Each chapter concludes with a summary, a concept check, and review
activities
1. 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.
2. 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.
3. 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.
4. ANALYZING CHANGE: APPLICATIONS OF DERIVATIVES.
Linearization. Relative Extreme Points. Relative Extreme Points.
Inflection Points and Second Derivatives. Marginal Analysis.
Optimization of Constructed Functions. Related Rates.
5. 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.
6. 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
1. Calculus in Probability--Part 2. Differential Equations--Slope
Fields and Solutions. Differential Equations--Proportionality and
Common Forms.
7. 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.
8. 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.
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