# Module Information

Module Identifier

PH06020

Module Title

Introduction to Mathematical Methods for Physicists i

Academic Year

2014/2015

Co-ordinator

Semester

Semester 1

Co-Requisite

None

Mutually Exclusive

Not available to students doing 3 year BSc or 4 year MPhys

Pre-Requisite

GCSE Mathematics or Equivalent

Other Staff

#### Course Delivery

Delivery Type | Delivery length / details |
---|---|

Lecture | 40 hours lectures |

Seminars / Tutorials | 5 hours tutorials |

#### Assessment

Assessment Type | Assessment length / details | Proportion |
---|---|---|

Semester Exam | 3 Hours End of semester examinations | 70% |

Semester Assessment | Weekly course work | 30% |

Supplementary Exam | 3 Hours Written examination. | 100% |

### Learning Outcomes

After taking this module the student should be able to:

- Use algebraic techniques confidently to solve physical and mathematical problems.
- Demonstrate a knowledge of trigonometrical functions and the relations between them.
- Demonstrate a knowledge of vectors and use them to solve simple problems.
- Demonstrate a knowledge of complex numbers and use them to solve simple problems.
- Demonstrate a knowledge of differentiation and 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 algabraic techniques, logarithms, trigonometry, an introduction to vectors, complex numbers and differentiation. Particular emphasis is placed on the use of mathematical techniques to solve physical 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.

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.

### Transferable skills

The teaching of this module incorporates a large element of self-paced problem solving, both for individual and tutorial work. This is essential to consolidate students understanding of the subject matter of this module.

### Reading List

**Essential Reading**

Bostock, L. (1990(1992 print) Core maths for A-level /L. Bostock, S. Chandler. Thornes Primo search Bostock, L. (2000.) Core maths for advanced level /L. Bostock, S. Chandler. 3rd ed. Stanley Thornes Primo search

**Recommended Text**

Sadler, A. J. (1987.) Understanding pure mathematics /A.J. Sadler, D.W.S. Thorning. Oxford University Press Primo search

**Supplementary Text**

Stroud, K. A. (2003.) Advanced engineering mathematics :a new edition of Further engineering mathematics. 4th ed. Palgrave Macmillan Primo search

### Notes

This module is at CQFW Level 3