Implicit Functions: Advanced Analysis

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Stochastic Models for Communications

Covers stochastic models for communication systems, including concepts like stochastic processes and Markov chains.

Linear Algebra Basics

Covers the basics of linear algebra, including solving equations and understanding systems of linear equations graphically.

Prime Gaps and Multiplicative Sieve Inequalities

Covers the Bombieri-Vinogradov theorem and its implications for prime gaps and multiplicative sieve inequalities.

Studying Mechanics: Vector Calculus

Covers vector calculus, including scalar and vector products, with insights from Dr. Sylvain Bréchet.

Implicit Functions Theorem

Explores the Implicit Functions Theorem, demonstrating how to find solutions to equations like x²+y²=1 through implicit differentiation and function properties.

Support Vector Machine: Primal Formulation with Hard Margin

Covers the Support Vector Machine with a hard margin formulation and the importance of maximizing the margin between classes.

Verifying Compiler: Spec# Approach

Explores the Spec# programming system, focusing on a verifying compiler for C# 2.0.

Fourier Analysis: Stokes Theorem

Explores the application of Stokes' theorem to surfaces and vector spaces in Fourier analysis.

Implicit functions theorem

Explores the implicit functions theorem, showcasing examples of implicit differentiation and function definition.

Gaussian Curvature and Geodesics

Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.