Algebra Review | |
Real Numbers | |
Exponents and Radicals | |
Multiplying and Factoring Algebraic Equations | |
Rational Expressions | |
Solving Polynomial Equations | |
Solving Miscellaneous Equations | |
Functions and Linear Models | |
Functions from the Numerical and Algebraic Viewpoints | |
Functions from the Graphical Viewpoint | |
Linear Functions | |
Linear Models | |
Linear Regression | |
Key Concepts | |
Review Exercises | |
Case Study: Modeling Spending on Internet Advertising | |
Technology Guides | |
Optional Internet Topic: New Functions from Old: Scaled and Shifted Functions | |
Nonlinear Models | |
Quadratic Functions and Models | |
Exponential Functions and Models | |
Logarithmic Functions and Models | |
Logistic Functions and Models | |
Key Concepts | |
Review Exercises | |
Case Study: Checking up on Malthus | |
Technology Guides | |
Optional Internet Topics: Inverse Functions | |
Using and Deriving Algebraic Properties of Logarithms | |
Introduction to the Derivative | |
Limits: Numerical and Graphical Approaches | |
Limits and Continuity | |
Limits: Algebraic Approach | |
Average Rate of Change | |
Derivatives: Numerical and Graphical Viewpoints | |
Derivatives: Algebraic Viewpoint | |
Derivatives of Powers, Sums, and Constant Multiples | |
A First Application: Marginal Analysis | |
Key Concepts | |
Review Exercises | |
Case Study: Reducing Sulfur Emissions | |
Technology Guides | |
Optional Internet Topics: Sketching the Graph of the Derivative | |
Proof of the Power Rule | |
Continuity and Differentiability | |
Techniques of Differentiation | |
The Product and Quotient Rules | |
The Chain Rule | |
Derivatives of Logarithmic and Exponential Functions | |
Implicit Differentiation | |
Key Concepts | |
Review Exercises | |
Case Study: Projecting Market Growth | |
Technology Guides | |
Optional Internet Topic: Linear Approximation and Error Estimation | |
Applications of the Derivative | |
Maxima and Minima | |
Applications of Maxima and Minima | |
The Second Derivative and Analyzing Graphs | |
Related Rates | |
Elasticity | |
Key Concepts | |
Review Exercises | |
Case Study: Production Lot Size Management | |
Technology Guides | |
The Integral | |
The Indefinite Integral | |
Substitution | |
The Definite Integral: Numerical and Graphical Approaches | |
The Definite Integral: Algebraic Approach and the Fundamental Theorem of Calculus | |
Key Concepts | |
Review Exercises | |
Case Study: Wage Inflation | |
Technology Guides | |
Optional Internet Topic: Numerical Integration | |
Further Integration Techniques and Applications of the Integral | |
Integration by Parts | |
Area Between Two Curves and Applications | |
Averages and Moving Averages | |
Applications to Business and Economics: Consumers' and Producers' Surplus and Continuous Income Streams | |
Improper Integrals and Applications | |
Differential Equations and Applications | |
Key Concepts | |
Review Exercises | |
Case Study: Estimating Tax Revenues | |
Technology Guides | |
Optional Internet Topic: Taylor Polynomials | |
Functions of Several Variables | |
Functions of Several Variables from the Numerical and Algebraic Viewpoints | |
Three Dimensional Space and the Graph of a Function of Two Variables | |
Partial Derivatives | |
Maxima and Minima | |
Constrained Maxima and Minima and Applications | |
Double Integrals and Applications | |
Key Concepts | |
Review Exercises | |
Case Study: Modeling Household Income | |
Technology Guides | |
Optional Internet Topic: The Chain Rule for Functions of Several Variables | |
Trignometric Models | |
Trigonometric Functions, Models, and Regression | |
Derivatives of Trigonometric Functions and Applications | |
Integrals of Trigonometric Functions and Applications | |
Key Concepts | |
Review Exercises | |
Case Study: Predicting Cocoa Inventories | |
Technology Guides | |
Answers to Selected EXERCISES | |
Index | |
Optional Internet Topic | |
S. Calculus Applied to Probability and Statistics | |
Introduction | |
Continuous Random Variables and Histograms | |
Probability Density Functions: Uniform, Exponential, Normal, and Beta | |
Mean, Median, Variance and Standard Deviation | |
Case Study: Creating a Family Trust | |
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