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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.)