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Calculus

Most of the 16 Articles in this section are original works. The most notable ones of which are Articles 1 and 4. Article 1 presents a method of implicit integration and Article 4 introduces a new class of differential equations that Ali has termed “abnormal" including how to solve them. Depending on the visitor’s taste, there might be even some more notable articles in this section.

  • 1. A Method of Implicit Integration
  • 2. A Poetic Characterization for Parabolas
  • 3. Analytical Geometric Characterizations of Cubic Functions
  • 4. Abnormal Differential Equations
  • 5. Altering Corners of Curves for Smoothness
  • 6. Converse Propositions for the Mean and Average Value Theorems of Calculus (Revised November 2025)
  • 7. n Times Differentiable Interpolating Curves and Pascal Triangle
  • 8. An Infinitely Many Times Differentiable Interpolation
  • 9. An n Times Smooth Interpolation Between a Horizontal and an Oblique Line
  • 10. Trigonometric Approximation of the Function Ln(x)
  • 11. Interesting Facts Regarding Inflection Point
  • 12. Remarkable Functions with Notable Compositions GoF = F-G and FoG = F over G
  • 13. A Calculus Proposition with Application
  • 14. Horizontal Asymptotes; a List of Possible Scenarios
  • 15. A Direct Formula for the nth Derivative of a Function
  • 16. Alternative Definition for Derivatives
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