Lectures related to Gradient Analysis

Derivative of an Integral with Parameter

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

Rolle's Theorem: Applications and Examples

Explores the practical applications of Rolle's Theorem in finding points where the derivative is zero.

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

Partial Derivatives: Definitions and Applications

Explores the definitions and applications of partial derivatives in functions of several variables, emphasizing the importance of specifying the choice of variables.

Taylor Polynomials: Approximating Functions in Multiple Variables

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

Integral Calculation

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

Derivatives and Continuity in Mathematics

Covers derivatives, continuity, Rolle's Theorem, function examples, and extrema.

Inflection Points

Explores inflection points in functions, emphasizing the role of the second derivative.

Laplacian in Polar and Spherical Coordinates: Derivatives

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

Differential Calculation: Trigonometric Derivatives

Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.

Integration by Substitution

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

Inverse Function Identity

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

Implicit Functions Theorem

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.

Limits and Derivatives in Multivariable Functions

Covers limits and derivatives in multivariable functions, focusing on continuity, partial derivatives, and the gradient.

Advanced Analysis II: Derivatives and Functions

Covers the review of derivatives and functions, including the concept of chain rule and graphical representation.

Implicit Functions and Taylor Polynomials

Covers implicit functions, Taylor polynomials, and tangent equations.

Bernoulli's Hospital Rule

Covers the statement of the Bernoulli's Hospital Rule and its application.

Applications of Theorems

Demonstrates the practical application of theorems in calculus through two clever examples.

Calculus: Derivatives and Integrals

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

Differential Calculus: Definition and Derivability

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