Conçu pour un cours de première année universitaire, ce manuel en algèbre …
Conçu pour un cours de première année universitaire, ce manuel en algèbre linéaire adopte une approche peu commune : il présente les espaces vectoriels dès le début et traite des systèmes linéaires qu’après une introduction approfondie aux espaces vectoriels. Cette approche est fondée sur l’expérience des auteurs ayant observé au cours des 25 dernières années que les étudiantes et étudiants ont souvent besoin davantage de temps pour maîtriser les espaces vectoriels alors que les manuels traditionnels relèguent plutôt le sujet à la fin du cours. De cette façon, ces nouvelles notions au coeur de l’algèbre linéaire qui sont souvent considérées comme abstraites et difficiles dans un cours d’introduction peuvent ensuite être utilisées dans le reste du cours ainsi que différents contextes.
This course will teach fundamentals of control design and analysis using state-space …
This course will teach fundamentals of control design and analysis using state-space methods. This includes both the practical and theoretical aspects of the topic. By the end of the course, you should be able to design controllers using state-space methods and evaluate whether these controllers are robust to some types of modeling errors and nonlinearities. You will learn to:
Design controllers using state-space methods and analyze using classical tools. Understand impact of implementation issues (nonlinearity, delay). Indicate the robustness of your control design. Linearize a nonlinear system, and analyze stability.
This course gives a mathematical introduction to neural coding and dynamics. Topics …
This course gives a mathematical introduction to neural coding and dynamics. Topics include convolution, correlation, linear systems, game theory, signal detection theory, probability theory, information theory, and reinforcement learning. Applications to neural coding, focusing on the visual system are covered, as well as Hodgkin-Huxley and other related models of neural excitability, stochastic models of ion channels, cable theory, and models of synaptic transmission. Visit the Seung Lab Web site.
This course offers an advanced introduction to numerical analysis, with a focus …
This course offers an advanced introduction to numerical analysis, with a focus on accuracy and efficiency of numerical algorithms. Topics include sparse-matrix/iterative and dense-matrix algorithms in numerical linear algebra (for linear systems and eigenproblems), floating-point arithmetic, backwards error analysis, conditioning, and stability. Other computational topics (e.g., numerical integration or nonlinear optimization) are also surveyed.
This course focuses on the use of modern computational and mathematical techniques …
This course focuses on the use of modern computational and mathematical techniques in chemical engineering. Starting from a discussion of linear systems as the basic computational unit in scientific computing, methods for solving sets of nonlinear algebraic equations, ordinary differential equations, and differential-algebraic (DAE) systems are presented. Probability theory and its use in physical modeling is covered, as is the statistical analysis of data and parameter estimation. The finite difference and finite element techniques are presented for converting the partial differential equations obtained from transport phenomena to DAE systems. The use of these techniques will be demonstrated throughout the course in the MATLAB® computing environment.
This course provides an introduction to linear systems, transfer functions, and Laplace …
This course provides an introduction to linear systems, transfer functions, and Laplace transforms. It covers stability and feedback, and provides basic design tools for specifications of transient response. It also briefly covers frequency-domain techniques.
The main aims of this seminar will be to go over the …
The main aims of this seminar will be to go over the classification of surfaces (Enriques-Castelnuovo for characteristic zero, Bombieri-Mumford for characteristic p), while working out plenty of examples, and treating their geometry and arithmetic as far as possible.
Created for a first-year university course, this linear algebra textbook takes an …
Created for a first-year university course, this linear algebra textbook takes an unusual approach: it introduces vector spaces at the outset and deals with linear systems only after a thorough introduction to vector spaces. This approach is based on the authors' experience over the past 25 years that students often need more time to master vector spaces while traditional textbooks relegate the topic to the end of the course. In this way, these new notions at the heart of linear algebra that are often considered abstract and difficult in an introductory course can then be used in the rest of the course as well as in different contexts.
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