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Related lectures (32)
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Derivative of Integral with Parameter Dependency
Explores the derivative of an integral with parameter dependency and its continuity.
Advanced Analysis II: Matrix Diagonalization
Covers matrix diagonalization, compact sets, continuity of functions, and the Mandelbrot set.
Advanced Analysis II: Consequences of Double Integrals
Explores the consequences of double integrals, including compact sets and continuity.
Local Lipschitz Functions
Explores locally Lipschitz functions, discussing differentiability, unique solutions, and function reduction.
Projected Gradient Descent: Quadratic Penalty
Covers projected gradient descent with a focus on quadratic penalty and optimality conditions.
Curve Length and Function Definition
Explores curve length, function definition, continuity, derivatives, integrals, and graphical representations of functions in two variables.
Demonstration of Uniqueness Theorem
Presents a detailed proof of the uniqueness theorem for functions f and g.
Optimization Methods
Covers optimization methods without constraints, including gradient and line search in the quadratic case.
Martingales and Brownian Motion
Explores the concept of martingales and their relation to Brownian motion through symmetric simple random walks and discusses the potential positive outcomes from the current crisis.
Advanced analysis II
Covers Jordan-measurable sets, Riemann-integrability, and function continuity on compact sets.
