Lectures related to Derivative: Linear Approximation

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

Explores derivability and continuity of functions, showcasing examples of functions with differentiability properties.

Differential Calculus: Definition and Derivability

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

Convexity and Optimization

Explores convexity, optimization, and critical points in mathematical functions using the second derivative.

Derivative of an Integral

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

Partial Derivatives and Functions

Covers partial derivatives for functions of one and two variables, emphasizing their importance and calculation.

Calculus: Derivatives and Integrals

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

Derivability and Continuity

Explores derivability, continuity, and composite functions with illustrative examples.

Derivatives and Approximations: Logarithmic Functions

Explores derivatives and approximations, focusing on logarithmic functions and their properties.

Taylor's approximation: Mean Value Theorem, l'Hopital rule, Examples

Covers the Mean Value Theorem, l'Hopital rule, Taylor's approximation, and more.

Derivatives: Definition and Properties

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

Derivatives and Reciprocal Functions

Covers derivatives, reciprocal functions, Rolle's theorem, and extremum local concepts.

Limits and Derivatives in Multivariable Functions

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

Linear Approximation and Derivative Parametric

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

Taylor Series: Derivatives and Approximations

Explores Taylor series, derivatives, and approximations in mathematical analysis.

Differential Calculation: Hyperbolic Functions

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

Taylor Series: Expansion and Properties

Explores Taylor series expansion, derivatives, uniqueness, and applications in function approximation.

Untitled

Generalized Finite Increments

Explores generalized finite increments, derivatives, reciprocals, and Bernoulli-L'Hospital rule.

Differentiation and Coordinate Changes in Multivariable Functions

Discusses differentiation of multivariable functions and coordinate transformations, including polar and cylindrical coordinates, along with the Laplacian operator and its applications.