Dirichlet Series: Properties and Examples

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Improper Integrals: Convergence and Comparison

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Fourier Series and Equations

Covers Fourier series, periodic functions, and Fourier transforms.

Laurent Series and Convergence: Complex Analysis Fundamentals

Introduces Laurent series in complex analysis, focusing on convergence and analytic functions.

Weak Solutions of Differential Equations

Explores weak solutions of differential equations and their properties.

Fourier Series: Convergence and Dirichlet Theorem

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

Convergence Criteria

Covers convergence criteria for series, including comparison, Cauchy's root test, and d'Alembert's ratio test.

Equivalence Relations and Construction of R

Covers the construction of R and equivalence relations in sequences and linear recurrences.

Optimization Methods: Convergence and Trade-offs

Covers optimization methods, convergence guarantees, trade-offs, and variance reduction techniques in numerical optimization.

Tensors: Motivations and Introduction

Covers the basics of tensors, including their definition, properties, and decomposition, starting with a motivating example involving Gaussian distributions.

Wurzelkriterium: Majorantenkriterium

Covers the Majorantenkriterium and Wurzelkriterium for convergence tests of series.