|Module Title||THEORETICAL PHYSICS 1|
|Co-ordinator||Dr Nicholas Mitchell|
|Other staff||Dr Philip Cadman, Dr Geraint Vaughan|
|Pre-Requisite||Normal entry requirements for Part I Physics|
|Course delivery||Lecture||20 lectures|
|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%|
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:
Additional learning activities
(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
K.A. Stroud. Engineering Mathematics. MacMillan
** Supplementary Text
M.L. Boas. Mathematical Methods in the Physical Sciences. Wiley