Lectures related to Hyperbolic functions

Hyperbolic Functions

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).

Functions and Periodicity

Covers functions, including even and odd functions, periodicity, and function operations.

Complex Hyperbolic and Trigonometric Functions

Explores complex hyperbolic and trigonometric functions, defining key properties and relationships with exponential functions.

Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

Symmetries of Trigonometric Functions

Explores the symmetries of trigonometric functions, periodicity, and properties of even and odd functions.

Differential Calculation: Hyperbolic Functions

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

Dynamics of Singular Riemann Surface Foliations

Explores the dynamics of singular Riemann surface foliations and their intricate behavior.

Mathematica Tutorial: Graphics and Functions

Introduces Mathematica basics, including graphics creation, list manipulation, and function definition.

Functions: Differentials, Taylor Expansions, Integrals

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.

Symmetries of Tangent and Cotangent

Explores the symmetries and properties of tangent and cotangent functions with different angles.

Introduction to Partial Differential Equations

Covers the basics of Partial Differential Equations, focusing on heat transfer modeling and numerical solution methods.

Functions Composition: Continuity & Elements

Covers the composition of functions, continuity, and elementary functions, explaining the concept of continuity and the construction of elementary functions.

Limits and Operations on Limits

Covers limits, algebraic operations, and infinite limits with examples of functions' behavior near limit points.

Trigonometric Functions: Sin and Cos

Covers the definition of sine and cosine functions, their graphs, and notable points.

Functional Derivatives

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

Taylor Series: Approximating Functions with Polynomials

Explores approximating functions with polynomials using Taylor series and discusses the convergence of series representations.

Reciprocal Trigonometric Functions

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

Partial Derivatives: Definitions and Examples

Covers the concept of partial derivatives and their applications in mathematical analysis.

Periodic Functions: Limits and Compositions

Explores periodic functions, limits, compositions, and properties of even and odd functions.