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  articleDescription: Good ideas inspire other ideas that might also be good.
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      articleDescription: An identity is an equivalence relation A = B where A and B are different expressions of the same value. For example, (a+b)² = a² + 2ab + b² expresses the same value on both sides of the equation regardless of the values chosen for a and b.
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      articleDescription: In geometry the objects point, line, and plane are described but not defined. Using Euclid's axiomatic methods, these objects are then used as a foundation for building and defining other geometric objects.
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      articleDescription: When working with right triangles it's usefull to think of sine, cosine, and tangent as the ratio of side lengths. When working with the unit circle, it's more helpful to think of sine, cosine, and tangent as functions.
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      articleDescription: The derivative of a smooth and continuous real valued function, is a measure of the function's rate of change at a given point along the axis of the independent variable.
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      articleDescription: Integration is a mathematical operation that sums an infinite collection of infinitesimally small values.
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      dateCreated: 2021-03-10 02:31:53
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      articleDescription: When taking the antiderivative of a polynomial, the result is a set of functions that differ by a constant. We call this set the general antiderivative.
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      permalink: /mathematics/fundamental-theorem-of-calculus
      title: The Fundamental Theorem of Calculus
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      shortDescription: Single Variable Calculus: The Fundamental Theorem of Calculus
      synopsis: Derivation and integration are inverse operations. This feature of derivation and integration is probably the most important aspect of the FTOC. It is, in fact, the very definition of calculus.

Read the Article...
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      articleDescription: "There have been several occasions in the history of mathematics when an important discovery was made independently and almost simultaneously by two individuals ... " - Mathematics and its history | John Stillwell
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      title: Calculus Cheat Sheet (Derivatives)
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      articleDescription: Definitions, Notations, Methods, Common Identities
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      permalink: https://medium.com/p/c1ac30af0ffc
      title: Notes on Gaussian Functions, the Gaussian Integral, and the Normal Distribution
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      articleDescription: The Normal distribution is a Gaussian probability distribution. Gaussian probability distributions are functions designed to reflect principles of the central limit theorem which states...
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      dateCreated: 2022-02-23 22:53:47
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      authorFullName: Ninja Torvez
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      articleDescription: Calculus required continuity and continuity was supposed to require the infinitely little; but nobody could discover what the infinitely little might be. -- Bertrand Russel
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      dateCreated: 2019-05-05 20:31:02
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      articleDescription: When I encounter some basic fact or formula that I have to review, recall, or learn, I'll add it to the appropriate page in this section.
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      dateCreated: 2021-06-25 01:19:32
      authorLink: /usr/mabocss
      authorFullName: Manin Bocss
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      authorEmail: maninbocss@gmail.com
      authorTitle: Contributing writer / contributing programmer
      authorBio:
    632:
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      permalink: /about
      title: About
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      articleDescription: This project was born from a simple idea: to allow me to enter notes on various subjects and provide a simple, point and click interface for viewing, editing, rewriting, and/or reorganizing them. I thought it would take me a few weeks. It was a good idea. That good idea led to other ideas, some good, some not so good. Five years later, I still have to enter these notes in HTML, but the overall architecture of the application is robust, configurable, and scalable. Plus, I can organize my notes in an organized way, if I choose. Not all ideas are good, but good ideas often inspire others. Some can also be good. Many turn out to be not so good. Often, you can only truly realize which is which after you try them out.
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      dateModified: 2025-10-27 01:43:24
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      dateCreated: 2019-05-10 18:59:59
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      authorFullName: Ninja Torvez
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      permalink: https://medium.com/p/7e08957391e4
      title: The Algebra and Geometry of Complex Numbers (Part 1)
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      shortDescription: Medium: The Algebra and Geometry of Complex Numbers (Part 1)
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      articleDescription: For centuries mathematicians had found ways to describe and manipulate the perfect geometries they used to represent phenomenon of the natural world. Orbits were round. Length...
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      dateModified: 2025-10-26 22:23:45
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      dateCreated: 2022-02-23 22:32:48
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      permalink: https://maninbocss.medium.com/the-rocket-equation-63d499dc62ee
      title: The Rocket Equation
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      shortDescription: Medium: The Rocket Equation
      synopsis:
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      articleDescription: Getting out of earth's gravity well and into orbit is hard. Apparently it's all about the Δv
      ogType: article
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      dateCreated: 2021-12-29 20:07:30
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      permalink: https://maninbocss.medium.com/differentiation-and-derivatives-8de437f7c5f5
      title: Differentiation and Derivatives
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      shortDescription: Differentiation and Derivatives
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      authorFullName: Ninja Torvez
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      contentId: 273
      lang: en
      permalink: https://maninbocss.medium.com/coulombs-torsion-balance-4479ed510db
      title: Coulomb's Torsion Balance
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      shortDescription: Medium: Coulomb's Torsion Balance
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      articleDescription: Coulomb’s torsion balance had no means to measure the amount of charge he had induced in the apparatus. He only new that the charge was…
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      dateCreated: 2021-07-08 15:35:04
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      authorFullName: Ninja Torvez
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      permalink: /mathematics/fundamental-theorem-of-calculus
      title: The Fundamental Theorem of Calculus
      sequence: 18
      target: _self
      shortDescription: Single Variable Calculus: The Fundamental Theorem of Calculus
      synopsis: Derivation and integration are inverse operations. This feature of derivation and integration is probably the most important aspect of the FTOC. It is, in fact, the very definition of calculus.

Read the Article...
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      articleDescription: "There have been several occasions in the history of mathematics when an important discovery was made independently and almost simultaneously by two individuals ... " - Mathematics and its history | John Stillwell
      ogType: article
      dateModified: 2025-10-26 22:23:45
      datePublished:
      dateCreated: 2021-03-10 02:33:07
      authorLink: /usr/mabocss
      authorFullName: Manin Bocss
      authorImage: [[content-folder]]/profiles/mabocss/mabocss.jpg
      authorEmail: maninbocss@gmail.com
      authorTitle: Contributing writer / contributing programmer
      authorBio:
  sidebarItems:
User Attributes  
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  * ID: -1
  type: 0
  theme: default
  prefLanguage:
  Mbocss\Tools\UserProxy groupsArray:
  userBlob:
  permalink:
  profileImage:
  email:
  username:
  title:
  fullName:
  addedBy: -1
  created_dt:
  modified_ts:
  bio:

""
Installed PHP Package List  
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  • mbocss/codeblocks: v01.01.15
    php source code for mbocss code blocks

  • mbocss/common-assets: v01.01.74
    html templates for mbocss applications

  • mbocss/database: v01.01.58
    Database classes for mbocss.

  • mbocss/dbcore: v01.01.11
    Core classes for database access

  • mbocss/dbdialogs: v01.01.73
    Dialogs for Database Updates

  • mbocss/dialogs: v01.01.53
    Dialog Core Utils for Mbocss

  • mbocss/framework: v01.01.82
    Mbocss MVC Framework

  • mbocss/model: v01.01.90
    mbocss data model objects.

  • mbocss/shared-apps: v01.01.14
    html and json for page types shared by mbocss apps

  • mbocss/tools: v01.01.99
    Tools for mbocss.

  • mbocss/utils: v01.01.27
    string and array utilities, defines utility and error and success utils for mbocss.

  • symfony/deprecation-contracts: v3.6.0
    A generic function and convention to trigger deprecation notices

  • symfony/http-foundation: v6.4.18
    Defines an object-oriented layer for the HTTP specification

  • symfony/polyfill-mbstring: v1.32.0
    Symfony polyfill for the Mbstring extension

  • symfony/polyfill-php83: v1.32.0
    Symfony polyfill backporting some PHP 8.3+ features to lower PHP versions

  • symfony/var-dumper: v7.3.0
    Provides mechanisms for walking through any arbitrary PHP variable

Debug Messages  
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