Calculus Concepts : An Applied Approach to the Mathematics of Change

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  • Edition: 4th
  • Format: Nonspecific Binding
  • Copyright: 2007-03-14
  • Publisher: Brooks Cole
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Designed for the two-semester Applied Calculus course, this graphing calculator-dependent text uses an innovative approach that includes real-life applications and technology such as graphing utilities and Excel spreadsheets to help students learn mathematical skills that they will draw on in their lives and careers. The text also caters to different learning styles by presenting concepts in a variety of forms, including algebraic, graphical, numeric, and verbal. Targeted toward students majoring in business economics, liberal arts, management and the life & social sciences,Calculus Concepts,4/e uses real data and situations to help students develop an intuitive understanding of the concepts being taught. The fourth edition has been redesigned for clarity and to emphasize certain concepts and objectives. New!The chapter openers have been updated with newChapter Applicationsand a greater emphasis placed on the chapter objectives. A NAVG (numeric, algebraic, verbal, and graphical) compass icon indicates places in the text where a concept is demonstrated through multiple representations. The feature helps students recognize connections between different representations and fosters students who possess alternative learning styles. Spreadsheet and Graphing Calculator Activitiesafford students the opportunity to use technology as they learn difficult calculus concepts. Section Activitiesreinforce concepts by presenting students with actual data and real-world problems that require independent thinking to solve. End-of-chapterProjectsare optional group assignments that allow students practice composing reports and giving oral presentations.

Table of Contents

Ingredients of Change: Functions and Models
Models and Functions
Linear Functions and Models
Exponential and Logarithmic Functions and Models
Logistic Functions and Models
Polynomial Functions and Models
Describing Change: Rates
Change, Percentage Change, and Average Rates of Change
Instantaneous Rates of Change
Derivative Notation and Numerical Estimates
Algebraically Finding Slopes
Determining Change: Derivatives
Drawing Rate-of-Change Graphs
Simple Rate-of-Change Formulas
Exponential and Logarithmic Rate-of-Change Formulas
The Chain Rule
The Product Rule
Limiting Behavior Revisited: L'H?pital's Rule
Analyzing Change: Applications of Derivatives
Approximating Change
Relative and Absolute Extreme Points
Inflection Points
Interconnected Change: Related Rates
Accumulating Change: Limits of Sums and the Definite Integral
Results of Change and Area Approximations
Accumulation Functions
The Fundamental Theorem
The Definite Integral
Average Value and Average Rate of Change
Integration by Substitution or Algebraic Manipulation
Analyzing Accumulated Change: Integrals in Action
Perpetual Accumulation and Improper Integrals
Streams in Business and Biology
Integrals in Economics
Probability Distributions and Density Functions
Repetitive Change: Cyclic Functions
Cycles and Sine Functions
Sine Functions as Models
Rates of Change and Derivatives
Extrema and Points of Inflection
Accumulation in Cycles
Dynamics of Change: Differential Equations and Proportionality
Differential Equations and Slope Fields
Separable Differential Equations
Numerically Estimating by Using Differential Equations: Euler's Method
Second-Order Differential Equations
Ingredients of Multivariable Change: Models, Graphs, Rates
Multivariable Functions and Contour Graphs
Cross-Sectional Models and Rates of Change
Partial Rates of Change
Compensating for Change
Analyzing Multivariable Change: Optimization
Multivariable Critical Points
Multivariable Optimization
Optimization Under Constraints
Least-Squares Optimization
Table of Contents provided by Publisher. All Rights Reserved.

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