Module Identifier PH16010  
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:

Additional learning activities

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.

Reading Lists
** Recommended Text
K.A. Stroud. Engineering Mathematics. MacMillan
** Supplementary Text
M.L. Boas. Mathematical Methods in the Physical Sciences. Wiley