# Gwybodaeth Modiwlau

Module Identifier
PH06020
Module Title
Introduction to Mathematical Methods 1
2024/2025
Co-ordinator
Semester
Semester 1
Pre-Requisite
GCSE Mathematics or Equivalent
Not available to students on a 3-year Bachelor's or on an Integrated Master's scheme.
Other Staff

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Assessment Weekly course work  30%
Semester Exam 3 Hours   End of semester examinations  70%
Supplementary Exam 3 Hours   Supplementary Examination  Written examination.  100%

### Learning Outcomes

On successful completion of this module students should be able to:

1. Solve mathematical problems by using algebraic techniques.

2. Identify linear, quadratic, trigonometric, exponential and logarithmic functions and recall fundamental relations between them.

3. Manipulate with vectors.

4. Examine complex numbers and use them to solve simple problems.

5. Solve simple questions on differentiation and recognise the relation between dy/dx and the gradient of the curve y(x).

### Brief description

This module introduces the student to some of the basic mathematical tools commonly used in the physical sciences. Topics covered include algebraic techniques, logarithms, trigonometry, an introduction to vectors and differentiation. Particular emphasis is placed on the use of mathematical techniques to solve physics problems.

### Content

Number: Fractions, decimal system, different bases, indices and logarithms.

Algebraic techniques: linear and quadratic equations, factorisation, transposition of formulae, equations involving fractions, simultaneous equations. Indicial, exponential and logarithmic equations.

Trigonometry: Sine and cosine rules. Unit circle representation. Graphs of trigonometrical functions. Trigonometric equations and identities including addition and double angle formulae.

Vectors: Vector representation, unit vectors, position vectors, vector components, vector addition, scalar product.

Complex Numbers: Introduction to complex numbers, multiplication and division in polar form, de Moivre's theorem, powers and roots of complex numbers.

Differentiation and its applications: Gradient of a curve, equation of a straight line, tangents and normals, rates of change, stationary values and turning points, curve sketching.

### Module Skills

Skills Type Skills details
Creative Problem Solving Problem solving skills are developed throughout the module and assessed in coursework and the semester examination.
Professional communication Presentation of the work by students in coursework and the semester examination develop written communication skills.
Subject Specific Skills Understanding and application of mathematical techniques are essential to solve problems in the physical sciences.

### Notes

This module is at CQFW Level 3