Physics with Astrophysics - U7UPHYAP

This year-long module covers the mathematical background required for the majority of undergraduate-level study of physics and astronomy. It will complement the material studied in other first-year physics degree modules.

The structure of the module has been designed to ease students into the level of maths required for the early stages of your degree. 

The topics covered in this module are:

• Complex numbers
• Differentiation and Taylor Series representations
• Stationary points of two-dimensional functions
• Integration techniques for functions of single and multiple variables
• Partial derivatives of functions of multiple variables
• Conic sections in plane geometry
• Fourier representation of functions and the Fourier transform
• Matrices and eigenvalue problems
• Solving first-order ordinary differential equations (ODEs)
• Solving homogeneous and inhomogeneous linear constant coefficient ODEs

In this module, you’ll develop your knowledge, understanding and problem-solving skills across several core areas of physics, including:

• classical mechanics
• relativity
• vibrations and waves
• quantum physics
• thermal physics

You’ll further explore how these theoretical principles explain a wide range of natural phenomena and examine their relevance to modern technological applications. 

This module builds on your foundation in both classical and modern physics, preparing you for more advanced topics and practical application.

In this module, you’ll continue to build your knowledge, understanding and problem-solving abilities in several core areas of physics, including:

• classical mechanics

• relativity

• vibrations and waves 

• quantum physics

• thermal physics

You’ll further explore how these theoretical principles explain a wide range of natural phenomena and examine their relevance to modern technological applications. 

This module builds on your foundation in both classical and modern physics, preparing you for more advanced topics and practical applications. 

New physical laws are discovered, and the consequences of known laws are understood through three main approaches: experimental, computational, and mathematical. This module provides a clear introduction to these methods. This module focuses on experimental and computational physics, along with concepts common to all three approaches.

In the experimental part of the module, you will carry out, record, and report on experiments, developing essential skills and learning standard experimental techniques.

The computational strand introduces you to Python programming for simulating physical models, analysing data and creating visualisations. The discovery strand ties everything together. You will use computational tools to analyse experimental and simulation data, assess and reduce random errors, and learn to communicate your findings clearly in a scientific style.

In this module, you’ll develop essential professional skills for a career in physics. You will focus on:

• professional communication

• teamworking

• professional behaviour and reflective practice

• academic integrity and ethics

• giving, receiving and reflecting on feedback

• equity, diversity and inclusion in physics

Through a series of activities, you’ll explore specialised areas of physics that you’ll study later in the programme, along with broader topics such as sustainability. You will also gain an understanding of how your degree is structured, the research that underpins it and the wide range of career paths available to physicists.

This module begins by developing the mathematical tools needed to describe classical fields, focusing on vector calculus. You will then explore the behaviour of static electric and magnetic fields, their sources, and their effects on charged particles.

The module progresses to dynamic situations where electric and magnetic fields interact, leading to the unified framework of Maxwell’s equations. You will see how these equations describe electromagnetic waves in empty space and apply this understanding to key concepts in optics.

Finally, the module introduces how electromagnetic fields behave in dielectric and magnetic materials, providing a foundation for further study in electromagnetism and optics.

This module builds on Investigations in Physics 1 and follows a similar structure, now focusing on mathematical, computational and discovery skills.

The mathematical aspect expands on techniques from the Mathematical Methods and Modelling for Physicists module. You will learn new methods for modelling physical systems, applying these to specific examples and exploring how models can be tested.

The computational part develops your coding skills further, covering data handling, analysis and modelling. You will work with more advanced data structures, algorithms, library functions, and learn modular design and code integration.

The discovery strand strengthens your abilities in data analysis, introducing more advanced hypothesis testing. You will also refine your skills in scientific report writing and presenting results effectively.

This module provides comprehensive training in three key areas: communicating science in different formats and for various audiences, working effectively in teams and applying practical problem-solving strategies.

You will have the opportunity to practice these skills in a range of settings, including synoptic tasks that integrate knowledge from across the core physics modules.

In this module you will learn how the same physics that works on Earth – gravity, electromagnetism, thermodynamics, optics, quantum physics, atomic and nuclear physics – is used to understand stars. You will explore the most important physical processes occurring in stars of different types. You will then use this knowledge to build mathematical models of stars and to understand their internal structure, their formation, evolution, and death.

You’ll study:

• How astronomers measure the most important properties of stars such as their mass, size, distance, brightness, temperature, chemical composition and age. This module will then teach you how physics is able to explain these properties.
• How energy is generated inside stars through nuclear fusion, and how it is transported to the surface to make stars shine.
• How to write the equations that describe the structure of stars, and how to use them to build mathematical models that explain their properties and evolution.
• How stars are born, how they evolve with time, how long they live, how they die, and what remnants they leave behind. You will be able to understand, for instance, how supernovae explode and how some black holes form.

This module provides an introduction to the theory and elementary applications of quantum mechanics, a theory that is one of the key achievements of physics. Quantum mechanics is an elegant theoretical construct that is both beautiful and mysterious. Some of the predictions of quantum mechanics are wholly counter-intuitive and there are aspects of it that are not properly understood. Nonetheless, it has been thoroughly tested empirically for nearly a century and, wherever predictions can be made, they agree with experiment.

The notes, videos, and simulations for the first semester of The Quantum World are all publicly available and freely accessible. Check out the notes online, which include embedded links to the videos and interactive simulations.

You’ll study:

• Quantum vs classical states
• Fourier series and transforms: translating from position to momentum space
• The Heisenberg uncertainty principle (particularly from a Fourier perspective)
• The time-dependent and time-independent Schrödinger equation
• Bound and unbound states, scattering and tunnelling
• Wavepackets
• The subtleties of the particle in a box
• Operators, observables, and the thorny measurement problem
• Matrix mechanics and Dirac notation
• The quantum harmonic oscillator
• Conservation and correspondence principles
• Angular momentum
• Stern-Gerlach experiment
• Spin
• Zeeman effect, Rabi oscillations
• 2D and 3D systems
• Degeneracies
• Hydrogen atom and the radial Schrödinger equation
• Entanglement and non-locality
• ... and, of course, that ever-frustrating feline...

This module explores the physical processes involved in the most extreme environments known in the Universe. Among the objects studied are neutron stars, black holes, supernova explosions, and active galactic nuclei.

This module explores the properties of matter across a wide range of scales, covering nuclear and particle physics, atomic physics, and solid state physics.

The focus will be on key concepts and models essential for understanding behaviour at each scale. You will also learn how quantum and statistical physics methods are applied to determine material properties, from microscopic systems to macroscopic bodies.

Cosmology is the scientific study of the Universe as a whole. It aims to understand what the Universe is made of, and its evolution from the Big Bang until today (and into the future).

You’ll study:

• observational evidence for the Big Bang
• how the expansion of the Universe depends on its contents and geometry
• how the contents of the Universe evolve as it expands and cools
• dark matter and dark energy: observational evidence and the latest theoretical models
• inflation, a proposed period of accelerated expansion in the very early Universe

In the first semester of this module, you'll engage in a series of lectures, workshops, and practical classes. Some sessions will build on the "Discovery" strand from Investigations in Physics I and II, while others will provide training on various computational techniques applied to astrophysics problems relevant to the offered projects. This foundational training will equip you with the skills needed for your upcoming project work.

During the second semester, you'll work in pairs on a computational astrophysics project chosen from a published list. By the end of the module, you'll have successfully used advanced computational techniques and developed a broader knowledge of computational astrophysics, including recent developments from current literature. You'll enhance your independent learning skills and further develop your investigative abilities by designing and conducting a computational study, analysing its results, and drawing critical conclusions. Additionally, you'll write a professional report summarising your background study and project results, preparing you for a career in astrophysics research and development.

You will carry out a project drawn from one of several areas of physics. The project may be experimental or theoretical in nature. Many of the projects reflect the research interests of members of academic staff. You will work in pairs and are expected to produce a plan of work and to identify realistic goals for your project. Each pair has a project supervisor responsible for setting the project. You will also be required to maintain a diary/laboratory notebook throughout.

Occasionally the work from these projects is used in scientific publications, and the students involved are named as authors on those publications.

Depending upon the type of project that you decide to do, you will design and carry out your own experiments, theoretical calculations or computational work and use them to generate what are often new and interesting results. The project culminates in your writing a scientific report which is submitted for assessment along with your laboratory notebook.

In this module, you'll deepen your knowledge and understanding of the frontiers in astrophysics, building on the basic principles of physics covered in Parts I and II. You'll engage with material informed by the forefront of current research, using the skills developed earlier in your programme. This module will allow you to critically engage with research literature and synthesize your knowledge to produce outputs in various formats.

By the end of the module, you'll have significantly enhanced your critical engagement with advanced topics in astrophysics. You'll strengthen your ability to independently research and gain a deep understanding of complex material. Additionally, you'll demonstrate high-level skills in communicating your understanding of advanced concepts and work successfully as part of a small team to research and present key aspects of cutting-edge astrophysical knowledge.

In this module, you'll have the opportunity to undertake an in-depth project in an advanced area of astrophysics, allowing you to demonstrate your abilities as an independent investigator. Each project starts with clear initial objectives but remains open-ended throughout the year. You'll begin by engaging with scientific literature to write a review article and then develop a detailed project proposal. You'll also participate in peer review panels to assess and rank proposals, gaining authentic experience of the research project lifecycle.

By the end of the module, you'll have written a substantial report (up to 7,500 words) on your project. This experience will help you develop critical skills, manage a substantial project, and effectively communicate your research findings. You'll demonstrate your ability to apply investigative skills to a significant research problem, critically engage with frontier research literature, and use advanced analytical, numerical, or experimental techniques. You'll also show proficiency in data analysis and manipulation, guiding your project to a successful completion.