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Graphical Definition: Level Sets and Domains
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Related lectures (46)
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.
Real Functions: Graphs and Properties
Explores real functions, their graphs, properties, and transformations, including symmetry and surjection.
Tangent to Graph of a Function
Explores finding the equation of the tangent line to a function's graph at a point.
Real Functions: Definitions and Properties
Covers the definitions and basic properties of real functions, including domain, image set, notation, and graph.
Transformations Affines
MOOC: Analysis I
MOOC: Analysis I (part 4) : Limit of a function, continuous functions
Covers the concept of affine transformations in functions, including shifting and compressing functions.
Terminologie: Functions Graph Discussion
MOOC: Analysis I
MOOC: Analysis I (part 6) : Study of functions, limited developments
Covers the terminology related to the graph of a function and intervals.
Coordinate Systems: Applications and Transformations
Explores coordinate systems, including polar and curvilinear coordinates, and their transformations.
Linear Algebra: Applications and Definitions
Covers the definition of applications, image of elements, and direct and reciprocal images.
Restriction, Prolongement et Graphe d'une Fonction
MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers
MOOC: Analysis I
Explains the relationship between two functions through restriction and prolongation, emphasizing the importance of defining a function by its graph.
Differential Forms on Manifolds
Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.
Exponential Family
Covers the concept of the exponential family and discusses forward and backward maps, expensive computations, parameters, functions, and convexity.
Definitions and Notations
MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers
MOOC: Analysis I
Covers the definitions and notations related to functions.
Mathematics: Analysis and Algebra Overview
Provides an overview of analysis and algebra courses, focusing on real numbers, limits, functions, and exams.
Relations in Computer Science
Explores the properties of relations in computer science, including equivalence relations and the partition of a set.
Function Properties: Injective, Surjective, Bijective
Explains injective, surjective, and bijective functions using examples and graphs.
Continuity and Fixed Points: Understanding Functions
Explores continuity, fixed points, and bijective functions in graphs.
Mathematical Analysis: Functions and Composition
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Covers the analysis of functions, composition, and mathematical induction.
Advanced Analysis II: Tangent Plan and Differentiability
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Explores tangent planes and differentiability in advanced analysis, emphasizing the properties of tangent planes and the conditions for differentiability.
Convex Functions
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Covers the properties and operations of convex functions.
Functions and Integers
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Covers functions, integers, GCD, and reasoning by recurrence, including the Euclidean algorithm and induction principle.
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