Lectures related to Linear Algebra: Applications and Examples

Explores injective functions in linear algebra, demonstrating how to prove injectivity step by step.

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

Functions: Limits, Continuity, Differentiability

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

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.

Definitions and Notations

Covers the definitions and notations related to functions.

Algebraic Identities and Trigonometry

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

Real Functions: Definitions and Properties

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

Functions: properties and convergence criteria

Explores convergence criteria, function properties, and unique element association.

Continuity and Fixed Points: Understanding Functions

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

Functions: Limits and Continuity

Explores functions, limits, continuity, differentiability, and important notions of limits and divergence.

Cartesian Products and Equivalence Relations

Introduces Cartesian products, equivalence relations, and functions, emphasizing the importance of order and discussing injective, surjective, and bijective functions.

Sets, Functions and Relations: Summary of Week 4

Covers sets, functions, and relations, including functions' properties and binary relations.

Real Numbers and Functions

Introduces Real Analysis I, covering real numbers, functions, limits, derivatives, and integrals.

Linear Algebra: Injections, Surjections, Bijections

Explores injections, surjections, and bijections in linear algebra, highlighting their significance in mathematics.

Mathematical Analysis: Functions and Composition

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

Functions and Periodicity

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

Mapping Functions and Surjections

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

Advanced Analysis II: Derivatives and Notations

Covers derivatives, notations, composition of functions, and multiple derivatives in advanced analysis.

Linear Algebra: Applications and Definitions

Covers the definition of applications, image of elements, and direct and reciprocal images.

Injectivity and Surjectivity

Covers injectivity, surjectivity, and bijectivity in mathematical functions, explaining unique mappings and pre-image existence.