Exact Linearization: Earth Dynamics and Stabilization

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

Differentiability: Partial Derivatives and Hessiennes

Explains partial derivatives, Hessienne matrix, and their properties.

Definite Integrals: Properties and Interpretation

Covers the calculation of minimum points and the concept of definite integrals.

Fundamental Theorem of Analysis: Integral (1st part)

Explains the concept of area under a curve and its derivative.

Introduction to Nonlinear Systems Control

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

Derivatives: Definition and Properties

Explores the definition and properties of derivatives, including slopes of tangent lines and differentiability conditions.

Differential Calculation: Hyperbolic Functions

Explores differential calculation with hyperbolic functions and Taylor series, emphasizing the importance of signed areas in integrals.

Integral: Motivation

Covers the motivation behind indefinite integrals and the non-injectivity of the derivative operator.

Laplacian in Polar and Spherical Coordinates: Derivatives

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.

Jacobian Matrix and Change of Variables

Covers Jacobian matrix, composite function derivative, change of variables, and integral derivative.