Lectures related to Exact Linearization: Earth Dynamics and Stabilization

Derivative of an Integral

Covers the derivative of an integral dependent on a parameter and its fundamental properties.

Exact Linearization: Determining Conditions and Transformations

Explores exact linearization, determining conditions and transformations using Lie bracket and hook of Lie.

Riemann Sums and Definite Integrals

Covers Riemann sums, definite integrals, Taylor series, and exponential of complex numbers.

Derivative of an Integral with Parameter

Covers deriving integrals with parameters and their derivatives, including special cases and proofs.

Linear Approximation and Derivative Parametric

Covers linear approximation, parametric derivatives, and differentiability conditions on intervals.

Integrals of Functions

Covers integrals as the reciprocal function of the derivative and explains displacement integral of velocity and variation of speed and acceleration in rectilinear motion.

Differential Calculus: Definition and Derivability

Explores the definition and derivability of functions in differential calculus, emphasizing differentiability at specific points.

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Tangent to Graph of a Function

Explores finding the equation of the tangent line to a function's graph at a point.

Riemann Integral: Techniques and Fundamentals

Explores Riemann integrability, the fundamental theorem of integral calculus, and various integration techniques.

Stability of ODE

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.