AP Calculus

Math is a language.  Like any language, calculus is not difficult if you understand the vocab behind it.  Unfortunately for some people, this language is mostly Physics, so some people who have not taken physics find themselves in quite a situation.  Even those who have taken physics get confused.  So here it is--my best explanation of the language of calculus. 

Outlines:

Chapter 1: Limits & An Introduction to Derivatives
Chapter 2: Differentiation Rules & Applications
Chapter 3: Functions & Their Derivatives
Chapter 4: Introduction to Derivatives
Chapter 5: Area and Volume
Chapter 6: Integration Techniques
Chapter 7: Arc Length & Area of a Surface of Revolution
Chapter 8: Parametric Equations & Polar Coordinates
Chapter 9: Sequences
Chapter 10: Series

AP Calculus Study Guide/Review

Vocab:

• position/distance function- "where, location"
• integration of velocity (v(t), s'(t))
• velocity- "the change in distance with respect to time"
  • derivative of distance with respect to time
• acceleration- "the change in velocity with respect to time"
• derivative of velocity with respect to time
• second derivative of distance with respect to time
• current- "the amount of charge that flows past a point in a given time"
• derivative of charge with respect to time
• Riemann Sums- used to approximate area under a curve using either left endpoints, right endpoints, or midpoints of the rectangles
  
• Trapezoidal Rule- also used to approximate area under a curve, uses trapezoids instead of rectangles
• Euler's Method- used to find a solution to am ordinary differential equation
• Newton's Method- used to approximate the root of a FCN (where it crosses the x-axis)