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Thomas' Calculus, Media Upgrade, Part One (Single Variable),9780321498755
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Thomas' Calculus, Media Upgrade, Part One (Single Variable)

by ; ; ;
Edition:
11th
ISBN13:

9780321498755

ISBN10:
0321498755
Format:
Paperback
Pub. Date:
1/5/2007
Publisher(s):
Pearson
List Price: $122.67
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Summary

Thomas'Calculus Part One Media Upgrade, Eleventh Edition,responds to the needs of today's readers by developing their conceptual understanding while strengthening their skills in algebra and trigonometry, two areas of knowledge vital to the mastery of calculus. This book offers a full range of exercises, a precise and conceptual presentation, and a new media package designed specifically to meet the needs of today's readers. The exercises gradually increase in difficulty, helping readers learn to generalize and apply the concepts. The refined table of contents introduces the exponential, logarithmic, and trigonometric functions in Chapter 7 of the text. Limits and Derivatives, Differentiation, Applications of Derivatives, Integration, Applications of Definite Integrals, Transcendental Functions, Techniques of Integration, Further Applications of Integration, Conic Sections and Polar Coordinates, Infinite Sequences and Series.For all readers interested in Calculus.

Table of Contents

(Practice Exercises, Additional Exercises, and Questions to Guide Your Review appear at the end of each chapter.)
Preliminaries Real Numbers and the Real Line Lines, Circles, and Parabolas
Functions and Their Graphs
Identifying Functions; Mathematical Models
Combining Functions; Shifting and Scaling Graphs
Trigonometric Functions
Graphing with Calculators and Computers
Limits and Derivatives
Rates of Change and Limits
Calculating Limits Using the Limit Laws
Precise Definition of a Limit
One-Sided Limits and Limits at Infinity
Infinite Limits and Vertical Asymptotes
Continuity
Tangents and Derivatives
Differentiation
The Derivative as a Function
Differentiation Rules
The Derivative as a Rate of Change
Derivatives of Trigonometric Functions
The Chain Rule and Parametric Equations
Implicit Differentiation
Related Rates
Linearization and Differentials
Applications of Derivatives
Extreme Values of Functions
The Mean Value Theorem
Monotonic Functions and the First Derivative Test
Concavity and Curve Sketching
Applied Optimization Problems
Indeterminate Forms and L'Hopital's Rule
Newton's Method
Antiderivatives
Integration
Estimating with Finite Sums
Sigma Notation and Limits of Finite Sums
The Definite Integral
The Fundamental Theorem of Calculus
Indefinite Integrals and the Substitution Rule
Substitution and Area Between Curves
Applications of Definite Integrals
Volumes by Slicing and Rotation About an Axis
Volumes by Cylindrical Shells
Lengths of Plane Curves
Moments and Centers of Mass
Areas of Surfaces of Revolution and The Theorems of Pappus
WorkFluid Pressures and Forces
Transcendental Functions
Inverse Functions and their Derivatives
Natural Logarithms
The Exponential Functionax and loga xExponential Growth and Decay
Relative Rates of Growth
Inverse Trigonometric Functions
Hyperbolic Functions
Techniques of Integration
Basic Integration Formulas
Integration by Parts
Integration of Rational Functions by Partial Fractions
Trigonometric Integrals
Trigonometric Substitutions
Integral Tables and Computer Algebra Systems
Numerical Integration
Improper Integrals
Further Applications of Integration
Slope Fields and Separable Differential Equations
First-Order Linear Differential Equations
Euler's Method
Graphical Solutions of Autonomous Equations
Applications of First-Order Differential Equations
Conic Sections and Polar Coordinates
Conic Sections and Quadratic Equations
Classifying Conic Sections by Eccentricity
Quadratic Equations and Rotations
Conics and Parametric Equations; The Cycloid
Polar Coordinates
Graphing in Polar Coordinates
Area and Lengths in Polar Coordinates
Conic Sections in Polar Coordinates
Infinite Sequences and Series
Sequences Infinite Series
The Integral Test
Comparison Tests
The Ratio and Root Tests
Alternating Series, Absolute and Conditional Convergence
Power Series
Taylor and Maclaurin Series
Convergence of Taylor Series; Error Estimates
Applications of Power Series
Fourier Series
Appendices
Mathematical Induction
Proofs of Limit Theorems
Commonly Occurring Limits
Theory of the Real Numbers
Complex Numbers
The Distributive Law for Vector Cross Products
Determinants and Cramer's Rule
Table of Contents provided by Publisher. All Rights Reserved.


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