Calculus Concepts An Informal Approach to the Mathematics of Change, Brief

by LaTorre, Donald R.; Kenelly, John W.; Reed, Iris B.; Harris, Cynthia R.; Carpenter, Laurel R.

• ISBN13: 9780618401277
• ISBN10: 061840127X
• Edition: 3rd
• Format: Hardcover
• Copyright: 2004-02-04
• Publisher: Brooks Cole

Summary

For full description, see catalog entry for La Torre et al.,Calculus Concepts,3/e.

Table of Contents

To Students	xiii
Preface	xv
Ingredients of Change: Functions and Linear Models	2	(74)
Models, Functions, and Graphs	4	(15)
Mathematical Models	5	(2)
Functions	7	(1)
Determining Outputs	8	(1)
Units of Measure	9	(1)
Graphically Recognizing Functions	10	(2)
Modeling in Business	12	(2)
Concept Inventory	14	(1)
Activities	14	(5)
Constructed Functions	19	(15)
Combining Functions	19	(6)
Piecewise Continuous Functions	25	(1)
Inverse Functions	26	(4)
Concept Inventory	30	(1)
Activities	30	(4)
Functions, Limits, and Continuity	34	(16)
Limits and the Infinitely Large	34	(2)
Limits and the Infinitesimally Small	36	(3)
Continuity	39	(2)
Continuity and Function Interpretation	41	(1)
Functions That Are Continuous without Restriction	42	(2)
A Financial Illustration of Continuity, Interpretation, and a Limit	44	(1)
Concept Inventory	45	(1)
Activities	46	(4)
Linear Functions and Models	50	(26)
Representations of a Linear Model	50	(1)
The Parameters of a Linear Model: Slope and Intercept	51	(3)
Finding a Linear Model from Data	54	(3)
Aligning Data	57	(2)
What Is ``Best Fit''?	59	(1)
Numerical Considerations: Reporting Answers	60	(1)
Numerical Considerations: Calculating Answers	61	(1)
The Four Elements of a Model	62	(1)
Concept Inventory	63	(1)
Activities	64	(6)
Summary	70	(1)
Concept Check	71	(1)
Review Test	72	(2)
Tuition Fees	74	(1)
United States Population	75	(1)
Ingredients of Change: Nonlinear Models	76	(80)
Exponential Functions and Models	78	(13)
Percentage Change and Exponential Models	79	(1)
Percentage Differences from Data	80	(2)
Finding Exponential Models	82	(2)
Doubling Time and Half-Life	84	(2)
Numerical Considerations	86	(1)
Concept Inventory	87	(1)
Activities	87	(4)
Logarithmic Functions and Models	91	(10)
Logarithmic Models	91	(3)
Aligning Log Data	94	(2)
An Important Inverse Relationship	96	(1)
Concept Inventory	97	(1)
Activities	97	(4)
Logistic Functions and Models	101	(16)
Exponential Growth with Constraints	101	(2)
Finding Logistic Models	103	(4)
Shifting Logistic and Exponential Data	107	(4)
Concept Inventory	111	(1)
Activities	111	(6)
Polynomial Functions and Models	117	(19)
Quadratic Modeling	118	(4)
Quadratic or Exponential?	122	(2)
Cubic Modeling	124	(5)
Concept Inventory	129	(1)
Activities	129	(7)
Choosing a Function to Fit Data	136	(20)
Shifting Data	136	(1)
Examining Scatter Plots	137	(3)
The Steps in Choosing a Model	140	(4)
Concept Inventory	144	(1)
Activities	144	(4)
Summary	148	(1)
Concept Check	149	(1)
Review Test	150	(2)
Compulsory School Laws	152	(2)
Fund-Raising Campaign	154	(2)
Describing Change: Rates	156	(76)
Change, Percentage Change, and Average Rates of Change	158	(15)
Interpreting Descriptions of Change	159	(2)
Finding Percentage Change and Average Rate of Change Using Graphs	161	(4)
Determining Percentage Change and Average Rate of Change Using an Equation	165	(2)
Concept Inventory	167	(1)
Activities	167	(6)
Instantaneous Rates of Change	173	(18)
Local Linearity and Tangent Lines	174	(3)
Secant and Tangent Lines	177	(1)
Sketching Tangent Lines	178	(2)
Where Does the Instantaneous Rate of Change Exist?	180	(2)
Approximating Instantaneous Rates of Change	182	(2)
Concept Inventory	184	(1)
Activities	184	(7)
Derivatives	191	(15)
Derivative Terminology and Notation	191	(2)
Interpreting Derivatives	193	(3)
Approximating with Derivatives	196	(2)
Does Instantaneous Refer to Time?	198	(1)
Percentage Rate of Change	199	(2)
Concept Inventory	201	(1)
Activities	201	(5)
Numerically Finding Slopes	206	(11)
Finding Slopes by the Numerical Method	206	(4)
Finding Slopes of Piecewise Functions	210	(2)
Concept Inventory	212	(1)
Activities	213	(4)
Algebraically Finding Slopes	217	(15)
Finding Slopes Using the Algebraic Method	217	(3)
A General Formula for Derivatives	220	(4)
Concept Inventory	224	(1)
Activities	224	(2)
Summary	226	(1)
Concept Check	227	(1)
Review Test	228	(2)
Fee-Refund Schedules	230	(1)
Doubling Time	231	(1)
Determining Change: Derivatives	232	(64)
Drawing Rate-of-Change Graphs	234	(14)
Extracting Rate-of-Change Information from a Function Graph	234	(4)
A Detailed Look at the Slope Graph	238	(3)
Points of Undefined Slope	241	(2)
Concept Inventory	243	(1)
Activities	243	(5)
Simple Rate-of-Change Formulas	248	(13)
The Simple Power Rule	248	(1)
The Constant Multiplier and Sum and Difference Rules	249	(5)
Derivatives of Piecewise Functions	254	(2)
Concept Inventory	256	(1)
Activities	256	(5)
More Simple Rate-of-Change Formulas	261	(10)
Exponential Rules	261	(3)
Natural Logarithm Rule	264	(3)
Concept Inventory	267	(1)
Activities	267	(4)
The Chain Rule	271	(9)
The First Form of the Chain Rule	271	(2)
The Second Form of the Chain Rule	273	(3)
Concept Inventory	276	(1)
Activities	276	(4)
The Product Rule	280	(16)
Applying the Product Rule without Equations	281	(2)
Applying the Product Rule with Equations	283	(2)
The Quotient Rule	285	(1)
Concept Inventory	285	(1)
Activities	285	(6)
Summary	291	(1)
Concept Check	292	(1)
Review Test	292	(2)
Superhighway	294	(1)
Fertility Rates	295	(1)
Analyzing Change: Applications of Derivatives	296
Approximating Change	298
Using Rates of Change to Approximate Change	298
Marginal Analysis	303
Concept Inventory	306
Activities	306
Relative and Absolute Extreme Points	311
Relative Extrema	311
Conditions When Relative Extrema Might Not Exist	315
Relative Extrema on Functions That Are Not Smooth	318
Absolute Extrema	319
Concept Inventory	322
Activities	322
Inflection Points	327
The Second Derivative	327
Concavity and the Second Derivative	333
Concept Inventory	334
Activities	334
Derivatives in Action	341
Concept Inventory	348
Activities	348
Interconnected Change: Related Rates	353
Concept Inventory	358
Activities	358
Summary	361
Concept Check	362
Review Test	362
Hunting License Fees	364
Fund-Raising Campaign	365