Lectures related to Toy example: linearization

Stability of ODE

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

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.

Linear Transformations: Polynomials and Bases

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

Linearization Method: Examples

Covers the linearization method through two examples in process control.

Linear Algebra: Multilinear Forms

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

Linear Equations: Vectors and Matrices

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

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.

Nonlinearity: Methods and Examples

Explores nonlinearity in numerical flow simulation, covering linearization methods and practical examples.

General Solution of Inhomogeneous ED

Covers the general solution of inhomogeneous differential equations and explores linear dependence, uniqueness theorems, and second-order equations.

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.

Linear Algebra: Linear Dependence and Independence

Explores linear dependence and independence of vectors in geometric spaces.

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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.

Linear Algebra: Matrices and Vector Spaces

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.