Exact Linearization: Earth Dynamics and Stabilization

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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.