Lectures related to Partial function

Algebraic Identities and Trigonometry

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

Sets, Functions and Relations: Summary of Week 4

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

Linear Algebra: Bijections and Cardinality

Explores bijections in linear algebra and the concept of cardinality between sets.

Cartesian Products and Equivalence Relations

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

Proofs and Sets: Applications

Covers the basics of proofs, defining sets, and applications between sets.

Functions: Limits and Continuity

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

Linear Algebra: Properties of Injective and Surjective Functions

Covers the properties of injective and surjective functions and the concept of bijections.

Linear Transformations: Matrices and Applications

Explores linear transformations, matrices, injective and surjective functions, and their applications.

Group Theory: Basics

Covers the basics of group theory, including sets, applications, and examples like permutations and rotations.

Mapping Functions and Surjections

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

Directed Graphs: Introduction and Categories

Covers the fundamental notion of composition in directed graphs and provides examples of their representation.

Inverse Function Theorem

Covers the inverse function theorem, Jacobian matrix, injective functions, bijective functions, and spherical coordinates.

Coordinate Changes: Definitions and Laplacian

Covers the definitions of coordinate changes and the Laplacian of a function.

Cylindrical Coordinates: Continuity and Class C

Explores cylindrical coordinates in R^3, emphasizing continuity and class C properties.

Group Theory: Definitions and Properties

Introduces group theory concepts, properties, and examples, including injective functions and group properties like associativity and inverses.

Discussion of Function f

Covers the discussion of the function f(x) = |2x-1| -x²+1 on a given domain and its continuity, zeros, and derivatives.

Functions: Limits, Continuity, Differentiability

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

Total Functions: How and Why

Explores hash table efficiency, total functions in code modeling, and well-founded relations for recursive function termination.

Linear Applications: Some Basic Concepts

Introduces the basic concepts of linear applications, including injective, surjective, and bijective functions, along with function composition.

Sequences and Convergence: Solutions to Exercises

Covers solutions to exercises related to sequences, convergence, bounded functions, and bijective functions.