|| PH16010 |
|| THEORETICAL PHYSICS 1 |
|| 2001/2002 |
|| Dr Philip Cadman |
|| Semester 1 |
|| Dr James Whiteway, Dr Nicholas Mitchell, Dr Xing Li |
|| Normal entry requirements for Part I Physics |
|| PH16520 |
| Course delivery
|| Lecture || 20 lectures |
|| Workshop || 2 example classes |
|| 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% |
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.
After taking this module students should be able to:
Apply the mathematical problem-solving techniques developed to analyse a range of simple physical systems.
(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:
(Introduction to Partial Differentiation)
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.
** Recommended Text
Engineering Mathematics. 5th. MacMillan 0333919394
** Supplementary Text
Mathematical Methods in the Physical Sciences. Wiley 0471044091