Brief Calculus and Its Applications

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  • Edition: 8th
  • Format: Hardcover
  • Copyright: 1999-01-01
  • Publisher: Prentice Hall
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A briefer version of the above full text by the same authors. Perfect for a one semester course.

Table of Contents

Functions and Their Graphs
Some Important Functions
The Algebra of Functions
Zeros of Functions - The Quadratic Formula and Factoring
Exponents and Power Functions
Functions and Graphs in Applications
Appendix: Graphing Functions Using Technology
The Derivative
The Slope of a Straight Line
The Slope of a Curve at a Point
The Derivative
Limits and the Derivative
Differentiability and Continuity
Some Rules for Differentiation
More About Derivatives
The Derivative as a Rate of Change
Applications of the Derivative
Describing Graphs of Functions
The First and Second Derivative Rules
Curve Sketching (Introduction
) Curve Sketching (Conclusion
) Optimization Problems
Further Optimization Problems
Applications of Derivatives to Business and Economics
Techniques of Differentiation
The Product and Quotient Rules
The Chain Rule and the General Power Rule
Implicit Differentiation and Related Rates
The Exponential and Natural Logarithm Functions
Exponential Functions
The Exponential Function e
Differentiation of Exponential Functions
The Natural Logarithm Function
The Derivative of ln x
Properties of the Natural Logarithm Function
Applications of the Exponential and Natural Logarithm Functions
Exponential Growth and Decay
Compound Interest
Applications of the Natural Logarithm Function to Economics
Further Exponential Models
The Definite Integral
Areas and Reimann Sums
Definite Integrals and the Fundamental Theorem
Areas in the xy-Plane
Applications of the Definite Integral
Functions of Several Variables
Examples of Functions of Several Variables
Partial Derivatives
Maxima and Minima of Functions of Several Variables
Lagrange Multipliers and Constrained Optimization
The Method of Least Squares
Nonlinear Regression
Double Integrals
The Trigonometric Functions
Radian Measure of Angles
The Sine and the Cosine
Differentiation of sin t and cos t
The Tangent and Other Trigonometric Functions
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