Module Identifier PH16020
Module Title THEORETICAL AND NUMERICAL PHYSICS
Co-ordinator Nicholas J 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
Other   Workshop. 10 example classes
Assessment
Assessment TypeAssessment Length/DetailsProportion
Semester Exam  70%
Semester 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%

#### Learning outcomes

After taking this module students should be able to:
• Understand the utility of elementary vectors, complex numbers, trigonometry, calculus and differential equations for analysis in Physics.
• Apply the mathematical problem solving techniques developed to treat a range of simple physical systems.
• Answer straight forward numerical and calculus related problems in Physics.

#### 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 I Physics.

#### Content

(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.
Phasors.

(d) Calculus