Course Details in 2023/24 Session

Module Title	LC Mathematics for Physicists 1A
School	Physics and Astronomy
Department	Physics & Astronomy
Module Code	03 34459
Module Lead	Dr Robert Smith
Level	Certificate Level
Credits	10
Semester	Semester 1
Pre-requisites
Co-requisites
Restrictions	None
Contact Hours	Lecture-33 hours Practical Classes and workshops-11 hours Guided independent study-56 hours Total: 100 hours
Exclusions
Description	Mathematics forms an extremely important part of your programme of studies. It is an important discipline in its own right and all students need to develop a significant competence in the subject. Physics has long played an important part in spurring the development of many important areas of Mathematics - Newton's development of the differential and integral calculus was motivated by the need to describe motion in the world around him. In recent years, the study of symmetry has blossomed into the major area of pure mathematics known as Group Theory, and many of the mathematical ideas developed in Group Theory are now part of the normal language of both crystallographers and particle physicists. Mathematics is the natural language in which Physics is expressed and, as in the study of any language, you need to become fluent both actively, so that you can set up and do calculations on your own, and passively, so that you can follow the mathematical arguments set out by other writers.Some of you will choose to study Mathematics more deeply through study of some of the more theoretical and mathematical modules offered either by this School or by the School of Mathematics, others of you will rely on the core material which all physicists must have mastered and which is covered in the core modules in both years 1 and 2. All the Mathematics which you learn in the first two years will be used somewhere - although in some cases you may need to wait a little while to see the relevance to physics of what you are learning. Where possible in this module, examples will always be given to illustrate where and why the mathematics you are studying is relevant to physics.To learn mathematics effectively it is not sufficient just to attend lectures and get a good set of notes, you need to practice the material you are studying in a fairly intensive way by doing lots of problems and by reading about both the mathematics you are studying and about its applications to physics. We will provide you with fortnightly sets of problems which you should attempt and specialist help will be provided for you in your Mathematics Examples Classes, which are sufficiently small in size that you should be able to get individual help from time to time if you get stuck and need help on a particular topic.Attendance at these Examples Classes is compulsory and part of the end of year module mark is made up of a component for attendance at these classes. The non-assessed Examples Sheets and the Examples Classes should help you get the practice and advice you need to cope with the fortnightly assessed Mathematics problems, the marks from which are used towards the assessment of the module. We also supplement the Examples Sheets by a series of computer-based practice problems on a number of basic mathematical topics that align directly with this module. Using this facility, you can test yourself, practice your mathematical skills and access the worked answers.Students on the Theoretical Physics Programme must get 70% or high in Mathematics for Physicists 1 in order to stay on the programme. A maths mark of lower than 70% will result in you being asked to transfer to a straight Physics programme. High marks in Mathematics for Physicists 2 and other theoretical modules may enable you to re-join the Theoretical Physics programme.
Learning Outcomes	By the end of the module students should be able to: Differentiate with fluency any reasonable function of one variable. Recognise, sketch and differentiate expressions involving trigonometric and hyperbolic functions and their inverses. Sketch functions of one variable, identify turning points and handle asymptotes correctly. Translate a piece of physics narrative involving rates of change into a mathematical expression. Sum an arithmetic or geometrical progression. Handle limits using de l'Hôpital's rule or other appropriate methods. Construct a Taylor series for a function of one variable. Handle the algebra of vectors and apply this to geometrical problems. Calculate and understand scalar and vector products and their physical applications. Construct the equations of lines and planes in vector and Cartesian form. Differentiate vector expressions with respect to a parameter such as time. Handle algebra and calculations involving complex numbers in Cartesian and polar form and use the Argand diagram to represent these. Use Euler's formula and de Moivre's Theorem to handle calculations involving trigonometric problems. Use a phasor to represent a simple harmonic oscillation. Integrate any reasonable function of one variable using all the standard techniques such as integration by parts, substitution etc. Resolve an expression into partial fractions.
Assessment	34459-01 : Examination : Exam (Centrally Timetabled) - Written Unseen (80%) 34459-02 : Assessed problems : Coursework (20%)
Assessment Methods & Exceptions	Coursework (20%); 3 hour Examination (80%). One single 3 hour exam to cover modules 34459 and 34462
Other
Reading List