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Related lectures (29)

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Advanced Analysis II: Hessians and Directional Derivatives

Explores Hessians, directional derivatives, and function continuity in advanced analysis.

Differentiable Functions: Definitions and Properties

Covers the definition and properties of differentiable functions, focusing on differentiability, limits, continuity, and partial derivatives.

Optimization Techniques: Gradient Descent and Convex Functions

Provides an overview of optimization techniques, focusing on gradient descent and properties of convex functions in machine learning.

Fourier Series: Convergence and Dirichlet Theorem

Covers Fourier series convergence, Dirichlet theorem, and applications in signal processing.

Proximal and Subgradient Descent: Optimization Techniques

Discusses proximal and subgradient descent methods for optimization in machine learning.

Existence of Solutions for Poisson-Dirichlet Problem

Covers the existence of solutions for the Poisson-Dirichlet problem, focusing on showing that certain conditions hold for locally bounded and Hölder continuous functions.

Tangent to Graph of a Function

Explores finding the equation of the tangent line to a function's graph at a point.

Monotonicity Criteria in Differentiable Functions

Explores monotonicity criteria, L'Hopital's rule, and Lipschitz continuity in differentiable functions and deep neural networks.

Functions and Coordinate Changes

Explores bijective functions, coordinate transformations, and graphical representations in two dimensions.

Rolle's Theorem and Mean Value Theorem

Covers Rolle's Theorem and the Mean Value Theorem with illustrative examples.