Lectures related to Model Extension and Composition of Functions

Mathematical Analysis: Functions and Composition

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

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.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.

Differential Calculation: Trigonometric Derivatives

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

Terminologie: Functions Graph Discussion

Covers the terminology related to the graph of a function and intervals.

Transformations Affines

Covers the concept of affine transformations in functions, including shifting and compressing functions.

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

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Algebraic Identities and Trigonometry

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

Real Functions: Graphs and Properties

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

Linear Algebra: Matrices and Linear Applications

Covers matrices, linear applications, vector spaces, and bijective functions.

Sets and Functions

Introduces sets, functions, and their properties, including injective and surjective functions, composition, and inverse functions.