Lectures related to Power Functions: Properties and Derivatives

Generalized Powers: Derivatives and Exponentials

Covers properties of logarithms, derivatives, exponentials, and sine-cosine functions.

Differential Calculation: Trigonometric Derivatives

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

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

Differential Calculus: Definition and Derivability

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

Derivatives: Definition and Properties

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

Real Numbers and Functions

Introduces Real Analysis I, covering real numbers, functions, limits, derivatives, and integrals.

Differentiability and Partial Derivatives

Explores differentiability in two variables and the chain rule for compositions.

Holomorphic Functions: Cauchy-Riemann Equations and Applications

Discusses holomorphic functions, focusing on the Cauchy-Riemann equations and their applications in complex analysis.

Computing Derivatives: Derivatives and Algebraic Operations

Covers the computation of derivatives and the properties of differentiable functions.

Derivatives and Reciprocal Functions

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

Power Functions: Definition

Explores power functions with functions as base and exponent, emphasizing exponential function continuity and derivative analysis.

Logarithmic Functions: Properties and Applications

Explores the properties and applications of natural logarithmic functions, including area invariance and harmonic series divergence.

Derivatives and Tangent Planes

Covers derivatives, differentiability, and tangent planes for functions of one and two variables.

Natural Logarithm: Graph

Explores the properties and graph of the natural logarithm function, emphasizing its bijectivity and the Euler's number 'e'.

Analysis I Exam Solutions

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

Natural Logarithm: Definition and Properties

Explores the definition, properties, and limits of the natural logarithm function.

Differentiability of Functions in Two Variables

Covers differentiability of functions in two variables and the conditions for a function to be differentiable.

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.

Differentiability: Partial Derivatives and Hessiennes

Explains partial derivatives, Hessienne matrix, and their properties.

Derivability and Continuity

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