Lectures related to Derivative of an Integral with Parameter

Derivative of an Integral

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

Partial Derivatives: Derivative of an Integral with Parameter-dependent Bounds

Covers the derivative of an integral with parameter-dependent bounds and the gradient.

Inverse Function Identity

Explains the inverse function identity and provides examples with ln(x), sin(x), and cos(x).

Calculus: Derivatives and Integrals

Covers the fundamentals of calculus, focusing on derivatives and integrals.

Laplacian in Polar and Spherical Coordinates: Derivatives

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

Distributions and Derivatives

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

Riemann Sums and Definite Integrals

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

Integral Change of Variable Formula

Explores the integral change of variable formula and its applications in calculus.

Integration by Substitution

Explores integration by substitution with proofs and examples on anti-derivatives and function equivalence.

Integral Calculation

Covers the calculation of a specific integral using properties of logarithmic functions.

Improper Integrals: Convergence and Comparison

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

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.

Differentiating under the integral sign

Explores differentiating under the integral sign and continuity of functions in integrals.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Definite Integrals: Properties and Interpretation

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

Exact Linearization: Earth Dynamics and Stabilization

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

General Physics: Mechanics SV

Covers the basics of General Physics, focusing on Mechanics SV and key mathematical concepts.

Dirac Delta Function

Introduces the Dirac delta function and discusses its properties and applications in signal processing and physics.

Differentiating under the integral sign

Explores differentiating under the integral sign and conditions for differentiation, with examples and extensions to functions on open intervals.

Taylor Polynomials: Approximating Functions in Multiple Variables

Covers Taylor polynomials and their role in approximating functions in multiple variables.