Overview#

Acknowledgements#

These lecture notes are adapted from those given to me by colleagues who have previously taught this course in particular Rhoda Hawkins and Nigel Clarke have been incredibly helpful in sharing their materials with us.

Your input#

Please report any mistakes you find and feed back any comments you have to us so we can improve these notes. Thanks!

Appendix#

The material covered in each appendix is not needed for the PHY129 exam. This appendix is an “optional extra”. It is meant to give you an introduction to the ways in which you will come across techniques learnt in this module in physics you study later, and provide additional examples to suppoort learning of key concepts.

Information about Stream A and Stream B (PHY129)#

Learning objectives of Stream A#

Below are the learning objectives (LOs) of this module for Stream A. By the end of the module you should be able to:

  • Know how to apply the various rules of differentiation and integration to previously unseen functions.

  • Be able to apply the methods of differentiation to find stationary points of functions and series approximations to functions.

  • Know how to olve first and second order differential equations of relevance to physics.

Learning objectives of Stream B#

Below are the learning objectives (LOs) of this module for Streaam B. By the end of the module you should be able to:

  • Add, subtract, multiply and divide complex numbers.

  • Compute powers and roots of complex numbers by the application of De Moivre’s theorem.

  • To be able to convert between the various representations of complex numbers and to be aware of the definition of modulus, argument and conjugate of a complex number

  • Know how to manipulate matrices, vectors and scalars and their applications in physical problems

Format of PHY129#

As a course PHY129 is split into two streams (A & B) and within these streams you will have a lecture style session and a problem class session. In the lecture We will outline the key aspects of the material and work through some examples. These will relate to the problem class questions for the week’s session. The problem class and its associated questions will give you the opportunity to practise the material covered in the lecture and develop your skills tackling related mathematical problems. These lecture notes sit alongside the lecture and problem class. They are meant to form an overview of the material you will need for your assessments and the wider course. Whilst there are some worked examples within the lecture notes, the problem class is designed so that you will develop a set of worked examples to refer to in your revision for the exam.

FAQ: What should I know before starting this course?#

For this course you will need to remind yourself of some areas of maths you will have previously covered. Trigonometric identities will be required throughout the material covered in stream B. We will not revisit this material as you will have learnt this before. We recommend refreshing your memory in these areas before starting the course.

FAQ: How do I ask questions about the course and material?#

During the course you might have questions about the material covered in the course. When this happens you have several options for how to ask for help. During the session you can ask either myself or the graduate teaching assistants for help relating to the material covered in the lecture or in the problem class sheets. If you have a question outside of the session you can email us (p.stowell@sheffield.ac.uk for Stream A, a.ramadan@sheffield.ac.uk for Stream B) and we will aim to respond within 48 hours during the semester (not including weekends) or you can book a slot in my office hours so we can go over your problem in person. If you email during the winter holiday (late December - early January) you will get a response when we return to work in early January. If we think my answer to your question may be of wider interest to other students we will share your question and the response with all students (without any information identifying you).

FAQ: How will I be assessed in this course?#

You will have two assessed, online class tests during the semester (Weeks 6 and 10) and an in-person exam at the end of Semester 1. We will outline clearly before the class tests which weeks’ material will be covered in each test. The exam can cover any of the material in the course not in the appendix. We am happy to organise a problem class prior to the final exam if enough students are interested.