# Calculus and Its Applications

• ISBN13:

• ISBN10:

## 0130797669

• Edition: 8th
• Format: Hardcover
• Publisher: Prentice Hall, Inc.
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### Summary

This is the best-selling applied calculus text for the 4 year marketplace. More rigorous than Barnett, Goldstein/Lay/Schneider still provides an accessible text to students and instructor's alike. Integrating more usage of Excel and Optional Graphing calculator examples and exercises, this revision is sure to bring this classic to the classroom in an up-to-date approach. A full website with Excel sownloadable projects/tutuorials accompanies the text.

Perface ix
Introduction 1(2)
 0 Functions
3(58)
 0.1 Functions and Their Graphs
3(15)
 0.2 Some Important Functions
18(9)
 0.3 The Algebra of Functions
27(4)
 0.4 Zeros of Functions--The Quadratic Formula and Factoring
31(9)
 0.5 Exponents and Power Functions
40(7)
 0.6 Functions and Graphs in Applications
47(14)
 1 The Derivative
61(70)
 1.1 The Slope of a Straight Line
62(10)
 1.2 The Slope of a Curve at a Point
72(6)
 1.3 The Derivative
78(9)
 1.4 Limits and the Derivative
87(11)
 1.5 Differentiability and Continuity
98(5)
 1.6 Some Rules for Differentiation
103(7)
110(5)
 1.8 The Derivative as a Rate of Change
115(16)
 2 Applications of the Derivative
131(72)
 2.1 Describing Graphs of Functions
131(13)
 2.2 The First and Second Derivative Rules
144(10)
 2.3 Curve Sketching (Introduction)
154(8)
 2.4 Curve Sketching (Conclusion)
162(7)
 2.5 Optimization Problems
169(9)
 2.6 Further Optimization Problems
178(9)
 *2.7 Applications of Calculus to Business and Economics
187(16)
 3 Techniques of Differentiation
203(28)
 3.1 The Product and Quotient Rules
203(8)
 3.2 The Chain Rule and the General Power Rule
211(6)
 3.3 Implicit Differentiation and Related Rates
217(14)
 4 The Exponential and Natural Logarithm Functions
231(30)
 4.1 Exponential Functions
231(4)
 4.2 The Exponential Function e(x)
235(6)
 4.3 Differentiation of Exponential Functions
241(5)
 4.4 The Natural Logarithm Function
246(5)
 4.5 The Derivative of In x
251(4)
 4.6 Properties of the Natural Logarithm Function
255(6)
 5 Applications of the Exponential and Natural Logarithm Functions
261(40)
 5.1 Exponential Growth and Decay
262(10)
 5.2 Compound Interest
272(8)
 *5.3 Applications of the Natural Logarithm Function to Economics
280(6)
 *5.4 Further Exponential Models
286(15)
 6 The Definite Integral
301(56)
 6.1 Antidifferentiation
302(9)
 6.2 Areas and Riemann Sums
311(10)
 6.3 Definite Integrals and the Fundamental Theorem
321(11)
 6.4 Areas in the xy-Plane
332(10)
 6.5 Applications of the Definite Integral
342(15)
 7 Functions of Several Variables
357(54)
 7.1 Examples of Functions of Several Variables
357(7)
 7.2 Partial Derivatives
364(11)
 7.3 Maxima and Minima of Functions of Several Variables
375(8)
 7.4 Lagrange Multipliers and Constrained Optimization
383(11)
 *7.5 The Method of Least Squares
394(7)
 *7.6 Double Integrals
401(10)
 8 The Trigonometric Functions
411(32)
411(4)
 8.2 The Sine and the Cosine
415(9)
 8.3 Differentiation of sin t and cost
424(10)
 8.4 The Tangent and Other Trigonometric Functions
434(9)
 9 Techniques of Integration
443(46)
 9.1 Integration by Substitution
445(6)
 9.2 Integration by Parts
451(5)
 9.3 Evaluation of Definite Integrals
456(5)
 *9.4 Approximation of Definite Integrals
461(12)
 *9.5 Some Applications of the Integral
473(5)
 9.6 Improper Integrals
478(11)
 10 Differential Equations
489(46)
 10.1 Solutions of Differential Equations
489(7)
 *10.2 Separation of Variables
496(9)
 *10.3 Numerical Solution of Differential Equations
505(7)
 10.4 Qualitative Theory of Differential Equations
512(10)
 10.5 Applications of Differential Equations
522(13)
 11 Taylor Polynomials and Infinite Series
535(46)
 11.1 Taylor Polynomials
535(9)
 *11.2 The Newton-Raphson Algorithm
544(9)
 11.3 Infinite Series
553(10)
 *11.4 Series with Positive Terms
563(7)
 11.5 Taylor Series
570(11)
 12 Probability and Calculus
581
 12.1 Discrete Random Variables
581(8)
 12.2 Continuous Random Variables
589(10)
 12.3 Expected Value and Variance
599(6)
 12.4 Exponential and Normal Random Variables
605(11)
 12.5 Poisson and Geometric Random Variables
616
Appendices A1
A Calculus and the TI-82 Calculator A1
B Calculus and the TI-83 Calculator A6
C Calculus and the TI-85 Calculator A11
D Calculus and the TI-86 Calculator A16
E Areas Under the Standard Normal Curve A22