Linear Applications: Some Basic Concepts

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Mapping Functions and Surjections

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

Algebraic Identities and Trigonometry

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

Linear Algebra: Bijections and Cardinality

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

Linear Algebra: Properties of Injective and Surjective Functions

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

Cartesian Products and Equivalence Relations

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

Linear Transformations: Matrices and Applications

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

Sets, Functions and Relations: Summary of Week 4

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

Inverse Function Theorem

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

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.