Module Identifier | PH16520 | ||

Module Title | THEORETICAL AND NUMERICAL PHYSICS | ||

Academic Year | 2000/2001 | ||

Co-ordinator | Dr Nicholas Mitchell | ||

Semester | Semester 2 (Taught over 2 semesters) | ||

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

Pre-Requisite | Normal entry requirements for Honours Physics degree | ||

Co-Requisite | Part 1 core modules | ||

Mutually Exclusive | PH16010 | ||

Course delivery | Lecture | 30 Hours | |

Seminars / Tutorials | 10 Hours | ||

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

Course work | Example sheet deadlines (by week of semester):
Example sheets 1,2,3,4,7 & 10 in weeks 2,3,4,5,8 & 11 of semester 1
Example sheets 11,13,15,17,19,21,23,25 & 27 in weeks 2 to 11 of semester 2 | 30% |

**Brief description**

Problem solving and numeracy are fundamental requirements in Physics and highly valued skills in the work place. This module is aimed at enabling students to solve numerical problems and to perform basic operations in calculus. Provision will be through lectures, weekly example sheets and problem solving seminars based on the applications of elementary vectors, complex numbers, trigonometry, calculus and differential equations encountered in Part 1 Physics.

**Learning outcomes**

After taking this module students should be able to:

- Understand the utility of elementary vectors, complex numbers, trigonometry, calculus and differential equations for analysis in Physics.
- Apply the mathematical problem solving techniques developed to treat a range of simple physical systems.
- Answer straight forward numerical and calculus related problems in Physics.

**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