In this video I go over a general overview on differential equations as well as a few of the definitions and terms associated with them. I discuss briefly about the order of a differential equation as well as what the solution to a differential equation is. I also allude to how most real-world models of differential equations are complex and thus don't usually have explicit solutions to them. Instead we often have to approximate the solutions and I will show how in later videos so stay tuned! Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhsFhf69mv--wxTqDtQ View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-general-overview Related Videos: Differential Equations: Spring Motion: Example 1: https://youtu.be/Twu30EJ93Wg Differential Equations: Motion of a Spring: https://youtu.be/mk2TiR5dwVs Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: Official Website: https://MES.fm Steemit: https://steemit.com/@mes Gab: https://gab.ai/matheasysolutions Minds: https://minds.com/matheasysolutions Twitter: https://twitter.com/MathEasySolns Facebook: https://fb.com/MathEasySolutions LinkedIn: https://mes.fm/linkedin Pinterest: https://pinterest.com/MathEasySolns Instagram: https://instagram.com/MathEasySolutions Email me: contact@mes.fm Try our Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Try our Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps ... https://www.youtube.com/watch?v=jit59tIY4UI

In this video I go over derivative notation and more specificially Leibniz notation. I also go over a brief biography of the genius and renaissance man, Gottfried Wilhelm Leibniz. From theology to politics to mathematics, Leibniz was very versatile in his studies and his version of calculus which was published in 1684 established the notation and rules for finding derivatives that we use today! Download the notes in my video: https://www.dropbox.com/s/q2rt4xxq5q8ogbw/359%20-%20Derivatives%20Notation%20and%20Bio%20of%20Leibniz.pdf Related Videos: Is the function Differentiable?? + Notation and Graphing of Derivatives: http://youtu.be/TjDApzC2D7I Derivative as a function: Graphing Derivatives: http://youtu.be/9LOLieu4G3I Definition of Derivative Simple Explanation: http://youtu.be/0rjGMpM06Eg Fundamental Theorem of Calculus - Introduction and Part 1 of the Theorem: http://youtu.be/3o8Q6UJzJyk . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: Official Website: https://MES.fm Steemit: https://steemit.com/@mes Gab: https://gab.ai/matheasysolutions Minds: https://minds.com/matheasysolutions Twitter: https://twitter.com/MathEasySolns Facebook: https://fb.com/MathEasySolutions LinkedIn: https://mes.fm/linkedin Pinterest: https://pinterest.com/MathEasySolns Instagram: https://instagram.com/MathEasySolutions Email me: contact@mes.fm Try our Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Try our Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps ... https://www.youtube.com/watch?v=ROKtFQqJOBE

In this video I go over Part 4 of the Laboratory Project titled Running Circles Around Circles and in this part I deal with hypocycloids in which the outer circle has a radius that is irrational. I test out how the curves change for the radius being equal to the irrational number 2^(1/2) and e - 2. I use the amazing Desmos graphing calculator again to plot out these parametric equations, and play around with the curves for larger and larger values of the parameter θ. For irrational radii less than 1, we obtain hypocycloids with cusps that are on the "inside ring" of the outer circle. For greater than 1 we get hypocycloids with cusps on the "outside ring". Also, I show how the curves change when we have simple, rational, radii such as 3 but when as we increase the number of decimal place values, such as 3.1, 3.12, 3.123, etc., we get increasingly more complex hypocycloids. But when ever there is a pattern, such as 3.121212, the curve also obtains a pattern that repeats itself. But for irrational numbers, as we get larger and larger ranges of values for θ we eventually will obtain a parametric curve that has points arbitrarily close to all other points, thus looking like a solid ring or washer. This is one of the coolest and most amazing videos on the power of parametric equations and curves to graph not only amazing shapes and curves, but also as a way to graph seemingly solid filled shapes. So make sure to watch this video! Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhuFxSw6viMdEkL657g View Video Notes on Steemit: https://steemit.com/mathematics/@mes/running-circles-around-circles-part-4-irrational-hypocycloids Related Videos: Laboratory Project: Running Circles Around Circles: Part 3: https://youtu.be/uCdvK29T5Z0 Laboratory Project: Running Circles Around Circles: Part 2: https://youtu.be/-hCw2HJF0YQ Laboratory Project: Running Circles Around Circles: Part 1: https://youtu.be/MiCqDNQN7_E Parametric Curves: Superellipses: https://youtu.be/JqkjQjtenPQ Parametric Curves: Example 11: Conchoids of Nicomedes: https://youtu.be/Ir1tVdwGWec Parametric Curves: Example 7: The Cycloid: Proof Part 1: https://youtu.be/XmHpIZqeRKk Parametric Curves: Example 6: Graphing Devices: https://youtu.be/cwpEasc9mhQ Parametric Curves: Example 5: Lissajous Figure: https://youtu.be/0OT1OnnAQ9I Parametric Equations and Curves: https://youtu.be/Kd3XF4LZoFE Parametric Equations and Polar Coordinates: https://youtu.be/usSors49Gdw Types of Numbers: Natural, Integers, Rational, Irrational, and Real Numbers . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: Official Website: https://MES.fm St ... https://www.youtube.com/watch?v=sypHRx10RXM

In this video I go over a very interesting algebra proof and which is to show that (x – a) is a factor, i.e. divides evenly, into the function x^k – a^k. The derivation of this can be shown by using polynomial long division until we start noticing a pattern. Once the pattern of decreasing powers of x and increasing powers of a is revealed, we can then use it to show that eventually the remainder will be 0. Thus proving the formulation! This is a very interesting method of derivation and I will be using this proof in my later videos on algebra so make sure to watch this video! Video notes and playlist: - PDF notes: https://1drv.ms/b/s!As32ynv0LoaIh4Il87_E56J68Cgb4A - HIVE notes: https://peakd.com/mathematics/@mes/polynomial-long-division-x-a-is-a-factor-of-x-k-a-k-proof - Polynomial Long Division playlist: https://www.youtube.com/playlist?list=PL599994D41692CF90 Related Videos: Polynomials - A Simple Explanation: http://youtu.be/IHIh7Y0kStE Polynomial Long Division - In depth Look on why it works!: http://youtu.be/E1H584xJS_Y Polynomial Long Division - Examples: http://youtu.be/7XbzCQgqBPc Factoring Quadratic Polynomials by Guessing: http://youtu.be/biEfGwT5pn4 Direct Substitution for Polynomials - Simple Proof: http://youtu.be/Fnb72ERTLqY Polynomial Long Division: Multiple Variables: http://youtu.be/vrElU5SR6Aw Euclidean Division of Polynomials: Theorem and Proof: https://youtu.be/ONxn17okl5c Polynomial Remainder Theorem: Proof + Factor Theorem: https://youtu.be/q4lwSBObkXc . ------------------------------------------------------ Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate SUBSCRIBE via EMAIL: https://mes.fm/subscribe MES Links: https://mes.fm/links MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps