Department of Mathematics Grand Valley State University, 2012. — 262 pages.Contents.
Preface.
Understanding the Derivative.
How do we measure velocity.
The notion of limit.
The derivative of a function at a point.
The derivative function.
Interpreting, estimating, and using the derivative.
The second derivative.
Limits, Continuity, and Differentiability.
The Tangent Line Approximation.
Computing Derivatives.
Elementary derivative rules.
The sine and cosine functions.
The product and quotient rules.
Derivatives of other trigonometric functions.
The chain rule.
Derivatives of Inverse Functions.
Derivatives of Functions Given Implicitly.
Using Derivatives to Evaluate Limits.
Using Derivatives.
Using derivatives to identify extreme values of a function.
Using derivatives to describe families of functions.
Global Optimization.
Applied Optimization.
Related Rates.
he Definite Integral.
Determining distance traveled from velocity.
Riemann Sums.
The Definite Integral.
The Fundamental Theorem of Calculus.
