Lectures related to Inverse Hyperbolic Functions

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

Covers hyperbolic functions, including definitions, properties, and derivatives, explained with detailed examples and derivations.

Hyperbolic Functions

Explores hyperbolic functions, their properties, and derivatives, including tanh(x) and arctanh(x).

Hyperbolic Functions: Tangent and Cotangent

Covers the definitions and examples of hyperbolic tangent and cotangent functions.

Inverse Hyperbolic Functions

Explores inverse hyperbolic functions and their parallels with trigonometric functions, deriving explicit expressions and discussing their properties.

Trigonometric Functions and Derivatives

Covers trigonometric functions, derivatives, and their applications in solving mathematical problems.

Derivatives and Extrema: Theory and Applications

Explores derivatives, extrema, and their practical applications in function analysis.

Derivatives and Hyperbolic Functions

Covers derivatives, hyperbolic functions, and theorems of Rolle and finite increments.

Derivatives and Continuity

Explores derivatives, reciprocal functions, and continuity of functions with examples and formulas.

Functional Derivatives

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

Differential Calculation: Hyperbolic Functions

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

Implicit Functions Theorem

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

Reciprocal Trigonometric Functions

Explores reciprocal trigonometric functions, hyperbolic functions, and area theorems.

Derivatives and Continuity

Covers derivatives, continuity, and reciprocal functions with examples of exponential and trigonometric functions.

Advanced Analysis II: Derivatives and Notations

Covers derivatives, notations, composition of functions, and multiple derivatives in advanced analysis.

Partial Derivatives and Functions

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

Real Numbers and Functions

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

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.

Generalized Powers: Derivatives and Exponentials

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

Derivatives and Tangent Lines: Understanding Functions and Limits

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