Calculus: Applications and Technology, 3/e

Description:

CALCULUS: APPLICATIONS AND TECHNOLOGY is a modern text that is guided by four basic principles: The Rule of Four, technology, the Way of Archimedes, and an exploratory teaching method. Where appropriate, each topic is presented graphically, numerically, algebraically, and verbally, helping students gain a richer, deeper understanding of the material. A pronounced emphasis in the text on technology, whether graphing calculators or computers, permits instructors to spend more time teaching concepts. Additionally, applications play a central role in the text and are woven into the development of the material. More than 500 referenced exercises and hundreds of data sets contained in the text make this text useful and practical for students. Most importantly, this text lets students investigate and explore calculus on their own, and discover concepts for themselves.

 

Table of Contents:

1. FUNCTIONS.
Graphers Versus Calculus. Functions. Mathematical Models. Exponential Models. Combinations of Functions. Logarithms.
2. MODELING WITH LEAST SQUARES.
Method of Least Squares. Quadratic Regression. Cubic, Quartic, and Power Regression. Exponential and Logarithmic Regression. Logistic Regression. Selecting the Best Model.
3. THE DERIVATIVE.
Introduction to Calculus. Limits. Rates of Change. The Derivative. Local Linearity.
4. RULES FOR THE DERIVATIVE.
Derivatives of Powers, Exponents, and Sums. Derivatives of Products and Quotients. The Chain Rule. Derivatives of Exponential and Logarithmic Functions. Elasticity of Demand. Management of Renewable Natural Resources.
5. CURVE SKETCHING AND OPTIMIZATION.
The First Derivative. The Second Derivative. Limits at Infinity. Additional Curve Sketching. Absolute Extrema. Optimization and Modeling. The Logistic Model. Implicit Differentiation and Related Rates.
6. INTEGRATION.
Antiderivatives. Substitution. Distance Traveled. The Definite Integral. The Fundamental Theorem of Calculus. Area Between Two Curves. Additional Applications of the Integral.
7. ADDITIONAL TOPICS IN INTEGRATION.
Integration by Parts. Integration Using Tables. Numerical Integration. Improper Integrals.
8. FUNCTIONS OF SEVERAL VARIABLES.
Functions of Several Variables. Partial Derivatives. Extrema of Functions of Two Variables. Lagrange Multipliers. Total Differentials and Approximations. Double Integrals.
OPTIONAL CD-ROM CHAPTERS.
9. THE TRIGONOMETRIC FUNCTIONS.
Angles. The Sine and Cosine. Differentiation of the Sine and Cosine Functions. Integrals of the Sine and Cosine Functions. Other Trigonometric Functions.
10. TAYLOR POLYNOMIALS AND INFINITE SERIES.
Taylor Polynomials. Errors in Taylor Polynomial Approximation. Infinite Sequences. Infinite Series. The Integral and Comparison Tests. The Ratio Test and Absolute Convergence. Taylor Series.
11. PROBABILITY AND CALCULUS.
Discrete Probability. Continuous Probability Density Functions. Expected Value and Variance. The Normal Distribution.
12. DIFFERENTIAL EQUATIONS.
Differential Equations. Separation of Variables. Approximate Solutions to Differential Equations. Qualitative Analysis. Harvesting a Renewable Resource.
Appendix A: Review.
Appendix B: Tables.