Student Records
Programme & Unit Catalogues

## PH10008: Mathematics for scientists 2

Owning Department/School: Department of Physics
Credits: 6
Level: Certificate (FHEQ level 4)
Period: Semester 2
Assessment Summary: EX 100%
Assessment Detail:
• Examination (EX 100%)
Supplementary Assessment: PH10008 - Mandatory Extra Work (where allowed by programme regulations)
Requisites: Before taking this module you must take PH10007
Description: Aims:
The aim of this unit is to introduce basic mathematical techniques required by science students, both by providing reinterpretation of material already covered at A-level in a more general and algebraic form and by introducing more advanced topics.

Learning Outcomes:
After taking this unit the student should be able to:
* integrate functions using a variety of standard techniques;
* find the general solution of first and second order ordinary differential equations and show how a particular solution may be found using boundary conditions;
* solve some first and second order partial differential equations by separation of variables;
* calculate the determinant and inverse of a matrix, and the product of two matrices;
* use matrix methods to solve simple linear systems.

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

Content:
Integration (6 hours): Review of integration. Meaning of integration. Methods of integration. Multiple integral, change of order in integration. Applications of integration (area, volume, etc). Numerical integration methods.
Ordinary differential equations (8 hours): Origin of ODEs. Solution of first order ODEs by integrating factors and separation of variables. Solution of second order ODEs with constant coefficients. Complementary function and particular integral. Applications in the natural sciences. Numerical solution of ODEs; Euler method, Runge-Kutta methods.
Introduction to partial differential equations (2 hours): Origin of PDEs. Solution of PDEs by separation of variable. Wave equation in one dimension.
Matrices and determinants (6 hours): Introduction to matrices. Special matrices. Transpose of a matrix. Matrix multiplication. Linear transformations. Determinants. Inverse of a matrix. Simultaneous linear equations. Solution of simultaneous equations, Gaussian elimination.
Programme availability:

#### PH10008 is Compulsory on the following programmes:

Department of Physics
• USPH-AFB01 : BSc(Hons) Physics (Year 1)
• USPH-AAB02 : BSc(Hons) Physics with Study year abroad (Year 1)
• USPH-AKB02 : BSc(Hons) Physics with Year long work placement (Year 1)
• USPH-AFM02 : MPhys(Hons) Physics (Year 1)
• USPH-AKM04 : MPhys(Hons) Physics with Professional and Research Placements (Year 1)
• USPH-AKM03 : MPhys(Hons) Physics with Professional Placement (Year 1)
• USPH-AFM04 : MPhys(Hons) Physics with Research placement (Year 1)
• USPH-AAM03 : MPhys(Hons) Physics with Study year abroad (Year 1)
• USPH-AFB10 : BSc(Hons) Physics with Astrophysics (Year 1)
• USPH-AAB10 : BSc(Hons) Physics with Astrophysics with Study year abroad (Year 1)
• USPH-AKB10 : BSc(Hons) Physics with Astrophysics with Year long work placement (Year 1)
• USPH-AFM10 : MPhys(Hons) Physics with Astrophysics (Year 1)
• USPH-AKM11 : MPhys(Hons) Physics with Astrophysics with Professional and Research Placements (Year 1)
• USPH-AKM10 : MPhys(Hons) Physics with Astrophysics with Professional Placement (Year 1)
• USPH-AFM11 : MPhys(Hons) Physics with Astrophysics with Research placement (Year 1)
• USPH-AAM10 : MPhys(Hons) Physics with Astrophysics with Study year abroad (Year 1)
• USPH-AFB05 : BSc(Hons) Physics with Computing (Year 1)
• USPH-AAB06 : BSc(Hons) Physics with Computing with Study year abroad (Year 1)
• USPH-AKB06 : BSc(Hons) Physics with Computing with Year long work placement (Year 1)

#### PH10008 is Optional on the following programmes:

Department of Chemistry
Programmes in Natural Sciences
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Year 1)
• UXXX-AAB02 : BSc(Hons) Natural Sciences with Study year abroad (Year 1)
• UXXX-AKB02 : BSc(Hons) Natural Sciences with Year long work placement (Year 1)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Year 1)
• UXXX-AKM02 : MSci(Hons) Natural Sciences with Professional Placement (Year 1)
• UXXX-AAM02 : MSci(Hons) Natural Sciences with Study year abroad (Year 1)

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.