Lectures related to Toy example: linearization

Bilinear Forms: Theory and Applications

Covers the theory and applications of bilinear forms in various mathematical contexts.

Introduction to Nonlinear Systems Control

Covers the analysis and control of nonlinear systems, including methods like phase plan and passivity.

State-Space Control Design

Covers state-space control design, including state-feedback, observer, and linearization.

Hermitian Forms: Definition and Properties

Explores the definition and properties of Hermitian forms in complex vector spaces.

Conformity and Compliancy in Geometry

Explores conformity and compliancy in geometry, emphasizing angle preservation and function conditions.

Weingarten Application of Regular Surfaces

Covers the application of the Weingarten map on regular surfaces and the shape operator.

Exact Linearization: Earth Dynamics and Stabilization

Explores exact linearization techniques for transforming non-linear systems into linear ones, emphasizing system stability.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Quadratic Forms and Symmetric Bilinear Forms

Explores quadratic forms, symmetric bilinear forms, and their properties.

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Applications of Laplace Transform: State Space Modeling

Explores the application of Laplace transform in state space modeling of linear systems and the control of dynamic systems.

Spectral Theorem Recap

Revisits the spectral theorem for symmetric matrices, emphasizing orthogonally diagonalizable properties and its equivalence with symmetric bilinear forms.

Modeling Dynamic Systems: Definitions and Examples

Covers the modeling of dynamic systems, including definitions, examples, and linearization processes for easier analysis.

Pseudo-Euclidean Spaces: Isometries and Bases

Explores pseudo-Euclidean spaces, emphasizing isometries and bases in vector spaces with non-degenerate quadratic forms.

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Stability of ODE Log in to Mediaspace to watch this video

Explores the stability of Ordinary Differential Equations, focusing on solution dependence, critical data, linearization, and control of nonlinear systems.

Linear Transformations: Polynomials and Bases Log in to Mediaspace to watch this video

Covers linear transformations between polynomial spaces and explores examples of linear independence and bases.

Linearization Method: Examples Log in to Mediaspace to watch this video

Covers the linearization method through two examples in process control.

Linear Algebra: Multilinear Forms Log in to Mediaspace to watch this video

Explores multilinear forms in linear algebra, emphasizing their properties and applications.

Linear Equations: Vectors and Matrices Log in to Mediaspace to watch this video

Covers linear equations, vectors, and matrices, exploring their fundamental concepts and applications.