Module Identifier PH16520  
Academic Year 2001/2002  
Co-ordinator Dr Philip Cadman  
Semester Semester 2 (Taught over 2 semesters)  
Other staff Dr James Whiteway, Dr Nicholas Mitchell, Dr Xing Li  
Pre-Requisite Normal entry requirements for Honours Physics degree  
Co-Requisite Part 1 core modules  
Mutually Exclusive PH16010  
Course delivery Lecture   36 lectures  
  Workshop   4 Example Classes  
Assessment Course work   Example Sheets 1,2,3,4,7,10,11,12,13,14,17 and 19 Deadlines are given in the Year 1 Example Sheet schedule distributed by the Department   30%  
  Exam   3 Hours End of semester examination   70%  

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:

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