Model Extension and Composition of Functions

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Related lectures (27)

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Mathematical Analysis: Functions and Composition

Covers the analysis of functions, composition, and mathematical induction.

Functions: Definitions and Notations

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

Functions and Integers

Covers functions, integers, GCD, and reasoning by recurrence, including the Euclidean algorithm and induction principle.

Tangent to Graph of a Function

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

Mathematics: Sets and Functions

Introduces sets, functions, Cartesian products, and compositions, discussing images, preimages, and function properties.

Graphical Definition: Level Sets and Domains

Covers the graphical definition of functions, focusing on level sets and domains.

Convex Functions

Covers the properties and operations of convex functions.

Advanced Analysis II: Tangent Plan and Differentiability

Explores tangent planes and differentiability in advanced analysis, emphasizing the properties of tangent planes and the conditions for differentiability.

Real Functions: Definitions and Properties

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

Mapping Functions and Surjections

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.