Calculus of Variations: Principles and Applications

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Related lectures (32)

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Banach Spaces: Reflexivity and Convergence

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

Bolzano-Bastra-Sterl: Applications and Uniform Continuity

Explores the Bolzano-Bastra-Sterl theorem and uniform continuity in sequences.

Calculus of Variations: Ground States in Quantum Mechanics

Covers the Calculus of Variations to find ground states in quantum mechanics by minimizing energy, discussing the Euler Lagrange equation and the Fundamental Theorem of Young Measure Theory.

Preliminaries in Measure Theory

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Generalized Integrals: Type 2

Covers the integration of limit expansions and continuous functions by pieces.

Function Approximations

Covers continuous functions with compact support, density, and approximation, focusing on the heat equation.

Uniform Integrability and Convergence

Explores uniform integrability, convergence theorems, and the importance of bounded sequences in understanding the convergence of random variables.

Quadratic Penalty Method: Finer Analysis

Covers the quadratic penalty method and augmented Lagrangian, including the setup and convergence of sequences.

Convergence and Limits in Real Numbers

Explains convergence, limits, bounded sequences, and the Bolzano-Weierstrass theorem in real numbers.

Distribution Interpolation Spaces

Covers the proof of UE Lipschitz constant and distribution interpolation spaces.