Imperial College London

This course provides a basic understanding of the fundamental laws of fluid mechanics and the ability to use them in solving a range of simple engineering problems. Students develop analytical skills and some design appreciation, involving awareness of the interaction between fluid mechanics and considerations of energy resources, materials, solid mechanics, economics, and the environment. The course examines the historical development of the subjects as well as current trends. Laboratory work reinforces lecture material, provides experience of relevant measuring techniques, and develops skills in group working and in written communication.

This applied analysis course leads to an introduction to some of the standard algorithms in numerical analysis. Students explore orthogonality, alongside inner/outer products on Rn; linear dependence/independence; orthogonal/orthonormal vectors; classical Gram-Schmidt; orthogonal matrices; Givens rotations, QR factorization, and Cauchy-Schwartz inequality. The course also covers gradients/Hessians, exploring Taylor series for f: Rn à? R; classification of stationary points; positive definite matrices; generalized inner products on Rn; and Cholesky factorization of symmetric positive definite matrices.

This course introduces students to basic philosophical terminology and some of the basic philosophical notions and debates. Students learn forms of non-scientific argumentation, relate classic philosophical problems to contemporary issues, and develop essential transferable skills, including written and oral communication skills. Students also gain experience in the synthesis and analysis of a range of information sources.

In this course, students create a piece of technology (for example and application) that is the basis of their project. Alongside this, students write an extensive report.

This course addresses conservation of mass; concept of stream function; conservation of momentum; derivation of governing equations using vector calculus and concepts of stress tensors; comparison with control volume approach; direct analytical solution of equations for unidirectional flows in (micro-)channels, pipes, and falling films; extension to flows that are not unidirectional; evolving flows; and concept of boundary layers. Example problems include unsteady shear flows, Blasius boundary layer, and jets.

This course examines the analysis of stresses and strains in solid deformable bodies subjected to bending, shearing, and twisting actions. The course provides a basic understanding of the physical behavior of complex structural elements, and gives students familiarity with the methods required to analyze them. Students calculate the stresses and strains in, and displacements of, a number of complex but commonly used structural elements which are assumed to deform elastically.

This class addresses the fundamental concepts and advanced methodologies of deep learning and relates them to real-world problems in a variety of domains. The aim is to provide an overview of different approaches, both classical and emerging. The class will equip you with the necessary knowledge and skills to work in the field of deep learning and to contribute to ongoing research in the area.

In this class you will have the opportunity to be provided with the necessary mathematical background and skills in order to understand, design and implement modern statistical machine learning methodologies, as well as inference mechanisms. You will be provided with examples regarding the use of mathematical tools for the design of foundational machine learning and inference methodologies, such as Principal Component Analysis (PCA), Bayesian Linear Regression and Support Vector Machines Learning outcomes Upon successful completion of this module you will be able to implement foundational machine learning algorithms from scratch. Students will be able to apply appropriate mathematical techniques in a machine learning setting and critically assess the quality of machine learning models, as well as evaluate connections between different machine learning algorithms.

This course teaches the nature of statistical data and what statistics is about. Students interpret basic statistical graphical displays and numerical summaries of data, as well as distinguish discrete and continuous random variables. Students learn to state and apply the properties of statistical distributions, alongside performing parameter estimation and hypothesis testing. Students also calculate the likelihood function for a set of data under a statistical model.