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# Calculus and Its Applications - Package - 11th edition

## ISBN10: 0131746251

Edition: 11TH 07
Publisher: Prentice Hall, Inc.
Published: 2007
International: No

## ISBN10: 0131746251

Edition: 11TH 07

### Summary

This text is geared towards a one semester course in applied calculus.

This extremely readable, highly regarded, and widely adopted text presents innovative ways for applying calculus to real-world situations in the business, economics, life science, and social science disciplines. The texts' straightforward, engaging approach fosters the growth of both the student's mathematical maturity and his/her appreciation for the usefulness of mathematics. The authors' tried and true formula--pairing substantial amounts of graphical analysis and informal geometric proofs with an abundance of hands-on exercises--has proven to be tremendously successful with both students and instructors.

Features

• Exercise sets:
• Carefully designed, building in level of difficulty so that instructors can chose those exercises appropriate for their students.
• Thoroughly tested and very diverse.
• Technology exercises offered at the ends of each section.
• Applications: Contain up-to-date and realistic data to illustrate to students the relevance of these concepts.
• Examples: Contains many more worked examples than is customary, many of which include real data.
• Practice Problems: Each section concludes with ~5 problems that focus on concepts that are potentially confusion. Complete solutions are provided.
• ''Warnings!'' which provide tips on common pitfalls and mistakes appear at relevant times.
• Extensive TI Calculator help: Easy-to-understand instructions for using calculators are provided in 4 appendices

Preface
Introduction

0 Functions

0.1 Functions and Their Graphs
0.2 Some Important Functions
0.3 The Algebra of Functions
0.4 Zeros of Functions--The Quadratic Formula and Factoring
0.5 Exponents and Power Functions
0.6 Functions and Graphs in Applications

1 The Derivative

1.1 The Slope of a Straight Line
1.2 The Slope of a Curve at a Point
1.3 The Derivative
1.4 Limits and the Derivative
1.5 Differentiability and Continuity
1.6 Some Rules for Differentiation
1.8 The Derivative as a Rate of Change

2 Applications of the Derivative

2.1 Describing Graphs of Functions
2.2 The First and Second Derivative Rules
2.3 The First and Second Derivative Tests and Curve Sketching
2.4 Curve Sketching (Conclusion)
2.5 Optimization Problems
2.6 Further Optimization Problems
2.7 Applications of Derivatives to Business and Economics

3 Techniques of Differentiation

3.1 The Product and Quotient Rules
3.2 The Chain Rule and the General Power Rule
3.3 Implicit Differentiation and Related Rates

4 Logarithm Functions

4.1 Exponential Functions
4.2 The Exponential Function ex
4.3 Differentiation of Exponential Functions
4.4 The Natural Logarithm Function
4.5 The Derivative of ln x
4.6 Properties of the Natural Logarithm Function

5 Applications of the Exponential and

Natural Logarithm Functions
5.1 Exponential Growth and Decay
5.2 Compound Interest
5.3 Applications of the Natural Logarithm Function to Economics
5.4 Further Exponential Models

6 The Definite Integral

6.1 Antidifferentiation
6.2 Areas and Riemann Sums
6.3 Definite Integrals and the Fundamental Theorem
6.4 Areas in the xy-Plane
6.5 Applications of the Definite Integral

7 Functions of Several Variables

7.1 Examples of Functions of Several Variables
7.2 Partial Derivatives
7.3 Maxima and Minima of Functions of Several Variables
7.4 Lagrange Multipliers and Constrained Optimization
7.5 The Method of Least Squares
7.6 Double Integrals

8 The Trigonometric Functions

8.2 The Sine and the Cosine
8.3 Differentiation and Integration of sin t and cos t
8.4 The Tangent and Other Trigonometric Functions

9 Techniques of Integration

9.1 Integration by Substitution
9.2 Integration by Parts
9.3 Evaluation of Definite Integrals
9.4 Approximation of Definite Integrals
9.5 Some Applications of the Integral
9.6 Improper Integrals

10 Differential Equations

10.1 Solutions of Differential Equations
10.2 Separation of Variables
10.3 First-Order Linear Differential Equations
10.4 Applications of First-Order Linear Differential Equations
10.5 Graphing Solutions of Differential Equations
10.6 Applications of Differential Equations
10.7 Numerical Solution of Differential Equations

11 Taylor Polynomials and Infinite Series

11.1 Taylor Polynomials
11.2 The Newton-Raphson Algorithm
11.3 Infinite Series
11.4 Series with Positive Terms
11.5 Taylor Series

12 Probability and Calculus

12.1 Discrete Random Variables
12.2 Continuous Random Variables
12.3 Expected Value and Variance
12.4 Exponential and Normal Random Variables
12.5 Poisson and Geometric Random Variables

Appendix A Calculus and the TI-82 Calculator
Appendix B Calculus and the TI-83/TI-83 Plus/TI-84 Plus
Calculators
Appendix C Calculus and the TI-85 Calculator
Appendix D Calculus and the TI-86 Calculator
Appendix E Areas under the Standard Normal Curve