Intuitive Explanations
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Recent content on Intuitive ExplanationsHugo -- gohugo.ioen-usRadon RosboroughSun, 07 Jan 2018 23:15:56 +0000Integration
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Sun, 07 Jan 2018 23:15:56 +0000https://intuitiveexplanations.com/integration/Integration is one of the two most important operations in calculus (the other being, of course, differentiation). It is important both because it has countless applications both inside and outside of mathematics, and also because it is extraordinarily versatile.
Some applications of integration include:
deriving formulas for calculating the area of a circle, volume of a sphere, or in general any measure (weight, density, center of mass, rotational inertia) of a real object of any geometric shape using information about forces to derive the path of motion of an object, or calculating an object's position at any time given its velocity running the mathematical machinery responsible for Laplace transforms, which allow complex circuitry and mechanical systems to be modeled easily, and Lagrangian mechanics, which allow computing the behavior of physical systems for which a direct approach is intractable As you might guess from its many applications, integration can be used in many different situations, so each use can at first seem quite different.Other Projects
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Thu, 26 May 2016 19:48:00 -0800https://intuitiveexplanations.com/other-projects/In chronological order:
TerrariaClone: My first major project, a clone of Terraria, preserved as an example of how terrible code can be if you don't pay attention to its quality. Chrono Count: iOS app to manage countdowns and countups under arbitrarily complex schedules, previously available from the iOS App Store. Mazegen: Java application to generate and visualize laser-cutter schematics for three-dimensional marble mazes. layerize: Clojure application to generate and visualize laser-cutter schematics for a cross-sectional model of a "Möbius solid".Calculus Bowl: Expert Edition
https://intuitiveexplanations.com/calculus-bowl-expert-edition/
Thu, 21 Apr 2016 22:25:00 -0800https://intuitiveexplanations.com/calculus-bowl-expert-edition/After participating in the Rocky Mountain Area Calculus Bowl, I thought it would be fun to come up with some questions myself. Fair warning: they are quite a bit harder than the ones given in the competition—even the ones from the final round.
The document is set up as a slide presentation, but it is formatted as a PDF file rather than a PowerPoint or Keynote presentation, so it is completely cross-platform and viewable in your browser.Probability Distributions: Means and Variances
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Tue, 08 Mar 2016 18:18:00 -0800https://intuitiveexplanations.com/probability-distributions-means-and-variances/This document is simply a collection of proofs of the formulas for the means and variances of seven different probability distributions that are important in statistics.
You can read the document here (PDF, ~200 KB, 7 pages). For more information about how it was created, see the About page.The Picard-Lindelöf Theorem
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Tue, 08 Mar 2016 17:18:00 -0800https://intuitiveexplanations.com/picard-lindelof-theorem/This is my rendition of the proof of the existence-uniqueness theorem for first-order differential equations, also known as the Picard-Lindelöf theorem. I tried to be as formal and explicit as possible while also making the proof easy to read and comprehend.
You can read the proof here (PDF, ~200 KB, 7 pages). For more information about how it was created, see the About page.Differential Equation Solution Strategies
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Sun, 14 Feb 2016 13:28:00 -0800https://intuitiveexplanations.com/differential-equation-solution-strategies/As anyone in a Differential Equations class could tell you, there are a lot of different strategies for solving differential equations. I found it helpful to organize many of these strategies into a single document.
This document is intended primarily as a reference guide. It contains complete proofs of each of the techniques it discusses, and also covers the relevant definitions and properties relevant to the various types of differential equations.Linear Algebra Summary Sheet
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Thu, 28 Jan 2016 17:26:00 -0800https://intuitiveexplanations.com/linear-algebra-summary-sheet/There are lots of theorems in linear algebra—many more than there are in most other math classes. I found it useful to assemble many of the important theorems into a concise, organized, single document.
This document does not contain any proofs or explanations; its power, rather, lies in its organization, which is such that the theorems that are most closely related are placed next to one another.
You can read the document here (PDF, ~200 KB, 10 pages).Calculus: Intuitive Explanations
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Thu, 28 Jan 2016 00:56:00 -0800https://intuitiveexplanations.com/calculus-intuitive-explanations/Calculus is one of my favorite areas of math, primarily because it is both extremely powerful and intuitively understandable. However, many classes and textbooks ruin the magic of calculus by focusing on formulas and theorems without explaining why they are true.
Enter Intuitive Explanations, a collection of intuitive, graphical, easy-to-understand explanations of many of the more complex concepts in calculus. It covers topics such as the formal definitions of limits and integrals, the product and quotient rules, the fundamental theorem of calculus, theorems about the convergence of sequences and series, and the definitions and theorems of vector analysis.About This Site
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Thu, 28 Jan 2016 00:36:00 -0800https://intuitiveexplanations.com/about-this-site/Hi! My name is Radon Rosborough, and I like to write about math. This website collects several of the mathematical documents I've written.
The documents If you want to get an intuitive understanding of some of the more complex concepts in calculus, take a look at Intuitive Explanations. I recommend starting here!
If you want to review Linear Algebra or Differential Equations, check out my Linear Algebra Summary Sheet or Differential Equation Solution Strategies.