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- Product code: 15929
- ISBN: 0131217313,
ISBN13: 9780131217317,
736 pages, paperback
Published by FT Prentice Hall on 2003
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Description of Calculus and Its Applications |
For Applied Calculus courses.
These extremely readable, highly regarded, and widely adopted texts present 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 students 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 and Benefits
NEW - Graphing functions using technology featured. Details the way in which graphing can be used to foster understanding of topics.
NEW - Delta Notation featured. Provides students with clearer presentation of derivatives.
NEW - Derivative as rate of change. Reinforces students ability to interpret the derivative as rate of change.
NEW - Analysis of data. Provides students with real-life applications whose functions are defined by tables of data.
NEW - Added emphasis on regression and technology. Familiarizes students with spreadsheets and other technologies so they can perform computations for various regressions.
NEW - Real-life data. Provides students and instructors with access to relevant statistical data on web site.
NEW - Targeted projects added. Provides open-ended problem solving, critical thinking, verbal expression and integration of mathematical techniques.
Carefully designed exercise sets.
Challenges students to make their own connections.
Practice problems. Motivates students with supported tasks.
Self-contained material. Allows students with limited math knowledge to access information.
Real-life applications/scenarios. Demonstrates to students the relevance of their studies.
Easy-to-understand instructions for using calculators are provided. Eliminates the need for a manual.
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Contents of Calculus and Its Applications |
Preface
Introduction
0. Functions
Functions and Their Graphs. Some Important Functions. The Algebra of Functions. Zeros of Functions - The Quadratic Formula and Factoring. Exponents and Power Functions. Functions and Graphs in Applications. Appendix- Graphing Functions Using Technology.
1. The Derivative
The Slope of a Straight Line. The Slope of a Curve at a Point. The Derivative. Limits and the Derivative. Differentiability and Continuity. Some Rules for Differentiation. More About Derivatives. The Derivative as a Rate of Change.
2. Applications of the Derivative
Describing Graphs of Functions. The First and Second Derivative Rules. Curve Sketching (Introduction.) Curve Sketching (Conclusion.) Optimization Problems. Further Optimization Problems. Applications of Derivatives to Business and Economics.
3. Techniques of Differentiation
The Product and Quotient Rules. The Chain Rule and the General Power Rule. Implicit Differentiation and Related Rates.
4. The Exponential and Natural Logarithm Functions
Exponential Functions. The Exponential Function e^x. Differentiation of Exponential Functions. The Natural Logarithm Function. The Derivative of ln x. Properties of the Natural Logarithm Function.
5. Applications of the Exponential and Natural Logarithm Functions
Exponential Growth and Decay. Compound Interest. Applications of the Natural Logarithm Function to Economics. Further Exponential Models.
6. The Definite Integral
Antidifferentiation. Areas and Reimann Sums. Definite Integrals and the Fundamental Theorem. Areas in the xy-Plane. Applications of the Definite Integral.
7. Functions of Several Variables
Examples of Functions of Several Variables. Partial Derivatives. Maxima and Minima of Functions of Several Variables. Lagrange Multipliers and Constrained Optimization. The Method of Least Squares. Nonlinear Regression. Double Integrals.
8. The Trigonometric Functions
Radian Measure of Angles. The Sine and the Cosine. Differentiation of sin t and cos t. The Tangent and Other Trigonometric Functions.
9. Techniques of Integration
Integration by Substitution. Integration by Parts. Evaluation of Definite Integrals. Approximation of Definite Integrals. Some Applications of the Integral. Improper Integrals.
10. Differential Equations
Solutions of Differential Equations. Separation of Variables. Numerical Solution of Differential Equations. Qualitative Theory of Differential Equations. Applications of Differential Equations.
11. Taylor Polynomials and Infinite Series
Taylor Polynomials. The Newton-Raphson Algorithm. Infinite Series. Series with Positive Terms. Taylor Series.
12. Probability and Calculus
Discrete Random Variables. Continuous Random Variables. Expected Value and Variance. Exponential and Normal Random Variables. Poisson and Geometric Random Variables.
Appendices
A: Calculus and the TI-82 Calculator
B: Calculus and the TI-83 Calculator
C: Calculus and the TI-85 Calculator
D: Calculus and the TI-86 Calculator
E: Areas Under the Standard Normal Curve
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