This is a snippet of a conversation from Reddit: I wrote: Gaffluence wrote: Does the first law of Thermodynamics apply to magical energies too? The law being that, energy cannot be created or destroyed, only transformed (simplified version). The answer is no. Conservation of energy is due a temporal translation invariance as described in Noether’s theorem and the Lagrangian. Energy conservation is a consequence of invariance under time translations. Something more abstract than time would not be beholden to that invariance and thus would not be conserved. Basically, if it is not physical, it would not be temporal, and Read More

## Tag: Calculus

## Constructs Are Inside and Outside Your Head

“Psychic” objects are phenomenal objects. Phenomenal objects are ones that fit our intuitions of what we think about when we think of “mental” things. Broadly, they are things like concepts, intentionality, intuition, attention, awareness, perception, experience, consciousness, etc. A construct is anything that is an intentional arrangement of elements. This means that any thought that you intentionally think about is a construct because it is an intentional arrangement of experiences, intuitions, concepts, and other things of that nature. This implies that whenever you imagine something, you are technically creating a construct. Metaphysically, there is a question of how this construct Read More

## Modern Physics with Numerical Methods

This is an open-source, modern physics textbook typically for the third semester students majoring in engineering, physics or chemistry. An emphasis is placed on fundamental principles as well as numerical solutions to equations where no analytical solutions exist. The content begins with optics and uses that as a stepping stone to wave phenomena and quantum systems.

## A Breakthrough in Higher Dimensional Spheres

Higher dimensional spheres, or hyperspheres, are counter-intuitive and almost impossible to visualize. Mathematician Kelsey Houston-Edwards explains higher dimensional spheres and how recent revelations in sphere packing have exposed truths about 8 and 24 dimensions that we don’t even understand in 4 dimensions.

## Understanding Dark Energy

## SageMath

SageMath is a computer algebra system with features covering many aspects of mathematics, including algebra, combinatorics, graph theory, numerical analysis, number theory, calculus and statistics. SageMath is a free open-source mathematics software system licensed under the GPL. It builds on top of many existing open-source packages: NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R and many more. Access their combined power through a common, Python-based language or directly via interfaces or wrappers. Mission: Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab.

## OpenStax: Calculus Volume 1

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 1 covers functions, limits, derivatives, and integration.

## OpenStax: Calculus Volume 2

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates.

## OpenStax: Calculus Volume 3

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.