Module Identifier PH16020  
Academic Year 2001/2002  
Co-ordinator Dr Nicholas Mitchell  
Semester Intended for use in future years  
Next year offered N/A  
Next semester offered N/A  
Other staff Professor Geraint Vaughan, Dr Philip Cadman  
Pre-Requisite Normal Entry to Part 1 Physics  
Co-Requisite Part 1 Core Modules  
Mutually Exclusive PH16010  
Course delivery Lecture   30 lectures  
  Workshop   10 example classes  
Assessment Course work   /Example Sheets Coursework Deadlines (by week of semester): Example Sheets 1,2,3,4,7 and 10 (sem 1) Weeks 2,3,4,5,8 & 11 Example Sheets 11,13,15,17,19,21,23,25 and 27 Weeks 2 to 11 (sem 2)   30%  
  Exam     70%  

Module objectives / Learning outcomes

After taking this module students should be able to:

Module 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 I Physics.

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.
i) 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.   

(d) Calculus

Reading Lists

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