Calculus Concepts : An Applied Approach to the Mathematics of Change

by LATORRE

• ISBN13: 9780618789818
• ISBN10: 0618789812
• Edition: 4th
• Format: Nonspecific Binding
• Copyright: 2007-03-14
• Publisher: Brooks Cole

Summary

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

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