Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics.

Eric Temple Bell

sections:

      11.1, 11.2, 11.3, and 11.4

Calculus is one of the most important mathematical branches to solve problems in physics, economics, and many other disciplines. Many mathematical models involve the "rate of change" and optimization These concept are the heart of calculus!

objectives:

• describe what is meant by a limit
• use limit notation
• find limits by using a table
• distinguish between one-sided and two-sided limits
• discuss limit properties
• use limit properties to find limits
• explain the connection between a limit and continuity of a function
• determine points where a function is not continuous
• explain how to determine a slope of a curve
• define a derivative
• calculate a derivative as a limit
• determine basic derivative formulae
• use derivative formulae to determine the slope of a curve
• define an anti-derivative
• derive basic anti-derivative formulae