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The module will begin by looking at differential manifolds and the
differential calculus of maps between manifolds. Manifolds are an abstraction of the idea of a smooth surface in Euclidean space. The module will then look at calculus on manifolds including the study of vector fields, tensor fields and the Lie derivative.

The module will then go on to study Riemannian geometry in general by showing how the metric may be used to define geodesics and parallel transport, which in turn may be used to define the curvature of a Riemannian manifold.

As another major application the module will investigate groups, such as the rotation group SO(3), which also have the structure of a manifold. Such objects are called Lie groups and play an important role in both theory and application of geometry. As an example of this we look at the symmetries of Riemannian manifolds. The isometries of a Riemannian metric form a group and the corresponding infinitesimal isometries form a Lie algebra. Another class of examples will be provided by matrix groups.

Aerospace design is a multidisciplinary task involving different disciplines, such as aerodynamics, structure, flight dynamics and performance, propulsion, etc. An accurate and reliable assessment of aircraft characteristics in various fields is essential to each design project. Traditional methods in design were using empirical and statistical models at the beginning of the design and massive use of experiments later. In modern design approaches, digital design is taking over the role of traditional design approaches. In a digital design environment, numerical analysis is widely used instead of empirical/statistical methods and even experiments in many cases.
In this course, students get familiar with the fundamentals of digitalization in aerospace engineering, e.g., digital design environment and the digital twin concept, as well as the two widely used numerical analysis methods in aerospace design, i.e., the Finite Element Method (FEM) and Computational Fluid Dynamics (CFD).
FEM is a numerical approach for solving complex equations (including ODE/PDE), which might not even have known analytical solutions. FEM is widely used for structural analysis, fluid dynamics, heat transfer, and multi-physics problems. In this course, students get familiar with the fundamental theories of FEM and its application to structural analysis. It involves hands-on experience with commercial FEM software for analyzing aerospace structures.
CFD is an approach for numerically solving governing equations describing flow motion. Despite the structural analysis, where mostly FEM models are used, for CFD, besides FEM approaches, other approaches such as the Finite Volume Method (FVM) and Finite Difference Methods (FDM) are also applicable. Currently, the FVM is the most popular method in CFD. In this course, students get familiar with the fundamental theories of CFD and their application to aerodynamic/hydrodynamic analysis. It includes hands-on experience with commercial CFD software for studying aerospace aerodynamics.
A digital design environment is a tool to create a digital twin of the product and connect it to different solvers for various numerical analyses. The digital design tool should be capable of creating the required inputs for different solvers, executing them, and reading their outputs. The outputs are then integrated into the digital twin model for the different design processes.

Aerospace design is a multidisciplinary task involving different disciplines, such as aerodynamics, structure, flight dynamics and performance, propulsion, etc. An accurate and reliable assessment of aircraft characteristics in various fields is essential to each design project. Traditional methods in design were using empirical and statistical models at the beginning of the design and massive use of experiments later. In modern design approaches, digital design is taking over the role of traditional design approaches. In a digital design environment, numerical analysis is widely used instead of empirical/statistical methods and even experiments in many cases.
In this course, students get familiar with the fundamentals of digitalization in aerospace engineering, e.g., digital design environment and the digital twin concept, as well as the two widely used numerical analysis methods in aerospace design, i.e., the Finite Element Method (FEM) and Computational Fluid Dynamics (CFD).
FEM is a numerical approach for solving complex equations (including ODE/PDE), which might not even have known analytical solutions. FEM is widely used for structural analysis, fluid dynamics, heat transfer, and multi-physics problems. In this course, students get familiar with the fundamental theories of FEM and its application to structural analysis. It involves hands-on experience with commercial FEM software for analyzing aerospace structures.
CFD is an approach for numerically solving governing equations describing flow motion. Despite the structural analysis, where mostly FEM models are used, for CFD, besides FEM approaches, other approaches such as the Finite Volume Method (FVM) and Finite Difference Methods (FDM) are also applicable. Currently, the FVM is the most popular method in CFD. In this course, students get familiar with the fundamental theories of CFD and their application to aerodynamic/hydrodynamic analysis. It includes hands-on experience with commercial CFD software for studying aerospace aerodynamics.
A digital design environment is a tool to create a digital twin of the product and connect it to different solvers for various numerical analyses. The digital design tool should be capable of creating the required inputs for different solvers, executing them, and reading their outputs. The outputs are then integrated into the digital twin model for the different design processes.

Aerospace design is a multidisciplinary task involving different disciplines, such as aerodynamics, structure, flight dynamics and performance, propulsion, etc. An accurate and reliable assessment of aircraft characteristics in various fields is essential to each design project. Traditional methods in design were using empirical and statistical models at the beginning of the design and massive use of experiments later. In modern design approaches, digital design is taking over the role of traditional design approaches. In a digital design environment, numerical analysis is widely used instead of empirical/statistical methods and even experiments in many cases. In this course, students get familiar with the fundamentals of digitalisation in aerospace engineering, e.g., digital design environment and the digital twin concept, as well as the two widely used numerical analysis methods in aerospace design, i.e. the Finite Element Method (FEM) and Computational Fluid Dynamics (CFD).

FEM is a numerical approach for solving complex problems in engineering and mathematical physics, which might not even have known analytical solutions due to, for example, complexities in geometry, material properties and boundary conditions. FEM is widely used for structural analysis, fluid dynamics, heat transfer, acoustic and vibrations, and multi-physics problems. In this course, students get familiar with the fundamental theories of FEM and its application to structural analysis. It involves hands-on experience with commercial FEM software for analysing aerospace structures.

CFD is an approach for numerically solving governing equations describing flow motion. Finite Volume Methods (FVM) and Finite Difference Methods (FDM) are most commonly used. In this course, students get familiar with the fundamental theories of CFD and their application to aerodynamic/hydrodynamic analysis. It includes hands-on experience with commercial CFD software for studying aerospace aerodynamics.

Aerospace design is a multidisciplinary task involving different disciplines, such as aerodynamics, structure, flight dynamics and performance, propulsion, etc. An accurate and reliable assessment of aircraft characteristics in various fields is essential to each design project. Traditional methods in design were using empirical and statistical models at the beginning of the design and massive use of experiments later. In modern design approaches, digital design is taking over the role of traditional design approaches. In a digital design environment, numerical analysis is widely used instead of empirical/statistical methods and even experiments in many cases. In this course, students get familiar with the fundamentals of digitalisation in aerospace engineering, e.g., digital design environment and the digital twin concept, as well as the two widely used numerical analysis methods in aerospace design, i.e. the Finite Element Method (FEM) and Computational Fluid Dynamics (CFD).

FEM is a numerical approach for solving complex problems in engineering and mathematical physics, which might not even have known analytical solutions due to, for example, complexities in geometry, material properties and boundary conditions. FEM is widely used for structural analysis, fluid dynamics, heat transfer, acoustic and vibrations, and multi-physics problems. In this course, students get familiar with the fundamental theories of FEM and its application to structural analysis. It involves hands-on experience with commercial FEM software for analysing aerospace structures.

CFD is an approach for numerically solving governing equations describing flow motion. Finite Volume Methods (FVM) and Finite Difference Methods (FDM) are most commonly used. In this course, students get familiar with the fundamental theories of CFD and their application to aerodynamic/hydrodynamic analysis. It includes hands-on experience with commercial CFD software for studying aerospace aerodynamics.

To introduce you to the key concepts of digital analytics in the marketing discipline and how analytics can build knowledge of online customer behaviour and campaign effectiveness that can be used effectively in the business environment within which marketers now operate.

To introduce you to the key concepts of digital analytics in the marketing discipline and how analytics can build knowledge of online customer behaviour and campaign effectiveness that can be used effectively in the business environment within which marketers now operate.

The focus of this module is on the nature of marketing in the context of today's rapidly changing business environment, which primarily means digital and data-driven marketing. The module will provide you with a broad overview of marketing theory and practice. Its emphasis is on where and how the organisation competes and, in doing this, highlights the strategic significance of marketing in the digital and data-driven age.

The focus of this module is on the nature of marketing in the context of today's rapidly changing business environment, which primarily means digital and data-driven marketing. The module will provide you with a broad overview of marketing theory and practice. Its emphasis is on where and how the organisation competes and, in doing this, highlights the strategic significance of marketing in the digital and data-driven age.

To introduce you to the key concepts of digital analytics in the marketing discipline and how analytics can build knowledge of online customer behaviour and campaign effectiveness that can be used effectively in the business environment within which marketers now operate.