- Student Records
Programme & Unit Catalogues

PH20019: Mathematics for scientists 3

Follow this link for further information on academic years Academic Year: 2014/5
Further information on owning departmentsOwning Department/School: Department of Physics
Further information on credits Credits: 6
Further information on unit levels Level: Intermediate (FHEQ level 5)
Further information on teaching periods Period: Semester 1
Further information on unit assessment Assessment Summary: EX 100%
Further information on unit assessment Assessment Detail:
  • Examination (EX 100%)
Further information on supplementary assessment Supplementary Assessment: PH20019 - Mandatory Extra Work (where allowed by programme regulations)
Further information on requisites Requisites: Before taking this unit you must take PH10008 and take PH10007
Further information on descriptions 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:
* find the eigenvalues and eigenvectors of matrices;
* calculate the normal modes of coupled vibrational systems;
* calculate and interpret derivatives of vector functions of 1 variable;
* parameterise curves;
* define and transform between Cartesian, plane polar, cylindrical polar and spherical polar coordinates;
* visualise points, lines, planes and volumes in these coordinates;
* define scalar, vector and conservative fields;
* evaluate and interpret grad, #2 and directional derivatives of scalar fields in the above coordinate systems;
* evaluate and interpret div and curl of vector fields in the above coordinate systems;
* evaluate and interpret line, surface and volume integrals in the above coordinate systems;
* identify conservative fields and find their potential functions;
* use and interpret vector integral theorems.

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

Eigenvalues and eigenvectors (6 hours): Revision of matrix algebra. Eigenvalues and eigenvectors of symmetric/Hermitian matrices and their properties. Linear transformations. Normal modes of ball and spring systems.
Vector calculus (16 hours): Differentiation of vectors. Space curves; parameterisation of curves, unit tangent vector. Scalar and vector fields in Cartesian coordinates. Gradient and directional derivative of a scalar field, # as a vector operator. Div and curl in Cartesian coordinates, physical interpretation. Identities involving #, definition of #2. Tangential line integrals. Conservative fields and potential functions. Surface, flux and volume integrals in Cartesian coordinates. Orthogonal curvilinear coordinate systems. Plane polar coordinates; velocity and acceleration, equations of motion. Spherical polar and cylindrical polar coordinates. Line, surface and volume integrals integrals in curvilinear coordinates. Grad, div, curl and #2 in curvilinear coordinates; div and curl as limits of integrals. Meaning and uses of #2. Vector integral theorems; Divergence, Stoke's and Green's theorems. Use of vector integral theorems.
Further information on programme availabilityProgramme availability:

PH20019 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

PH20019 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)

* This unit catalogue is applicable for the 2014/15 academic year only. Students continuing their studies into 2015/16 and beyond should not assume that this unit will be available in future years in the format displayed here for 2014/15.
* 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.