Lectures related to Implicit Functions: Local Existence Theorem

Implicit Functions: Advanced Analysis

Covers the advanced analysis of implicit functions, focusing on the application of the theorem of implicit functions.

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Divergence of Vector Fields

Explores divergence of vector fields, rotational definitions, and integral derivation applications.

Derivability on an Interval: Rolle's Theorem

Covers derivability on an interval, including Rolle's Theorem and practical applications in function analysis.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Derivatives and Functions: Definitions and Interpretations

Covers the definition of derivative functions and their interpretation, focusing on differentiability, velocity, and curve lengths.

Cohomology: Cross Product

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.

Length of Curves and Tangent Vectors

Covers the calculation of the length of curves and the properties of tangent vectors.

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.

Concept of Proof in Mathematics

Delves into the concept of proof in mathematics, emphasizing the importance of evidence and logical reasoning.

Vectorworks Educational Version

Introduces Vectorworks Educational Version for architectural drawings, covering tools, layers, and annotations.

Prime Gaps and Multiplicative Sieve Inequalities

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

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.

Advanced Analysis II: Gradient Generalizations

Explores gradient generalizations and applications in advanced analysis.

Fourier Series: Extension and Periodicity

Covers the extension and periodicity of Fourier series and the interpretation of coefficients.

Implicit Functions Theorem

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.

Determinantal Point Processes and Extrapolation

Covers determinantal point processes, sine-process, and their extrapolation in different spaces.

Logistic Regression: Probabilistic Interpretation

Covers logistic regression's probabilistic interpretation, multinomial regression, KNN, hyperparameters, and curse of dimensionality.

Initial Problem Solutions

Covers the description of all solutions of the initial problem and related concepts such as compactness and closure.

Central Limit Theorem

Covers the Central Limit Theorem and its application to random variables, proving convergence to a normal distribution.