues and eigenvectors

A4: Complex numbers: Argand plane representation, polar form, complex
eigenvalues

C1: The differential calculus, rules of differentiation;optimisation

C2: Exponential and logarithmic functions, inverse functions

C3: The integral calculus, rules of integration.

### Transferable Skills

Methodical working, problem solving.

### Bibliography

R.A. ADAMS, "Calculus: A Complete Course", Addison-Wesley

H. ANTON and C. RORRES, "Elementary Linear Algebra with Applications",
Wiley

F. AYRES and E. MENDELSON, "Calculus", (Schaum's Easy Outline Series)
McGraw-Hill

L. ALCOCK, "How to Study for a Mathematics Degree", Oxford University
Press

### Teaching Format

4 one-hour lectures and a 1.5 hour tutorial per week.

### Assessment

40% coursework (2 class tests) and 60% examination

(Students may take MAT912 without taking MAT911 at the discretion of the
Head of the Mathematics and Statistics Group.)