Lectures related to Mathematical Analysis: Functions and Composition

Functions and Integers

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

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.

Mathematics: Analysis and Algebra Overview

Provides an overview of analysis and algebra courses, focusing on real numbers, limits, functions, and exams.

Real Functions: Definitions and Properties

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

Function Properties: Injective, Surjective, Bijective

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

Convex Functions

Covers the properties and operations of convex functions.

Real Functions: Graphs and Properties

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

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.

Graphical Definition: Level Sets and Domains

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

Derivatives and Continuity in Multivariable Functions

Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

Functions and Periodicity

Covers functions, including even and odd functions, periodicity, and function operations.

Relations in Computer Science

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Definitions and Notations

Covers the definitions and notations related to functions.

Tangent to Graph of a Function

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

Graph and Diagonal

Discusses the graph of a relation and the concept of separation.

Terminologie: Functions Graph Discussion

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

Analyse II: Directional Derivative

Covers the concept and calculation of directional derivatives in multivariable calculus.

Applications between Sets: Functions and Graphs

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

Transformations Affines

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