Lectures related to Finite Differences Proof

Finite Differences: Definition and Proof

Covers the definition of the center of a function using finite differences and provides step-by-step proofs.

Theoreus Chain Role: Lipschitz Sit

Covers the Theoreus Chain Role for Lipschitz functions and its practical applications.

Fourier Series: Understanding Coefficients and Periodicity

Explores Fourier series coefficients, periodicity, and series relations.

Numerical Derivatives of Order 1

Covers the concept of numerical derivatives of order 1 and the importance of choosing a small fixed value for h.

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

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Hitting Probabilities: Markov Chains

Covers hitting probabilities in Markov chains with disjoint subsets, the function h(i), theorems, proofs, and expected time to hit calculations.

Numerical Analysis: Advanced Topics

Covers advanced topics in numerical analysis, focusing on techniques for solving complex mathematical problems.

Linear Algebra: Equivalence and Calculations

Explains equivalence in linear algebra and set calculations with illustrative examples.

Markov Chains: Hitting Probabilities

Explores hitting probabilities in Markov chains, covering minimal solutions, proofs, and recursive relationships.

Differentiability in Analysis

Explores differentiability in analysis, discussing conditions for functions to be differentiable and continuous.

Implicit Functions: Unique Solutions and Class C Functions

Covers the proof of the theorem of implicit functions and the concept of class C functions.

Mapping Functions and Surjections

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Numerical Differentiation and Integration

Covers numerical differentiation and integration techniques using examples and quadrature formulas.

Extension of Fields: Norm and Valuation

Covers the extension of fields, defining the norm of an element from one field to another, and introducing the p-adic valuation.

Positive Definite Coxeter Graphs

Explores the classification of positive definite connected Coxeter graphs through detailed calculations and proofs.

Measure Spaces: O-Finite and Probability Measures

Explores o-finite and finite measure spaces, probability measures, and inequalities, concluding with LP space completeness.

Geometric Series: Convergence and Applications

Explores the convergence of geometric series and their applications in real-world problems.

Least Common Multiple: Basics

Explains the concept of the least common multiple for two natural numbers.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.