# Module – Mathematics 39013

FHEQ Level: Level 4 (First Year)
Credits: 20
Module Code: F300 —–
Course Reference Number (CRN): 39013
Delivery: September Start, Trimester 1 (Short Fat)

#### Syllabus Outline

– Algebra: Equations, identities and inequalities. Functions and functional notation. Quadratic equations. Partial fractions. Indices and logarithms. Simultaneous linear equations. Graphing simple functions. Binomial theorem.
– Trigonometry: Degrees, radians, arcs and sectors. Trig. Functions, trig identities and trig equations.
– Hyperbolic Functions: Definitions, graphs, properties, evaluation and inverses.
– Geometry: Co-ordinate systems. Lines. Conic sections.
– Vectors: Position vectors. Components of vectors. Addition, subtraction, multiplication by a scalar. Magnitude of a vector and unit vectors. Scalar and vector products (including applications).
– Matrices: Two simultaneous equations, matrix order and arithmetic, Cramer’s rule, Laplace expansion, classifications, augmented coefficient matrix, echelon form, Gaussian elimination, linear independence, matrix inverse, applications.
– Complex Numbers: Operations with complex numbers. Geometric representation and the Argand diagram. Polar and exponential forms. Powers and roots of complex numbers.
– Ordinary Differentiation: Differentiation of elementary functions. Techniques of ordinary differentiation. Differentiation of implicit functions. Applications of differentiation.
– Partial Differentiation: Techniques of partial differentiation. Small increments (error analysis). Exact differentials. Rates of change problems.
– Integration: Integration as the reverse of differentiation and as the limit of a sum. Standard integrals I. Techniques of integration.

#### Assessment

Coursework: Assignment 1, 50%
Coursework: Assignment 2, 50%

#### Texts

Engineering Mathematics – K.A. Stroud and D.J. Booth (8th Edition) MacMillan (2020)

Understanding Pure Mathematics – A.J. Thorning, D.W.S., Oxford, Oxford University Press, 1987

Further updates and supplementary texts may be found in the University Reading Lists system.

#### Description

You will learn core mathematics techniques essential to physics and engineering. Topics include: algebra, functions, geometry, vectors, complex numbers, differentiation and integration. The module is taught through a combination of lectures and problem tutorial classes.

#### Aims

1. To review essential fundamental mathematical techniques relevant to physics and engineering
2. To introduce the subjects of algebra, functions, geometry, vectors, complex numbers, differentiation and integration, with emphasis on their applications to physics and engineering
3. To provide the mathematical training in support of physics and engineering modules.

#### Knowledge & Understanding

On successful completion of this module, you will be able to:

1. Solve numerate problems in the fields of algebra, properties of elementary functions, coordinate systems, vector algebra, complex numbers, differentiation and integration.
2. Apply mathematical techniques in relevant areas of physics and engineering.
3. Demonstrate application of numerical and mathematical skills.
4. Demonstrate problem solving skills using mathematics.

#### Learning, Teaching and Assessment

This module is taught by weekly lectures supported by problem tutorial classes

A set of problem-solving exercises is provided for guided independent learning, which forms the basis of formative assessment and feedback in the tutorial classes.