Module Identifier | PH16010 | ||

Module Title | THEORETICAL PHYSICS 1 | ||

Academic Year | 2000/2001 | ||

Co-ordinator | Dr Nicholas Mitchell | ||

Semester | Semester 1 | ||

Other staff | Dr Philip Cadman, Dr Geraint Vaughan | ||

Pre-Requisite | Normal entry requirements for Part I Physics | ||

Mutually Exclusive | PH16020 | ||

Course delivery | Lecture | 20 lectures | |

Seminar | 2 seminars | ||

Assessment | Exam | End of semester examination | 70% |

Course work | Example sheet deadlines ( by week of semester):
Example Sheets 1,2,3 and 4 Weeks 2,3,4 & 5
Example Sheets 7 and 10 Weeks 8 & 11 | 30% |

**Brief description**

This module illustrates by reference to physical examples the mathematical techniques necessary to investigate physical laws. Topics covered include the applications of complex numbers, vectors and simple differential equations to problem solving in physics.

**Learning outcomes**

After taking this module students should be able to:

- Apply the mathematical problem-solving techniques developed to analyse a range of simple physical systems.

**Additional learning activities**

None

**Outline syllabus**

(a) Differential Equations

Introduction and definition of terms Solving simple DEs by direct integration

Linear first order DEs, both homogeneous and inhomogeneous solved by three methods:

i) The method of separation of variables.

ii) The integrating factor method.

iii) Direct integration by product rule.

Second order linear DEs with constant coefficients. Defining the auxiliary equation

Homogeneous case - forcing function = 0. Inhomogeneous case - solutions if forcing function is:

i) polynomial.

ii) exponential.

iii) sinusoidal.

(Introduction to Partial Differentiation)

(b) Vectors

Scalar and vector quantities. Vector notation and unit vectors. Vector addition, scalar and vector products, rates of change of vectors

(c) Complex Numbers

Real and imaginary numbers. Complex numbers and their operations.

Graphical representation of complex numbers: the Argand diagram and polar form. Elementary functions of a complex variable: Euler's formula, trigonometric, hyperbolic and logarithmic functions.

Powers and roots of a complex number - de Moivre's theorem.

Phasors.

**Reading Lists**

**Books**
**** Recommended Text**

K.A. Stroud.
*Engineering Mathematics*. MacMillan
**** Supplementary Text**

M.L. Boas.
*Mathematical Methods in the Physical Sciences*. Wiley