In the first part of this module we build on multivariate calculus studied in the first year and extend it to the calculus of scalar and vector functions of several variables. Line, surface and volume integrals are considered and a number of theorems involving these integrals (named after Gauss, Stokes and Green) will be discussed. In particular Green’s theorem, which gives a formula for the line integral of a vector field in the plane round a closed curve, is closely related to complex integration considered in the second part of the module. The integral theorems are also useful in many branches of Applied Mathematics and to describe physical quantities that vary in space and in time. For example, this module is a pre-requisite for MATH2044, Fields and fluids, where these methods are used to describe the behaviour of fluids and of electromagnetic fields. In the second part of this module, we extend our investigation of calculus to functions of a complex variable, once again building on the material studied in the first year. This theory has both great aesthetic appeal and a large number of applications. We focus here on the integration of these functions, particularly along curves in the complex plane. We develop the basic theory and ideas of the integration of a function of a complex variable, use the main theorems such as Cauchy’s theorem and the Cauchy integral formula, and explore some of their consequences, such as the Fundamental Theorem of Algebra and the evaluation of real integrals.
In the first part of this module we build on multivariable calculus studied in the first year and extend it to the calculus of scalar and vector fields. Cartesian as well as curvilinear coordinates are used, and we study gradient, divergence and curl. Line, surface and volume integrals over scalar and vector fields are studied in detail. The most important results are the integral theorems by Stokes and Gauss, which bring together nearly all concepts studied in the first part of the module. As a corollary, Green’s theorem is derived, which is closely related to complex integration considered in the second part of the module. The integral theorems are essential in many branches of Applied Mathematics. For example, this module is a pre-requisite for the module Fields and Fluids, where the techniques learned here are employed to describe the behaviour of fluids and of electromagnetic fields. In the second part of this module, we extend our investigation of calculus to functions of a complex variable, once again building on the material studied in the first year. This theory has both great aesthetic appeal and a large number of applications. We study differentiability of complex functions and then focus on integration along curves in the complex plane, discussing Cauchy's theorem and integral formula. Series expansion of complex functions is developed and then used to classify singularities and define the residue. This leads to the residue theorem, which is employed in many examples, in particular for the evaluation of real integrals. Complex variable theory is crucial for various applications in Applied Mathematics, in particular Theoretical Physics, and elements of it will be used in Fields and Fluids.
This module provides the second year student with the basic concepts of human and other vertebrate animal development. Students will come to understand the main mechanisms behind both animal development and organised cellular differentiation and how these processes are studied. They will also become aware of how various changes in developmental pathways can play a role in human and animal health. Lectures will be accompanied by practicals, some of which involve the use of animal tissue, with alternatives in place if required to meet minimum learning outcomes.
Vertebrates are amongst the most successful animal groups. From fish, amphibians, lizards, crocodiles, birds and mammals, you will gain an understanding how the basal members of the clade have diversified and evolved to fill every imaginable niche on land, sea and air. You will develop an overview of the anatomy, physiology, behaviour and the ecological interactions across this group of vertebrates.
This module provides an in-depth introduction to vestibular audiology, including the anatomy and physiology of the vestibular system within the wider contexts of the systems of eye movement and balance control, the vestibulo-ocular reflex, important pathologies of the vestibular system, the assessment of patients with vestibular orders, the impact of vestibular disorders on people, recovery mechanisms to vestibular disorders and vestibular rehabilitation. This module is available for (i) MSc students taken on campus and (ii) also for CPD students (such as audiologists, physiotherapists and hearing therapists) taken as distance learning. This module profile describes the teaching approach for on-campus students. Potential CPD students should contact the module lead for further information about the separate, specific arrangements for distance learning: dr@soton.ac.uk
Vibration and shock of engineered structures occur due to dynamic loads arising during operation, e.g. in transportation vehicles, motors/generators and buildings. Analytical and numerical prediction tools are required during virtual prototyping to design structures to withstand their in-service loads, whilst experimental techniques are generally applied to scale models, components and assembled structures for model validation, parameter estimation and trouble-shooting purposes. By the end of this module you will have gained an appreciation for commonly occurring vibration and shock phenomena and the predictive and experimental tools available to design and mitigate against them. Whilst focussed on industrial tools of the trade, this module begins briefly with analytical descriptions of beams and plates. Such simple structural components often prove useful qualitative models in practical situations and provide helpful insight into vital concepts. For quantitative predictions, finite element (FE) analysis is universally used to obtain mass and stiffness matrices of distributed and complex structures. FE analysis is introduced briefly but the emphasis is on analysis options available in commercial software for condensing such models, computing modal and harmonic solutions and incorporating damping. Common sources of vibration are discussed, and methods are met for characterising and modelling sources. Two specific and ubiquitous examples are considered in detail: random excitation and rotating machinery. The most commonly used experimental technique is that of transfer function measurement, from which modes of vibration can be inferred. Almost invariably, transfer functions are measured using either an instrumented hammer test or a shaker test, both of which enable the structure to be excited in a controlled and measurable way. Both techniques are discussed in detail, and you will become competent at hammer testing through a practical laboratory. Another type of vibration testing concerns the structural integrity of components and structures that are subjected to large dynamic loads, such as electronic equipment during a rocket launch. Commonly used standards for such tests are outlined, and a visit to a commercial test facility may be possible. The capstone to the module is an investigation in which students select and apply the most appropriate measurement, analysis, simulation and mitigation strategies studied throughout the semester to address a practical problem. The exercise is assessed through a consultancy style report.
This module combines the disciplines of social gerontology, social psychology, and sociology to address the intersection of crime and later life, including experiences of crime and criminal behaviour and social responses to these. It encourages students to challenge stereotypes about older people and their relationship to crime and the criminal justice system. It will use examples from UK and international literature.
This module primarily explores questions of video game ontology
This module will introduce you to the social, political and cultural history of Vienna and Berlin in the 20th century, German using a wide range of sources which will include literature, film and architecture. Topics covered may include the following: - The emergence of Vienna and Berlin and modern metropolises - Modernist culture in Vienna and Berlin - Jewish life in Vienna - The post-war division of Berlin and its aftermath - The legacy of the the Holocaust in post-war Berlin and Vienna
Would you like to understand why people - mostly men - are violent, or commit rape, or sexually abuse young children? Are people who do such things mentally ill? What might have happened to them in their lives that makes them commit such serious offences? Can such people be rehabilitated? Or should they just be locked up forever? These are the kind of challenging but intriguing questions which this third year optional module asks you to consider. It brings together theory and practice from forensic psychiatry and psychology, sociological criminology, and psychoanalysis to consider some of the possible causes of violent and sexually violent crime, and possible ways of working effectively with these offenders to help them to change.
This module gives you the opportunity to explore an allergy-related topic of your choice in greater depth and to translate your learning discovery into an educational resource, thereby feeding forward your knowledge and skills to your chosen learner. Based on your chosen topic, you will design and produce a Virtual Patient (VP), an interactive patient scenario, for health care professionals (or students), with the aim of producing a teaching or training resource that develops their clinical reasoning and decision-making skills. Through the VP, your learner will be able to explore your chosen allergy-related topic and learn about aspects such as obtaining a history and making diagnostic, therapeutic and management decisions in a ‘safe’ (virtual) environment. Having chosen the topic and target learners, you will create this learning environment by constructing activities and assessment questions that are aligned with topic-specific learning outcomes and supported with rich feedback. Our online module is delivered using a blend of live teaching and pre-recorded sessions. You are expected to attend all live sessions which allow you to engage with our expert teachers and your fellow students and benefit from rich discussions. Our recorded sessions allow you to learn at your convenience within each teaching week. Most of our students continue to work while studying and benefit from this flexibility. Engaging with these live sessions allows you to gain support from your peers and the module leads, synthesise your learning and reflect on your progress as you go. This module is taught once a year and typically involves approximately 10 hours of student engagement per week. The module will take place during the following weeks (exact timetable to be confirmed): •Teaching & guided learning: 06/03/26-20/03/26 •Self-directed learning: 21/03/26-15/04/26
This module gives you the opportunity to explore an allergy-related topic of your choice in greater depth and to translate your learning discovery into an educational resource, thereby feeding forward your knowledge and skills to your chosen learner. Based on your chosen topic, you will design and produce a Virtual Patient (VP), an interactive patient scenario, for health care professionals (or students), with the aim of producing a teaching or training resource that develops their clinical reasoning and decision-making skills. Through the VP, your learner will be able to explore your chosen allergy-related topic and learn about aspects such as obtaining a history and making diagnostic, therapeutic and management decisions in a ‘safe’ (virtual) environment. Having chosen the topic and target learners, you will create this learning environment by constructing activities and assessment questions that are aligned with topic-specific learning outcomes and supported with rich feedback. Our online module is delivered using a blend of live teaching and pre-recorded sessions. You are expected to attend all live sessions which allow you to engage with our expert teachers and your fellow students and benefit from rich discussions. Our recorded sessions allow you to learn at your convenience within each teaching week. Most of our students continue to work while studying and benefit from this flexibility. Engaging with these live sessions allows you to gain support from your peers and the module leads, synthesise your learning and reflect on your progress as you go. This module is taught once a year and typically involves approximately 10 hours of student engagement per week.
In this module, you will conduct an extensive, independent investigation into a topic of your choice, culminating in a Final Major Project. The aim of the module is to test your ability to conduct an autonomous, comprehensive analysis of a specific topic. Your project should demonstrate master’s-level understanding as you engage in topic identification, research design, and analysis. This should culminate in a well-structured research project that could align with a business context relevant to you and/or your career ambitions, your chosen pathway, or that addresses a contemporary marketing and/or branding issue that is of interest to you. You may choose to focus your project on the creative industries or on another industry related to your career or pathway choices.
We live in a world that is saturated by images, from the far reaches of space to the sub-atomic level and just about everything in between. Images seem to have a special power in our lives, playing a part in the constructions of who and what we are and the ways in which we understand the world around us. Whether we like it or not we live in a ‘visual culture’ in which virtually everything is mediated by visual technologies. This module takes as its starting point the assumption that as future designers, artists and professionals in the creative industries you will be future producers as well as consumers of visual culture. You will be introduced to some of the core theoretical issues that underpin the production and consumption of visual culture including questions of what an image is, how it works, its relationship to ideology and theories of representation.
Design hierarchical modules using a layout editor. Demonstrate project management and time management skills including working to deadlines and planning your work beyond the next deadline. Communicate your work accurately and concisely through written reports.
This modules provides an understanding of the design and layout of digital VLSI circuits and systems through laboratories and design exercises making use of appropriate CAD tools.
History, at its core, is made up of the stories of thousands of individuals. Often these individuals are the rich and powerful, but historians also study those with less authority and agency. In this module, you will look at sources and case studies about individual historical figures, specific texts, or small communities from the ancient world to the modern period, such as Anna Comnena, Pliny, and the sixteenth century miller, Domenico Scandella. By examining the sources made by and about these individuals and their surrounding historiography, this module invites you to think critically about how historians construct meaning out of documents and accounts written within specific contexts.
