Some Derivations

Chemistry

• Ideal Gas Law

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• S = k logW
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• Atmospheric Pressure Approximation and Average Height of Molecules

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• Bateman Equations ( For up to 3 successive Decays)
  

  

  

  

Mathematics

• Pythagorean Theorem ( Could be original but definitely not an elegant proof)
• Trigonometric Double Angle Formulas
  

  
• Hyperbola (Conic Section)

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• Quadratic Formula ( Without Completing Square and Minimizing Error Version)
• Why the Derivative of e^x is e^x.
• Variation of Parameters ( with Wronskian for Differential Equations)
• Sum of Powers
• Surface Area of Sphere (Without using Trig substitution in Integral)

Physics

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• In pdf format:

• Part 1: From Newton to Kepler’s First Two Laws

• Part 2: Keplers 3rd Law  

• Advanced Sesame Street Video: Deriving Kepler’s Laws

• • Einstein Special Relativity

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• • Why Speed of Light Cannot Be Exceeded
  • Relativistic Kinetic Energy Without Using Binomial Expansion
    

    
    
    

    Biology

  • Continuous  Logistic Equation for Population Dynamics
    

    

    

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