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Related lectures (32)
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Normed Spaces
Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.
Infimum and Supremum of Subsets
Covers the concepts of infimum and supremum of subsets in real numbers.
Real Numbers: Sets and Operations
Explores the fundamental concepts of real numbers, including sets, operations, and properties like supremum and infimum.
Weak Solutions of Differential Equations
Explores weak solutions of differential equations and their properties.
Real Analysis: Functions and Limits
Covers the basics of real analysis, including functions, limits, and max/min functions.
Global Properties of Continuous Functions
Explores the global properties of continuous functions, including behavior, limits, and interval characteristics.
Real Numbers: Definitions and Equivalence Classes
Covers the existence of real numbers and equivalence classes of Cauchy sequences.
Convergence of Numerical Sequences
Explores the convergence of numerical sequences through monotonicity, boundedness, linear recurrence, and subsequences.
Sobolev Spaces in Higher Dimensions
Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.
Norm Estimation and Continuity
Covers the estimation of norms and continuity in mathematical functions.
Bolzano-Weierstrass: Advanced Analysis I
Explores the Bolzano-Weierstrass theorem on bounded sequences and convergent subsequences.
Convergence of Monotonic Sequences
Covers the convergence of monotonic sequences, discussing how a monotonically increasing or decreasing sequence that is bounded converges to its supremum or infimum respectively.
Mathematics: Functions and Series
Explores functions, series, and critical points in mathematics, including maximum, minimum, supremum, and infimum concepts.
Supremum
Covers the concept of supremum in real numbers and its properties as the least upper bound of a set.
Properties of Continuous Functions
Covers the properties of continuous functions and explores inverse and injective functions with examples.
Math-101(en) / Min/Max, Inf/Sup
Covers minimum, maximum, infimum, and supremum concepts in real numbers with examples and proofs.
Exemple: Infimum and Supremum
Illustrates the calculation of infimum and supremum for a set of elements.
Real Numbers: sqrt(2)
Explores real numbers, focusing on the square root of 2 and the implications of its irrationality.
Characterization of Infimum and Supremum
Explores the definitions and properties of infimum and supremum in mathematical analysis.
Real Numbers: Sets and Operations
Covers the fundamental concepts related to real numbers, including sets, notations, and operations.
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