[Index] Calculus in a Single Variable

  1. Differential Calculus in a Single Variable
    1. Definition of Derivatives using big O notation
    2. Line Tangent to a Curve
    3. Exponential Function
    4. Tangent Lines as Linear Approximations
    5. Some Useful Trigonometric Limits
    6. Differentiating Trigonometric Functions
    7. Inverse Function Theorem
    8. The Natural Logarithm, the inverse function to the exponential mapping.
    9. Optimization: its motivation, the First Derivative Test, an example optimizing a rectangle’s area
    10. Implicit Differentiation
    11. Curve Sketching
      1. Curve Sketching (General Scheme)
    12. Applications
      1. L’Hopital’s Rule for Limits
    13. Techniques
      1. Differentiation Technique #1: Logarithmic Differentiation
  2. Integral Calculus in a Single Variable
    1. The Antiderivative part 1, part 2
    2. Finite Series
    3. Riemann Summation a first step towards definite integration
    4. Example Riemann Sum working with f(x)=x^{2}+1
    5. Fundamental Theorem of Calculus
    6. Properties of the Integral
    7. Not all functions are (Riemann) integrable!
    8. The Natural Logarithm Revisited!
    9. Integration Techniques:
      1. Integration Technique #1: Substitution
      2. Integration Technique #2: Integration By Parts
      3. Differentiation Under the Integral Sign
    10. Applications of Integrals
      1. Calculating Arc-Length of Curves
      2. Calculating the Area for a Surface of Revolution (Part 1) when we revolve about the x axis
    11. Optimization
      1. Calculus isn’t useless: When Velociraptors Attack, calculus solving matters of life and death!
    12. Thinking “Infinitesimally”

About Alex Nelson

I like math. I like programming. Most of all, I love puzzles.
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