# Study-Unit Description

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CODE PHY1125

TITLE Mathematics for Physicists 1

LEVEL 01 - Year 1 in Modular Undergraduate Course

ECTS CREDITS 4

DEPARTMENT Physics

DESCRIPTION This study-unit lays the mathematical foundations on which is built the undergraduate physics degree. It introduces concepts that may be familiar to some of the students, such as complex numbers and the notion of functions, but also covers topics such as Fourier series that will be new to all students. It also establishes a common nomenclature and notation, and will therefore ensure that all students following the physics undergraduate degree possess a rigorous mathematical base.

Study-unit Aims:

This study-unit aims to provide students with the basic mathematical tools they require to read for an undergraduate degree in physics. It provides a solid foundation on which the physics courses can be built.

Learning Outcomes:

1. Knowledge & Understanding
By the end of the study-unit the student will be able to:

- describe the notion of a function;
- explain how to use basic calculus (derivatives and integrals) to find extrema;
- describe the geometric interpretation of eigenvalues and diagonalisation of matrices;
- describe the difference between first- and second-order ordinary differential equations, as well as between ordinary and partial differential equations;
- explain how Fourier series can be used to analyse the behaviour of functions.

2. Skills
By the end of the study-unit the student will be able to:

- solve arithmetic problems involving the use of complex numbers;
- calculate derivatives and integrals of a number of elementary functions (e.g., polynomials, exponentials, and trigonometric functions);
- classify turning points of a function using the first and second derivatives;
- calculate the determinant, eigenvalues, and eigenvectors of a matrix;
- use concepts from vector analysis and calculus to analyse multi-dimensional functions of one or more variables;
- solve first-order linear ordinary differential equations: Linear constant coefficient equations, seperable equations, Euler homogeneous equations, and the Bernoulli equation;
- solve second-order linear ordinary differential equations: Homogeneous equations, the linear oscillator, and homogeneous constant coefficient equations, and be able to transform to constant coefficients;
- solve partial differential equations: First-order equations and second-order equations, be able to use separation of variables, and be able to solve the Laplace and Poisson equations;
- obtain the cosine and sine series of basic functions.

Main Text/s and any supplementary readings:

- K. F. Riley, M. P. Hobson and S. J. Bence “Mathematical Methods for Physics and Engineering” 3rd Edition, Cambridge University press, 2006.
- Arfken, George “Mathematical Methods for Physicists” 7th Edition, Academic Press, New York, 2003.

STUDY-UNIT TYPE Lecture

METHOD OF ASSESSMENT
 Assessment Component/s Assessment Due Resit Availability Weighting Examination (2 Hours) SEM1 Yes 100%

LECTURER/S Iman Farhat

The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints.
Units not attracting a sufficient number of registrations may be withdrawn without notice.
It should be noted that all the information in the study-unit description above applies to the academic year 2019/0, if study-unit is available during this academic year, and may be subject to change in subsequent years.

https://www.um.edu.mt/course/studyunit