
Academic Year:  2013/4 
Owning Department/School:  Department of Physics 
Credits:  6 
Level:  Certificate (FHEQ level 4) 
Period: 
Semester 2 
Assessment:  EX 100% 
Supplementary Assessment: 
PH10008  Mandatory Extra Work (where allowed by programme regulations) 
Requisites:  Before taking this unit 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 Alevel 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, RungeKutta 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
PH10008 is Optional on the following programmes:Department of Chemistry
