Calculus Concepts An Informal Approach to the Mathematics of Change

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  • Edition: 5th
  • Format: Hardcover
  • Copyright: 2011-01-01
  • Publisher: Cengage Learning

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This innovative text features a graphing calculator approach, incorporating real-life applications and such technology as graphing utilities and Excel? spreadsheets to help students learn mathematical skills that they will use in their lives and careers. The texts overall goal is to improve learning of basic calculus concepts by involving students with new material in a way that is different from traditional practice. The development of conceptual understanding coupled with a commitment to make calculus meaningful to the student are guiding forces. Targeted toward students majoring in liberal arts, economics, business, management, and the life and social sciences, the text's focus on technology along with its use of real data and situations make it a sound choice to help you develop an intuitive, practical understanding of concepts.

Table of Contents

Ingredients Of Change: Functions And Limits
Functions--Four Representations
Function Behavior and End Behavior Limits
Limits and Continuity
Linear Functions and Models
Exponential Functions and Models
Models in Finance
Constructed Functions
Logarithmic Functions and Models
Quadratic Functions and Models
Logistic Functions and Models
Cubic Functions and Models
Cyclic Functions and Models
Representations of a Sine Function
Characteristics of Sine Functions
Describing Change: Rates
Measures of Change over an Interval
Measures of Change at a Point
Rates of Change--Notation and Interpretation
Rates of Change--Numerical Limits and Non-existence
Rates of Change Defined over Intervals
Sketching Rate-of-Change Graphs
Determining Change: Derivatives
Simple Rate-of-Change Formulas
Exponential, Logarithmic, and Cyclic Rate-of-Change Formulas
Rates of Change for Functions That Can Be Composed
Rates of Change of Composite Functions
Rates of Change for Functions That Can Be Multiplied
Rates of Change for Product Functions
Limits of Quotients and L'H?pital's Rule
Analyzing Change: Applications Of Derivatives
Relative Extreme Points
Relative Extreme Points
Inflection Points and Second Derivatives
Marginal Analysis
Optimization of Constructed Functions
Related Rates
Accumulating Change: Limits Of Sums And The Definite Integral
An Introduction to Results of Change
Limit of Sums and the Definite Integral
Accumulation Functions
The Fundamental Theorem
Antiderivative Formulas for Exponential, Natural Log, and Sine Functions
The Definite Integral--Algebraically
Differences of Accumulated Change
Average Value and Average Rate of Change
Integration of Product or Composite Functions
Analyzing Accumulated Change: Integrals And Action
Perpetual Accumulation and Improper Integrals
Streams in Business and Biology
Calculus in Economics--Demand and Elasticity
Calculus in Economics--Supply and Equilibrium
Calculus in Probability--Part
Calculus in Probability--Part
Differential Equations--Slope Fields and Solutions
Differential Equations--Proportionality and Common Forms
Ingredients Of Multivariable Change: Functions And Rates
Multivariable Functions and Contour Graphs
Cross-Sectional Models and Rates of Change
Partial Rates of Change
Compensating for Change
Analyzing Multivariable Change: Optimization
Extreme Points and Saddle Points
Multivariable Optimization
Optimization Under Constraints
Least-Squares Optimization
Answers to Odd Activities
Index of Applications
Subject Index
Table of Contents provided by Publisher. All Rights Reserved.

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