Lectures related to Hyperbolic Functions: Circle and Hyperbola

Parametrized Curves in 2D: Examples and Properties

Explores parametrized curves in 2D, including segments, straight lines, and circles with trigonometric functions.

Reciprocal Trigonometric Functions

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

Trigonometric Functions: Basics and Applications

Introduces the basics of trigonometric functions, their properties, and practical applications in geometry and physics.

Parametrized Curves in 2D

Covers the concept of parametrized curves in 2D and their properties.

Trigonometric Functions: Sin and Cos

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

Homogeneous Coordinates and Curves

Explores homogeneous coordinates, curves, and unique solutions in Cartesian coordinates.

Complex Hyperbolic and Trigonometric Functions

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

Surface of Revolution

Explains the parametric equations of surfaces of revolution generated by curves in space.

Integration Techniques: Trigonometric and Hyperbolic Functions

Covers integration techniques with trigonometric and hyperbolic functions, including square roots and trigonometric identities.

Trigonometric Equations: Tangent and Cotangent

Explores solving trigonometric equations with tangent and cotangent functions, along with arctangent and arccotangent definitions.

Residue Theorem: Calculating Integrals on Closed Curves

Covers the application of the residue theorem in calculating integrals on closed curves in complex analysis.

Curvature and Osculating Circle

Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.

Trigonometric Functions and Derivatives

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

Mathematical Reminders: Trigonometry

Covers mathematical reminders on trigonometry, focusing on angles in radians and trigonometric functions.

Derivatives and Extrema: Theory and Applications

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

Trigonometric Functions: Tangent and Cotangent

Explores the definition, properties, and geometric interpretations of tangent and cotangent functions in trigonometry.

Integral Techniques: Trigonometric/Hyperbolic Functions

Covers integration techniques using trigonometric and hyperbolic functions, with examples and variable changes.

Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

Triangle Relations: Sinus Theorem

Explores triangle relationships, including the Sinus Theorem and circumscribed circles.

Harmonic Oscillations: Superposition

Explores the principle of superposition for harmonic oscillations and provides geometric interpretations and examples.