Lectures related to Neural networks under SGD

Vector Calculus Review: Maxwell Equations

Covers a review of vector calculus and the Maxwell equations in electromagnetism.

Covers the analysis of scalar fields, including divergence, gradient, and Laplacian.

Covers vector fields, gradient, divergence, heat flux, and stress tensors.

Neural Networks: Training and Optimization

Explores the training and optimization of neural networks, addressing challenges like non-convex loss functions and local minima.

Curve Integrals: Gauss/Green Theorem

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

Curve Integrals of Vector Fields

Explores curve integrals of vector fields, emphasizing energy considerations for motion against or with wind, and introduces unit tangent and unit normal vectors.

Optimization Methods in Machine Learning

Explores optimization methods in machine learning, emphasizing gradients, costs, and computational efforts for efficient model training.

Surface Integrals: Parameterization and Divergence Theorem

Explores surface integrals using parameterization and the divergence theorem, with practical examples included.

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.

Gradient, divergence

Covers the definitions of gradient and divergence, including the Cartesian coordinate system and the divergence theorem.

Vectors and Tensors: Derivatives and Transformations

Explores gradient, divergence, and integral theorems in vector calculus.

Surface Integrals, Divergence Theorem and Stocks' Theorem

Covers surface integrals, the divergence theorem, and Stocks' theorem through examples and analogies.

Differential Operators: Gradient and Divergence

Introduces differential operators, gradient, and divergence in vector fields.

Surface Integrals: Change of Variables

Explores surface integrals, change of variables, and properties of regular surfaces.

Differential Operators: Theorems and Proofs

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

Optimization in Machine Learning: Gradient Descent

Covers optimization in machine learning, focusing on gradient descent for linear and logistic regression, stochastic gradient descent, and practical considerations.

Energy Equilibrium and Newton CG Method

Covers continuum mechanics, linear elasticity, force balance, divergence, finite element discretization, energy minimization, and Newton's method.

Feed-forward Networks

Introduces feed-forward networks, covering neural network structure, training, activation functions, and optimization, with applications in forecasting and finance.