Module Identifier PH16010 Module Title THEORETICAL PHYSICS 1 Academic Year 2000/2001 Co-ordinator Dr Nicholas Mitchell Semester Semester 1 Other staff Dr Philip Cadman, Dr Geraint Vaughan Pre-Requisite Normal entry requirements for Part I Physics Mutually Exclusive PH16020 Course delivery Lecture 20 lectures Seminar 2 seminars 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%

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:

• Apply the mathematical problem-solving techniques developed to analyse a range of simple physical systems.

None

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.
Phasors.