Obsah

1. Module 1: Introduction to History of Calculus
   1. Introduction
   2. The dilemma
2. Module 2a: Square Roots
   1. Babylonian Method of Extraction of Square Root
   2. Newton Vs Euler Method of Finding Square Roots
   3. Estimating Square Roots
3. Module 2b: Sequences
   1. Convergence of Sequences
   2. Convergent/divergent Test of a Sequence
   3. Sequences and Series
4. Module 3a: Some Useful Inequalities
   1. Bernoulli's Inequality Theorem
   2. Young's Inequality Theorem
   3. Holder's Inequality Theorem
5. Module 3b: The Number e and pi
   1. The Number e
   2. The Number Pi
   3. Discover & Approximate Pi with Circles and Regular Polygons
   4. Approximation of e
6. Module 4a: Parabola
   1. History of a Parabola
   2. Properties of Parabolas
   3. Parametric Equations of Parabolas
   4. Parabola (Locus): Quick Prompt
   5. Another Parabola Theorem!
7. Module 4b: Volume and Surface Area of Sphere
   1. History of the Sphere
   2. Volume of a Sphere
   3. Surface Area of a Sphere
   4. Sphere (Volume + Surface)
8. Module 5a: History of Trigonometry
   1. Plimpton 322
   2. Archimedes Method of Finding Pi
9. Module 5b: Continued Fraction-Babylon
   1. Babylonian and the Square Root of 2
   2. Continued Fractions and Pi
   3. Continued Fraction Approximation to Pi
10. Module 6a: Philo Line and the Astroid
    1. Philo Line
    2. Astroid
    3. Envelope of unit circles Centred on an Astroid
11. Module 6b: Apollonius' Problem on Conics
    1. Conics
    2. Conics by Newton's Method
12. Module 7a: The Spiral and Other Ancient Curves
    1. Ancient Curves
    2. Archimedes' Spiral
    3. Witch of Agnesi
    4. 2D Parametric Curves
13. Module 7b: Early Calculations of the Area Under the Graph y=x^k
    1. Area Under the Curve
    2. Fermat's Calculation of the Area Under y = x^n
    3. Area under the Curve
14. Module 8a: Area Under the Graph of the Sine Function
    1. Sine Function
    2. Exploring Reiman Sum with GeoGebra
    3. Fundamental Theorem of Calculus
15. Module 8b: Logarithms and Exponential Functions
    1. Log vs Exponents
    2. Exploring Exponential and Logarithmic Graphs
16. Module 9a: Volume and Surface Area
    1. Volume of a Solid of Revolution
    2. Meat-Slicer Method
    3. Surface Area of Solid of Revolution
17. Module 9b: The Art of Integration 1
    1. Integration by Parts
    2. Tubular Integration by Parts
    3. Which Integration Method?
    4. Integration Visualizations
18. Module 10a: The Art of Integration 2
    1. Trigonometric Integrals
    2. Trig Intervals Summary
    3. Integration Using Substitution
    4. Integration by Partial Fractions
    5. Integration by U-Substitution
19. Module 10b: Infinite Series
    1. Power Series
    2. Integration of Power Series
    3. Power Series Representations of Functions
20. Module 11a. Functions Defined by Power Series
    1. Maclaurin Series
    2. Taylor Series
    3. Maclaurin/Taylor Series Expansion
    4. Power Series Representations of Functions
21. Module 11b: Uniform Convergence
    1. Uniform Convergent
    2. Pointwise Convergence
    3. Uniform vs Pointwise Convergence
    4. Convergent or Divergent Series
22. Module 12a: Infinite Products
    1. Infinite Products
    2. Infinite Product Examples
    3. Wallis Integral Formula
23. Module 12b: The Euler Constant and Bernoulli Number
    1. The Euler Constant
    2. The Bernoulli Number
    3. Fluid Dynamics and the Bernoulli Equation
24. Module 13a: Expansion of the Tangent and Secant Function
    1. Maclaurin Series of the Tangent Function
    2. Taylor Series of the Secant Function
    3. The General Tangent Function
    4. The General Secant Function
25. Module 13b: Euler's Solution of the Basel Problem
    1. The Basel Problem
    2. Euler's Solution to the Basel Problem