What will I learn on this module?
The module is designed to provide you with the advanced mathematical and statistical techniques required to underpin study of physics at level 5 and beyond. Techniques covered will include Matrices, Fourier Series and Fourier and Laplace Transforms, Probability distributions, and an introduction to vector calculus (including div, grad and curl).
Students will develop skills in the use of advanced mathematical and statistical techniques, applying suitable mathematical calculations over a range of key topics, including explaining how a periodic waveform can be represented as an infinite series of sinusoids, and applying Fourier Transforms. The concepts of the eigenvalue and eigenvectors of a matrix, and how these can be found by algebraic means will also be covered. Finally, students will be introduced to vector calculus and vector operators, including div, grad and curl, and the Kronecker delta and Levi-Civita epsilon.
Linear Algebra
Algebraic evaluation of the eigenvalues and eigenvectors of a matrix (i.e. Matrices to the level of eigenvalues and eigenvectors). Application to the solution of a system of linear ordinary differential equations.
Vector Calculus
Coordinate systems; line, surface and volume integrals; Vector operators Grad, Div and Curl; Gauss’ (Divergence) Theorem, Stokes’ Theorem; Introduction to Cartesian tensors. Applications of vector calculus.
Fourier Series and Fourier and Laplace Transforms
Fourier series and periodic functions. Full-range and half-range series. Even and odd functions. Coefficients in complex form. Application to the solution of partial differential equations by the method of separation of variables. Fourier Transforms. Laplace Transforms. The convolution theorem. An introduction to the solution of partial differential equations.
Probability Distributions
Sample space, types of events, definition of probability, addition and multiplication laws, conditional probability. Discrete probability distributions including Binomial, Poisson. Continuous probability distributions including the Normal distribution.
How will I learn on this module?
A wide range of learning and teaching approaches are used in this module. The module will be delivered using a combination of lectures, set work and skills periods in which you will be able to obtain help with problems associated with the module. Lectures allow you to experience and understand the formalism of advanced mathematical techniques and include relevant examples. You will have an opportunity to enhance your understanding of the subject through seminars which promote independent learning and tackle relevant problems. You will be provided with formative feedback on problems in seminars and have the opportunity to problem solve within peer groups. The mathematical rigour associated with this module naturally increases your potential for employability and is a highly transferable skill.
The module will be assessed by coursework (30%) and formal examination (70%). Exam feedback will provided individually and also generically to indicate where the cohort has a strong or a weaker answer to examination questions. Written feedback will be provided on the coursework. Formative feedback will be provided during the seminars.
Formative feedback will be provided on seminar work which will include problems designed to aid your learning and understanding.
Written feedback will be provided on the coursework. Exam feedback will provided individually and also generically to indicate where the cohort has a strong or a weaker answer to examination questions.
How will I be supported academically on this module?
In addition to direct contact with the module team during lectures and seminars, you will be encouraged to develop your curiosity by making direct contact with the module team either via email or the open door policy operated throughout the programme. You will also be regularly referred to supporting resources including relevant texts and relevant multimedia materials.
References to these resources will be made available through the e-learning portal and in lectures and seminars.
What will I be expected to read on this module?
All modules at Northumbria include a range of reading materials that students are expected to engage with. The reading list for this module can be found at: http://readinglists.northumbria.ac.uk
(Reading List service online guide for academic staff this containing contact details for the Reading List team – http://library.northumbria.ac.uk/readinglists)
What will I be expected to achieve?
Knowledge & Understanding:
1. Determine the eigenvalues and eigenvectors of a matrix and use them to solve a system of linear ordinary differential equations.
2. Determine the Fourier Series of a periodic waveform, and apply and obtain Fourier Transforms.
3. Apply vector calculus and manipulate Cartesian tensors.
4. Apply appropriate statistical methods to statistics problems.
Intellectual / Professional skills & abilities:
•
Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity) (PVA):
How will I be assessed?
SUMMATIVE
1. Coursework (30%) – 1, 2, 3, 4
2. Examination (70%) – 1, 2, 3, 4
FORMATIVE
1. Seminars – 1, 2, 3, 4
Students will be assessed by coursework (30%) and a formal examination (70%). The coursework will provide an opportunity for the student to demonstrate knowledge of the Fourier and Laplace Transforms topics. The examination will cover all topics from the module.
Formative feedback will be provided on seminar work which will include problems designed to aid student understanding. Written feedback will be provided on the coursework.
Pre-requisite(s)
None
Co-requisite(s)
None
Module abstract
The module is designed to provide you with the advanced mathematical and statistical techniques required to underpin study of physics at level 5 and beyond. You will develop your abilities in the utilisation of advanced mathematical and statistical techniques, applying suitable mathematical calculations over a range of key topics, including explaining how a periodic waveform can be represented as an infinite series of sinusoids, and applying Fourier Transforms. We will cover the concepts of the eigenvalue and eigenvectors of a matrix, and how these can be found by algebraic means. Finally, you will be introduced to vector calculus and vector operators, including div, grad and curl, and the Kronecker delta and Levi-Civita epsilon. Assessment of the module is by one class test (30%) and one formal examination (70%) and the module will be delivered using a combination of lectures and seminars.
Course info
UCAS Code F301
Credits 20
Level of Study Undergraduate
Mode of Study 4 years full-time or 5 years with a placement (sandwich)/study abroad
Department Mathematics, Physics and Electrical Engineering
Location City Campus, Northumbria University
City Newcastle
Start September 2024 or September 2025
All information is accurate at the time of sharing.
Full time Courses are primarily delivered via on-campus face to face learning but could include elements of online learning. Most courses run as planned and as promoted on our website and via our marketing materials, but if there are any substantial changes (as determined by the Competition and Markets Authority) to a course or there is the potential that course may be withdrawn, we will notify all affected applicants as soon as possible with advice and guidance regarding their options. It is also important to be aware that optional modules listed on course pages may be subject to change depending on uptake numbers each year.
Contact time is subject to increase or decrease in line with possible restrictions imposed by the government or the University in the interest of maintaining the health and safety and wellbeing of students, staff, and visitors if this is deemed necessary in future.
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