Lectures related to Implicit Functions: Advanced Analysis

Discusses implicit functions and the local existence theorem for finding solutions.

Covers logistic regression, probabilistic interpretation, and feature engineering techniques.

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

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

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

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

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

Covers linear classification using logistic regression, regularization, and multiclass classification.

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

Explores the tangent plane to implicit functions and its graphical representation in relation to defined variables.

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

Explores gradient generalizations and applications in advanced analysis.

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

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

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

Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.

Covers vector spaces, differentiable functions, scalar product, and norms in depth.

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

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