Algebra and Projections in Rn, Cross Product in Abstract:This series is the direct continuation of the series on the Euclidean Space of n dimensions. Here we will review some linear algebra concepts that help to better understand the n-dimensional Euclidean space, examine the concepts of projections of one vector onto...
What is an Ordinary Differential Equation (ODE)? Summary:In this class, we explore Ordinary Differential Equations (ODEs) of order k, starting with their definition and their representation in both normal and general form. Through concepts such as the Jacobian matrix and the Implicit Function Theorem, we build the foundation for understanding...
The Principle of Relativity Summary: The principle of relativity asserts that observations depend on the inertial frame, but in such a way that physical laws remain consistent. This class will present the concepts of inertial reference frame and the foundations that allow for the transformations between the coordinates observed by...
The Speed of Light and Electromagnetic Waves in a Vacuum Summary: In this class, we will review how, from the behavior of electromagnetic waves in a vacuum, it is derived from solving Maxwell's equations of electromagnetism in a vacuum. As a consequence, it is found that the speed of propagation...
Galileo's Transformations and Their Limitations Summary: The principle of relativity suggests that observations depend on the inertial frame, but in such a way that physical laws remain consistent. An initial and intuitive approach to this principle comes from Galileo's Transformations, which model how observations change between inertial reference frames in...
The Lorentz Transformations of Special Relativity Summary: The Lorentz transformations allow for the transformation of observed space and time coordinates between two inertial reference frames. In this article, we will review how the Lorentz transformations are derived as a linear coordinate transformation that emerges from considering the speed of light...
Indefinite Integrals and Basic Integration Techniques This class introduces the basic techniques to compute the most elementary indefinite integrals, as well as the properties of the integration operator. This includes polynomial, exponential, hyperbolic, and basic trigonometric integrals. Learning Objectives:By the end of this class, the student will be able to...
Statistical Simulations for Business and Industry Statistical Simulation for Business and Industry: The Normal Distribution as a Strategic Tool Discover the fascinating world of statistical simulations applied to various fields of commerce, business, and industry. In this article, we will explore four simulations, each addressing a different challenge: from optimizing...
The Spacetime of Special Relativity Summary: In this class, we will review Lorentz Transformations in the context of special relativity, challenging the notion of absolute time and establishing the constancy of the speed of light in all inertial frames. It explores how these transformations connect the space and time coordinates...
Hyperbolic Rotations of Spacetime Summary: In this class, we will review how Lorentz transformations can be reinterpreted as spacetime rotation transformations. We will start by examining rotations in the four-dimensional Minkowski space, distinguishing between purely spatial rotations and those involving spacetime axes. LEARNING OBJECTIVES: By the end of this class,...
