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Calculus and Its Applications
ISBN: 9780130466105 | 0130466107
Format: HardcoverPublisher: Prentice Hall
Pub. Date: 1/1/2004
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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 student's mathematical maturity and his/her appreciation for the usefulness of mathematics. The authors' tried and true formulapairing substantial amounts of graphical analysis and informal geometric proofs with an abundance of hands-on exerciseshas proven to be tremendously successful with both students and instructors.
| Preface | |
| Introduction | |
| 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 | |
| The Derivative | |
| The Slope of a Straight Line | ... MORE|
| 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 | |
| Applications of the Derivative | |
| Describing Graphs of Functions | |
| The First and Second Derivative Rules | |
| The First and Second Derivative Tests and Curve Sketching | |
| Curve Sketching (Conclusion) | |
| Optimization Problems | |
| Further Optimization Problems | |
| Applications of Derivatives to Business and Economics | |
| Techniques of Differentiation | |
| The Product and Quotient Rules | |
| The Chain Rule and the General Power Rule | |
| Implicit Differentiation and Related Rates | |
| Logarithm Functions | |
| Exponential Functions | |
| The Exponential Function ex | |
| Differentiation of Exponential Functions | |
| The Natural Logarithm Function | |
| The Derivative of ln x | |
| Properties of the Natural Logarithm Function | |
| 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 | |
| The Definite Integral | |
| Antidifferentiation | |
| Areas and Riemann Sums | |
| Definite Integrals and the Fundamental Theorem | |
| Areas in the xy-Plane | |
| Applications of the Definite Integral | |
| 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 | |
| Double Integrals | |
| The Trigonometric Functions | |
| Radian Measure of Angles | |
| The Sine and the Cosine | |
| Differentiation and Integration of sin t and cos t | |
| The Tangent and Other Trigonometric Functions | |
| Techniques of Integration | |
| Integration by Substitution | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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