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Lecture
Density Results in Sobolev Spaces
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Related lectures (39)
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Linear Operators and Bounded Domains
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Covers linear operators and bounded domains, focusing on the existence of such operators in domains with bounded boundaries.
Convergence of Fourier Series
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Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.
Trigonometric Polynomials: Fourier Inversion and Plancherel Formulas
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Explores trigonometric polynomials, emphasizing Fourier inversion and Plancherel formulas.
Implicit Functions: Unique Solutions and Class C Functions
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Covers the proof of the theorem of implicit functions and the concept of class C functions.
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Integer Cones
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Covers the concept of integer cones and Carathéodory's theorem with illustrative examples.
Proofs and Logic: Introduction
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Introduces logic, proofs, sets, functions, and algorithms in mathematics and computer science.
Fourier Inversion Formula
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Covers the Fourier inversion formula, exploring its mathematical concepts and applications, emphasizing the importance of understanding the sign.
Limits: Definition and Properties
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Explores the definition and properties of limits, including uniqueness and the two gendarmes theorem.
Lagrange Multipliers Theorem
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Explores the Lagrange multipliers theorem for n>2, demonstrating its application in optimization problems with constraints.
Finite Differences: Definition and Proof
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Covers the definition of the center of a function using finite differences and provides step-by-step proofs.
Fourier Series: Extension and Periodicity
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Covers the extension and periodicity of Fourier series and the interpretation of coefficients.
Newton's Laws: Fundamentals
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Explores Newton's laws of motion, fundamental forces in nature, and the unification of interactions.
Tensors: Motivations and Introduction
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Covers the basics of tensors, including their definition, properties, and decomposition, starting with a motivating example involving Gaussian distributions.
Analyse II: Directional Derivative
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Covers the concept and calculation of directional derivatives in multivariable calculus.
Heat Equation: Diffusion
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Covers the heat equation for diffusion and conservation of thermal energy.
Linear Equations: Introduction and Solutions
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Covers the introduction and solutions of linear equations, including methods for solving systems and determining the number of solutions.
Weak Fiat-Shamir: Vulnerabilities in Cryptographic Protocols
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Covers vulnerabilities in the Fiat-Shamir heuristic and its impact on Helios voting security.
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