Lectures related to Real Functions: Definitions and Properties

Covers the definitions and basic properties of real functions, including domain, image set, notation, and graph.

Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.

Covers the properties and operations of convex functions.

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

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

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

Covers real functions, definitions, graphs, parity, periodicity, and boundedness.

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

Explores definitions and examples of real functions of a real variable.

Covers the conditions for finding absolute extrema in multivariable functions.

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

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

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

Explains injectivity and surjectivity criteria in functions using graphical representations.

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

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

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

Covers the terminology and conventions of real functions of a real variable.

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

Explains extrema of functions in several variables, stationary points, saddle points, and the role of the Hessian matrix.