Lectures related to Continuity and Fixed Points: Understanding Functions

Real Functions: Graphs and Properties

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

Function Properties: Injective, Surjective, Bijective

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

Applications between Sets: Functions and Graphs

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

Level Curves and Graphs of Functions

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

Convex Functions

Covers the properties and operations of convex functions.

Mathematical Analysis: Functions and Composition

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

Functions: Real Numbers and Graphs

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

Graphs: Injection and Surjection

Explains injectivity and surjectivity criteria in functions using graphical representations.

Functions: Inverse, Composition, and Graphs

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

Real Functions: Definitions and Properties

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

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.

Graphical Definition: Level Sets and Domains

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

Mathematics: Sets and Functions

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

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.

Application to Recurrence Defined Sequences

Covers the application of functions defined by recurrence to sequences and the theorem of the fixed point.

Real Functions: Definitions and Properties

Covers real functions' definitions, properties, periodicity, and reciprocity, including maximum, minimum, and composition of functions.

Functions and Integers

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

Functions: Limits, Continuity, Differentiability

Explores the origin of functions, continuity, differentiability, and the physical representation of chemical bonds.

Functions: Basic Concepts

Covers the basic concepts of functions, including definitions, notations, and discussions on injectivity and surjectivity.

Real Functions: Definitions and Properties

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