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Programme & Unit Catalogues

## PH20020: Mathematics for scientists 4

Owning Department/School: Department of Physics
Credits: 6
Level: Intermediate (FHEQ level 5)
Period: Semester 2
Assessment Summary: EX 100%
Assessment Detail:
• Examination (EX 100%)
Supplementary Assessment: PH20020 - Mandatory Extra Work (where allowed by programme regulations)
Requisites: Before taking this module you must take PH20019
Description: Aims:
The aim of this unit is to introduce mathematical concepts and techniques required by science students, and to show how these may be used for different applications. It also aims to continue the development of students' problem-solving skills and their understanding of mathematical results.

Learning Outcomes:
After taking this unit the student should be able to:
* evaluate Fourier series and transforms, and use their properties to solve problems;
* use transform methods to solve differential equations;
* apply Fourier techniques to problems in the physical sciences;
* recognise and solve some of the key equations which arise in the natural sciences;
* apply the separation of variables method to linear partial differential equations, and solve the resulting ordinary differential equations by series solution.

Skills:
Numeracy T/F A, Problem Solving T/F A.

Content:
Fourier series (5 hours): Periodic functions. Harmonic synthesis. Representation as a Fourier series, Fourier components. Expansion of finite range functions. Applications of Fourier series. Complex form of Fourier series and coefficients. Discrete amplitude spectra.
Transition to aperiodic functions (7 hours): The Fourier transform. Integral definition and properties of the Fourier transform. Use of tables in evaluating transforms. Solution of differential equations. Dirac delta function. Convolution, sampling theorem. Uses and applications of Fourier techniques in the physical sciences.
Linear equations of science (10 hours): Derivation of the diffusion equation as an example of how PDEs arise in nature. Introduction to Laplace's, Poisson and wave equations. Linearity and superposition. Boundary conditions. Solution by separation of variables in Cartesian, cylindrical and spherical coordinate systems. Series solution of ODEs, including Legendre polynomials and Bessel functions.
Programme availability:

#### PH20020 is Compulsory on the following programmes:

Department of Physics
• USPH-AFB01 : BSc(Hons) Physics (Year 2)
• USPH-AAB02 : BSc(Hons) Physics with Study year abroad (Year 2)
• USPH-AKB02 : BSc(Hons) Physics with Year long work placement (Year 2)
• USPH-AFM02 : MPhys(Hons) Physics (Year 2)
• USPH-AKM04 : MPhys(Hons) Physics with Professional and Research Placements (Year 2)
• USPH-AKM03 : MPhys(Hons) Physics with Professional Placement (Year 2)
• USPH-AFM04 : MPhys(Hons) Physics with Research placement (Year 2)
• USPH-AAM03 : MPhys(Hons) Physics with Study year abroad (Year 2)
• USPH-AFB05 : BSc(Hons) Physics with Computing (Year 2)
• USPH-AAB06 : BSc(Hons) Physics with Computing with Study year abroad (Year 2)
• USPH-AKB06 : BSc(Hons) Physics with Computing with Year long work placement (Year 2)

#### PH20020 is Optional on the following programmes:

Programmes in Natural Sciences
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Year 2)
• UXXX-AAB02 : BSc(Hons) Natural Sciences with Study year abroad (Year 2)
• UXXX-AKB02 : BSc(Hons) Natural Sciences with Year long work placement (Year 2)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Year 2)
• UXXX-AKM02 : MSci(Hons) Natural Sciences with Professional Placement (Year 2)
• UXXX-AAM02 : MSci(Hons) Natural Sciences with Study year abroad (Year 2)
Department of Physics

Notes:
* This unit catalogue is applicable for the 2015/16 academic year only. Students continuing their studies into 2016/17 and beyond should not assume that this unit will be available in future years in the format displayed here for 2015/16.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.