Lectures related to Derivatives and Continuity

Partial Derivatives and Functions

Explores partial derivatives and functions in multivariable calculus, emphasizing their importance and practical applications.

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.

Derivability and Continuity

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

Implicit Functions Theorem

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

Advanced Analysis II: Differentiability and Continuity

Explores differentiability and continuity in advanced analysis with examples and counterexamples.

Derivatives and Functions

Covers the theorem of the intermediate value, corollaries, and geometric interpretation of derivatives.

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.

Fundamental Analysis: Integrals and Primitives

Covers the fundamental concepts of integrals and primitives, including properties and examples.

Introduction to Derivatives

Introduces derivatives, forward contracts, options, and their financial uses.

Derivatives and Local Extrema

Explores derivatives, local extrema, and function variation in mathematical analysis.

Demonstration of Theorem

Covers the demonstration of a theorem using mathematical expressions and hypotheses.

Partial Derivatives: Gradient and Theorem of Mean Value

Introduces the gradient concept and the Theorem of Mean Value for functions in several variables.

Differential Calculus: Definition and Derivability

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

General Physics: Mechanics SV

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

Derivatives and Continuity in Multivariable Functions

Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

Mathematical Notations and Functions in General Physics

Introduces mathematical notations and functions essential for general physics.

Functional Derivatives

Covers the concept of functional derivatives and their calculation process with examples.

Derivatives and Tangent Lines: Understanding Functions and Limits

Explores derivatives, functions, limits, and tangent lines in calculus.

Analysis I Exam Solutions

Provides solutions to an Analysis I exam, covering various topics.