Lectures related to Pairs of Functions

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

Explores exponential and logarithmic functions, their properties, relations, and graphs, including different bases and commonly used logarithms.

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

Explores derivatives, tangents, and elementary function rules in general mathematics.

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

Explores the construction of graphs for harmonic oscillations with different amplitudes and phases.

Explores real functions, their graphs, properties, and transformations, including symmetry and surjection.

Covers level curves and graphs of functions in two and three dimensions.

Explains injectivity and surjectivity criteria in functions using graphical representations.

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

Explains injective, surjective, and bijective functions using examples and graphs.

Covers functions of real numbers, graphing, and affine functions.

Explores automorphism groups in trees and graphs, focusing on ends and types of automorphisms.

Explores continuity, fixed points, and bijective functions in graphs.

Covers applications between sets, functions, and graphs, exploring injectivity, surjectivity, and bijectivity.

Explores partial derivatives and their role in determining tangents to graphs.

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

Covers inverse functions, function composition, partial functions, and graphs of functions.

Covers the definitions and properties of arcsin and arccos functions.

Explores automorphism groups of trees and graphs, including actions on trees and group homomorphisms.