Module Identifier PH16010  
Academic Year 2001/2002  
Co-ordinator Dr Philip Cadman  
Semester Semester 1  
Other staff Dr James Whiteway, Dr Nicholas Mitchell, Dr Xing Li  
Pre-Requisite Normal entry requirements for Part I Physics  
Mutually Exclusive PH16520  
Course delivery Lecture   20 lectures  
  Workshop   2 example classes  
Assessment Course work   Example Sheets 1,2,3,4, 7 and 10 Deadlines are given in the Year 1 Example Sheet Schedule distributed by the Department.   30%  
  Exam   2 Hours End of semester examination   70%  

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:

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. 5th. MacMillan 0333919394
** Supplementary Text
M.L. Boas. Mathematical Methods in the Physical Sciences. Wiley 0471044091