Lectures related to Four-dimensional space

Static Equivalence: Forces and Moments

Explores static equivalence of forces, replacing distributed forces with concentrated ones and calculating Cartesian components of forces and moments.

Lagrange Method: 2 Constraints

Explains the Lagrange method with 2 constraints and composite functions' derivatives.

Epicyclic Curves: Modeling Instruments for Plane Curves

Explores modeling instruments for generating plane epicyclic curves, including circles and ellipses, and their spatial counterparts.

Advanced Physics I: Orders of Magnitude

Explores the triumph of determinism in modern mechanics and the methodology of scientific development, with practical exercises on estimating surgical mask usage and analyzing atomic bomb energy.

Coordinate Calculations: Scalar Product in Coordinates

Covers the calculation of scalar products in coordinates and extends the concept to three-dimensional space.

Quantum Particle in Potential Well

Focuses on solving the first question of exercise 23 involving a quantum particle.

Physics: Introduction to Dynamics and Energy

Covers one-dimensional and two-dimensional motion, dynamics, and energy with a focus on mathematical modeling and rigorous approach.

Implicit Functions Theorem

Covers the implicit functions theorem and its applications in defining functions implicitly and differentiating them.

Vector Product: Definition and Properties

Covers the definition and properties of the vector product in three-dimensional space.

Scalar Fields: Basics and Applications

Covers the basics of scalar fields and their diverse applications in various scientific fields.

Scalar, Vector or Tensor? Gravity

Discusses defining tensors, space-time dimensionality, and challenges in formulating a relativistic theory of gravity.

Machine Learning Fundamentals: Overfitting and Regularization

Covers overfitting, regularization, and cross-validation in machine learning, exploring polynomial curve fitting, feature expansion, kernel functions, and model selection.

Decomposition into Line Metrics: Example and Outlook

Covers the decomposition into line metrics, providing examples and discussing its implications.

Computational Thinking Test: Evaluation and Design

Presents a test to evaluate computational thinking skills, discussing its design, analysis of previous tools, sample question, and study results.

Galilean Transformations

Explores Galilean relativity, transformations between inertial coordinate systems, synchronized clocks, and visualizing motion in four-dimensional space-time.

Geometry: Euclidean Elements & Vitruvius

Explores Euclid's first proposition, ancient symmetria, and Vitruvius' architectural figures.

Linear Applications: Kernel and Preimage (Part 2)

Explores the kernel of a linear transformation and the concept of preimage.

Threshold Functions in Neural Networks

Explores threshold functions in neural networks for classifying data points based on positive and negative values.

Tori: Character Forms and Monomials

Explores Tori in algebraic geometry, emphasizing character forms and monomials.

Dimensional Analysis & Scaling Laws

Explores dimensional analysis, scaling laws, physical similarity, and the interdependency of variables in physical systems.