Calculus : a complete course
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Bibliographic Information
Calculus : a complete course
Addison-Wesley, c2000
2nd. ed, international ed
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Includes index
Description and Table of Contents
Description
Written by an experienced author team with expertise in the use of technology and NCTM guidelines, this text provides an emphasis on multiple representations of concepts and an abundance of worked examples. Calculus is explored through the interpretation of graphs and tables as well as through the application of analytical methods. Rich exercises include graphical and data-based problems, and interesting real-life applications in biology, business, chemistry, economics, engineering, finance, physics, the social sciences and statistics. Stepped Explorations throughout the text provide guided investigations of key concepts and help students build problem-solving skills. A grapher is required.
Table of Contents
(All chapters end with Key Terms and Review Exercises.)
1. Prerequisites for Calculus.
Lines.
Functions and Graphs.
Exponential Functions.
Parametric Equations.
Functions and Logarithms.
Trigonometric Functions.
2. Limits and Continuity.
Rates of Change and Limits.
Limits Involving Infinity.
Continuity.
Rates of Change and Tangent Lines.
3. Derivatives.
Derivative of a Function.
Differentiability.
Rules for Differentiation.
Velocity and Other Rates of Change.
Derivatives of Trigonometric Functions.
Chain Rule.
Implicit Differentiation.
Derivatives of Inverse Trigonometric Functions.
Derivatives of Exponential and Logarithmic Functions.
Calculus At Work.
4. Applications of Derivatives.
Extreme Values of Functions.
Mean Value Theorem.
Connecting fe and f" with the Graph of f.
Modeling and Optimization.
Linearization and Newton's Method.
Related Rates.
5. The Definite Integral.
Estimating with Finite Sums.
Definite Integrals.
Definite Integrals and Antiderivatives.
Fundamental Theorem of Calculus.
Trapezoidal Rule.
Calculus At Work.
6. Differential Equations and Mathematical Modeling.
Antiderivatives and Slope Fields.
Integration by Substitution.
Integration by Parts.
Exponential Growth and Decay.
Population Growth.
Numerical Methods.
Calculus At Work.
7. Applications of Definite Integrals.
Integral as Net Change.
Areas in the Plane.
Volumes.
Lengths of Curves.
Applications from Science and Statistics.
Calculus At Work.
8. L'Hopital's Rule, Improper Integrals, and Partial Fractions.
L'Hopital's Rule.
Relative Rates of Growth.
Improper Integrals.
Partial Fractions and Integral Tables.
9. Infinite Series.
Power Series.
Taylor Series.
Taylor's Theorem.
Radius of Convergence.
Testing Convergence at Endpoints.
Calculus At Work.
10. Parametric, Vector, and Polar Functions.
Parametric Functions.
Vectors in the Plane.
Vector-Valued Functions.
Modeling Projectile Motion.
Polar Coordinates and Polar Graphs.
Calculus of Polar Curves.
11. Vectors and Analytic Geometry in Space.
Cartesian (Rectangular) Coordinates and Vectors in Space.
Dot Products.
Cross Products.
Lines and Planes in Space.
Cylinders and Cylindrical Coordinates.
Quadratic Surfaces.
12. Vector-Valued Functions and Motion in Space.
Vector-valued Functions and Space Curves.
Arc Length and the Unit Tangent Vector T.
Curvature, Torsion, and the TNB Frame.
Planetary Motion and Satellites.
13. Multivariable Functions and Their Derivatives.
Functions of Several Variables.
Limits and Continuity in Higher Dimensions.
Partial Derivatives.
Differentiability, Linearizations, and Differentials.
The Chain Rule.
Directional Derivatives, Gradient Vectors, and Tangent Planes.
Extreme Values and Saddle Points.
Lagrange Multipliers.
14. Multiple Integrals.
Double Integrals.
Area, Moments, and Centers of Mass.
Double Integrals in Polar Form.
Triple Integrals in Rectangular Coordinates.
Masses and Moments in Three Dimensions.
Triple Integrals in Cylindrical and Spherical Coordinates.
Substitutions in Multiple Integrals.
15. Integration in Vector Fields.
Line Integrals.
Vector Fields, Work, Circulation, and Flux.
Path Independence, Potential Functions, and Conservative Fields.
Green's Theorem in the Plane.
Surface Area and Surface Integrals.
Parametrized Surfaces.
Stokes's Theorem.
The Divergence Theorem and a Unified Theory.
Cumulative Review Exercises.
Appendices.
Formulas from Precalculus Mathematics.
Mathematical Induction.
Using the Limit Definition.
Proof of the Chain Rule.
Conic Sections.
Hyperbolic Functions.
A Brief Table of Integrals.
Determinants and Cramer's Rule.
Glossary.
Selected Answers.
Applications Index.
Index.
by "Nielsen BookData"