1. Basic
Antiderivatives
* e.g. --
the Direction Field of F'(x)
= ln(x)
2. Sigma
Notation and Area
3. The Fundamental Theorem of Calculus -- the FTC
----------Statement of the FTC and Proof of Part 2
4. Change of Variable Technique
------------ Two Equal Areas.
5. The Area between Two Curves
------------ A surprising (?) Area Calculation
6. Integration by Parts
7. Volume and Average Value
------------ Average Value and the Squaring of the Integral
8. Trigonometric Integrals
9. Trigonometric
Substitution
------------ The ArcSecant Function -- a work in progress -- all corrections are WELCOME.
e.g. * An area problem:finding the area of a rotated ellipse.
10. Partial Fractions Technique
11. Improper Integrals
12.
Sequences and Series
13 a. Separable Differential Equations
b. Here are three Differential Equations done served with "Maple Syrup."
c. The Logistic Growth problem, explained without the Maple Syrup.
14. Here is a nontrivial example concerning the circumference of a circle.
** Page updated on: Last updated 21.7.2005
