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2010/1 Module Catalogue
Module Provider: Physics Short Name: PH1M-MATHS
Level: HE1 Module Co-ordinator: TOSTEVIN JA Prof (Physics)
Number of credits: 30 Number of ECTS credits: 15
Module Availability
Semester 1 and Semester 2.
Assessment Pattern


Assessment Pattern


Unit(s) of Assessment


Weighting Towards Module Mark( %)


Semester 1 Coursework; Mathematics 1 Class Tests (x2)




Semester 2 Coursework; Mathematics 2 Class Test




Semester 2 Coursework; Mathematics 3 Class Test




Mathematics 2 Examination




Mathematics 3 Examination




Qualifying Condition(s) 


University general regulations refer.



Assessment Schedule


Semester 1 Coursework:


Two class tests in weeks 7 and 15



Semester 2 Coursework:


Two class tests in week 7, one on Mathematics 2 and one on Mathematics 3


Examination Paper 1 (June):


3 hour examination consisting of;



Section A; answer 4 questions on Mathematics 2 and 4 questions on Mathematics 3 (weighted at 35% of the examination paper)






Section B; answer 3 from 4 questions on Mathematics 2 and 3 from 4 questions on Mathematics 3 (weighted at 65% of the examination paper)












Module Overview


Mathematics 1:


This component is offered on a supervised self-study basis during semester 1. Delivery is primarily by supported workshop classes with only occasional lectures, as required. The units of work are a selected subset of the FLAP (Flexible Learning Approach to Physics) units developed by the Open University. Mathematics 1 enhances basic mathematical skills to a little beyond Advanced level standard, providing the mathematical foundations needed for the subsequent Mathematics 2 and 3 components and other introductory (level HE1) Physics modules.


Mathematics 2:


This component is a lecture, self-study, and workshop format course. It introduces hyperbolic functions and their properties, including their connection with spherical trigonometric functions. It will expand upon the use of Taylor and other series expansions and will derive and give practice in the use of Fourier series. Methods of solution of simple first- and second-order ordinary differential equations are discussed with reference to simple physical applications.


Mathematics 3:


This component is a lecture, self-study, and workshop format course. The component covers matrices, simple linear algebra concepts, and an introduction to vector analysis and its applications. The component deals with functions of more than one variable, their derivatives and their integrals, including line integrals, double and triple integrals, and their associated applications.




Mathematics 1:


Advanced Level/AS-Level Mathematics or equivalent



Mathematics 2:


PHY1012 - Mathematics 1 component



Mathematics 3:


PH1012 - Mathematics 1 component


Module Aims

Mathematics 1:


To provide background knowledge and practice and confidence in the use of basic mathematical manipulation skills to a little beyond Advanced level standard in algebra, functions, real and complex numbers, and the differential and integral calculus.


Mathematics 2:


To enable students to define hyperbolic functions, to derive and use Fourier series, and to solve simple first- and second-order ordinary differential equations, including the concepts and appreciation of convergence tests of numerical series.


Mathematics 3:


To provide an understanding of functions of more than one variable, their derivatives, and the location of minima and maxima of functions of two variables. To enable the use multiple integrals to calculate surface and volume properties. To introduce matrices and to define and give practice in the use matrices and of some of the important constructs of introductory linear algebra.



Learning Outcomes

Mathematics 1:


The component will bring students who begin this component at different levels of competence and expertise, based on their mathematics entry grades, to a more uniform level by the end of their first Semester. All students will have consolidated techniques covered at Advanced level, especially integration and differentiation, and had a first exposure or revision of complex numbers and series.



Mathematics 2:


By the end of this component students will be familiar with the definition and use of hyperbolic functions and the basis and application of Fourier series for a number of different functions and physical situations.  They will be able to test numerical and functional series for their convergence properties and will be able to solve simple first- and second-order ordinary differential equations.



Mathematics 3:


By the end of this component, students will be able to use matrices to represent and solve sets of linear equations. They will be able to evaluate derivatives and integrals of two- and multi-variable functions and be able to apply these to find maxima and minima and to the calculation of physical quantities such as volume, mass, moments of inertia and centre of gravity of various geometric shapes with both homogeneous and inhomogeneous densities.


Module Content


Mathematics 1: Semester 1


FLAP units: worked through at a rate of one unit per week


i.        Arithmetic and Algebra (M1.1)


ii.       Solving equations (M1.4)


iii.     Series expansions and approximations (M1.7)


iv.     Introducing  complex numbers (M3.1)


v.      Polar representation of complex numbers (M3.2)


vi.     Basic differentiation (M4.2)



vii.   Further differentiation (M4.3)


viii.     Stationary points and graph sketching (M4.4)


ix.      Taylor series and polynomial approximations (M4.5)


x.      Basic integration (M5.2)


xi.     Techniques of integration (M5.3)



Mathematics 2: Semester 2


1:                Introduction to hyperbolic functions and their properties, derivatives, and series forms.


2:                Further examples of sequences, limits, convergence and series analysis.


3:                Fourier series; Euler-Fourier formula on (-π,π), harmonics, Dirichlet convergence conditions, odd and even functions, sine and cosine series, extension to interval (-L,L)


4:                First-order differential equations; the method of separation of variables and integrating


                   Factors. Exact differential equations. Simple second order equations with constant


                   coefficients, general and particular solutions.



Mathematics 3: Semester 2


1:                Matrices and vectors and the rules of matrix algebra. Rotations expressed in matrix


                   form. Linear equation sets; eigenvectors.


2:                Functions of two or more variables. Partial derivatives and Taylor ’s theorem. Maxima,


                   minima and saddle points.


3:                Line integrals, multiple integrals; double and triple integrals, changes of variables, the


                  Jacobian, the use of spherical and cylindrical coordinates.



Methods of Teaching/Learning

Mathematics 1: Semester 1


52 hours of workshops to include two formative progress tests



Mathematics 2: Semester 2


36 hours of lectures/workshop sessions



Mathematics 3: Semester 2


36 hours of lectures/workshop sessions.



Selected Texts/Journals

Mathematics 1:


i.                R Lambourne and Michael Tinker, Basic Mathematics for the Physical Sciences, Wiley, 2000


ii.              Mary L Boas, Mathematical Methods for the Physical Sciences, Wiley, 1983.


iii.             K. Weltner, J. Grosjean, P. Schuster and W.J. Weber, Mathematics for Engineers and Scientists, Stanley Thornes, 1986.


iv.            Open University FLAP modules: copies distributed as Mathematics 1 Student Handbook



Mathematics 2:


In addition to the above,


i.                G Stephenson, Mathematical Methods for Science Students, Pearson, 1973.


ii.              Selected additional Open University FLAP modules.



Mathematics 3:


In addition to the above,  lecture notes which can be downloaded from;



Last Updated
August 2010.