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Partial Differential Equations (PDEs) are the mathematical language of change in space and time. They are used to describe a wide variety of real-world systems. Examples of their applications include describing how waves travel, how heat spreads, weather forecasting, how the fundamental laws of Nature work, the pricing of financial derivatives such as stock options, and many others.

The module begins with a review of ordinary differential equations (ODEs), discussing first- and second-order methods, boundary value problems, and eigenvalue problems. We then introduce Sturm-Liouville theory and Fourier Series, seeing that it is possible to express a general periodic function as a sum of sine and cosine functions.

Next, we introduce some of the basic concepts of PDEs. The three important classes of second order PDE appropriate for modelling different sorts of phenomena are introduced, and the appropriate boundary conditions for each of these are considered. The technique of separation of variables is used to reduce a PDE to a set of ODEs of the kind reviewed at the start of the module, and to derive the general solution using Fourier Series and Sturm-Liouville theory. Throughout the module there will be a strong emphasis on problem solving and examples.

The last part of the module is an introduction to integral transforms, comprising Laplace Transforms and Fourier Transforms. We show how Laplace transforms are a very powerful technique to solve ODEs and PDEs, and how Fourier Transforms are very useful to solve PDEs.

Partial Differential Equations (PDEs) are the mathematical language of change in space and time. They are used to describe a wide variety of real-world systems. Examples of their applications include describing how waves travel, how heat spreads, weather forecasting, how the fundamental laws of Nature work, the pricing of financial derivatives such as stock options, and many others.

The module begins with a review of ordinary differential equations (ODEs), discussing first- and second-order methods, boundary value problems, and eigenvalue problems. We then introduce Sturm-Liouville theory and Fourier Series, seeing that it is possible to express a general periodic function as a sum of sine and cosine functions.

Next, we introduce some of the basic concepts of PDEs. The three important classes of second order PDE appropriate for modelling different sorts of phenomena are introduced, and the appropriate boundary conditions for each of these are considered. The technique of separation of variables is used to reduce a PDE to a set of ODEs of the kind reviewed at the start of the module, and to derive the general solution using Fourier Series and Sturm-Liouville theory. Throughout the module there will be a strong emphasis on problem solving and examples.

The last part of the module is an introduction to integral transforms, comprising Laplace Transforms and Fourier Transforms. We show how Laplace transforms are a very powerful technique to solve ODEs and PDEs, and how Fourier Transforms are very useful to solve PDEs.

Relativistic wave equations with their predictions of anti-particles and fermion spin will be explored. The fundamental role of gauge symmetries in current theories of force will lead to the study of the standard model of particle physics, including the spontaneous electroweak symmetry breaking via the Higgs mechanism.
Finally theories of particle physics beyond the standard model will be briefly investigated concentrating on their motivations and testable consequences.

Relativistic wave equations with their predictions of anti-particles and fermion spin will be explored. The fundamental role of gauge symmetries in current theories of force will lead to the study of the standard model of particle physics, including the spontaneous electroweak symmetry breaking via the Higgs mechanism.
Finally theories of particle physics beyond the standard model will be briefly investigated concentrating on their motivations and testable consequences.

Relativistic wave equations with their predictions of anti-particles and fermion spin will be explored. The fundamental role of gauge symmetries in current theories of force will lead to the study of the standard model of particle physics, including the spontaneous electroweak symmetry breaking via the Higgs mechanism.
Finally theories of particle physics beyond the standard model will be briefly investigated concentrating on their motivations and testable consequences.

This unit entirely consists of a research-level project

Upon successful completion of the project the student will have completed the final year of their Physics with Particle Physics Year Abroad MPhys degree. The supervisor(s) at RAL and CERN will have directed completion of a significant research ideally of publishable quality.

This unit entirely consists of a research-level project

Upon successful completion of the project the student will have completed the final year of their Physics with Particle Physics Year Abroad MPhys degree. The supervisor(s) at RAL and CERN will have directed completion of a significant research ideally of publishable quality.

Equal opportunity

In line with the University’s Equal Opportunities Policy, individuals are treated on their relevant merits and abilities and are given equal opportunities within the module, School and University. The aim of the policy is to ensure that no prospective student or current student should receive any less favourable treatment on any grounds which are not relevant to academic ability and attainment. Every effort is made to ensure that disabled students are aware of and assisted in making use of the support provided by the University; to ensure access to lectures, classes, learning materials; and to ensure that where necessary appropriate variations to normal examining arrangements are made.

This course introduces key theories and models in the study of political behaviour and political psychology and seeks to encourage students to develop a critical appreciation of how people develop their political beliefs and preferences, and how this affects their engagement in politics. The course is also designed to provide a practical and applied introduction to the study of political behaviour, applying theories to everyday political life and making use of the wealth of empirical data available on public opinion and political psychology. It deals with questions such as how people form their political beliefs and their attachments to political parties, how they evaluate political candidates and leaders, and why people do or don’t get involved in different forms of politics, be it voting, protest or civic action.

This course introduces key theories and models in the study of political behaviour and political psychology and seeks to encourage students to develop a critical appreciation of how people develop their political beliefs and preferences, and how this affects their engagement in politics. The course is also designed to provide a practical and applied introduction to the study of political behaviour, applying theories to everyday political life and making use of the wealth of empirical data available on public opinion and political psychology. It deals with questions such as how people form their political beliefs and their attachments to political parties, how they evaluate political candidates and leaders, and why people do or don’t get involved in different forms of politics, be it voting, protest or civic action.