Periodic Solutions in Planar Systems

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Differential Operators: Theorems and Proofs

Covers the concept of differential operators and presents theorems and proofs related to scalar and vector fields.

Divergence of Vector Fields

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

Divergence Theorem: Green Identities in R²

Explores the divergence theorem and corollaries related to Green identities in the plane, demonstrating their application through examples.

Curve Integrals: Gauss/Green Theorem

Explores the application of the Gauss/Green theorem to calculate curve integrals along simple closed curves.

Green Theorem: Corollary 3 Proof

Demonstrates the relationship between the gradient and the divergence of a scalar field.

Variational Formulation: Information Measures

Explores variational formulation for measuring information content and divergence between probability distributions.

Graph Surfaces: Integration and Vector Calculus

Covers integrating functions over graph surfaces in vector calculus, emphasizing the interpretation of divergence theorem and special cases of domain between two graphs.

Nonlinear Equations: Bisection and Fixed-Point Methods

Explores nonlinear equations, bisection, fixed-point methods, error control, and graphical interpretations of fixed points.

Neural networks under SGD

Explores the optimization of neural networks using Stochastic Gradient Descent (SGD) and the concept of dual risk versus empirical risk.

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