title: Calculus: Concepts & Contexts
author:  James Stewart 
description: This text embodies the broad principles of calculus reform-conceptual understanding motivated by real-world applications and the application of the "Rule of Four" in numerical, visual, algebraic, and verbal interpretations. At the same time, this book retains traditional calculus. The author emphasizes visualization and problem solving.
zlib_text: Section 1.1
  
  Calculus: Areas And Tangents
  
  The study of calculus begins with questions about change. What happens to the
  velocity of a swinging pendulum as its position changes? What happens to the
  position of a planet as time changes? What happens to a population of owls as
  its rate of reproduction changes?
  
  Mathematically, one is interested in learning to what extent changes in one
  quantity affect the value of another related quantity. Through the study of
  the way in which quantities change we are able to understand more deeply the
  relationships between the quantities themselves. For example, changing the
  angle of elevation of a projectile affects the distance it will travel; by
  considering the effect of a change in angle on distance, we are able to
  determine, for example, the angle which will maximize the distance.
  
  Related to questions of change are problems of approximation. If we desire to
  approximate a quantity which cannot be computed directly (for example, the
  area of some pla