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What's the ideal balance? How can you make sure students get both the computational skills they need and a deep understanding of the significance of what they are learning? With your teachingsupported by Rogawski's Calculus Second Editionthe most successful new calculus text in 25 years! Widely adopted in its first edition, Rogawski's Calculusworked for instructors and students by balancing formal precision with a guiding conceptual focus. Rogawski engages students while reinforcing the relevance of calculus to their lives and future studies. Precise mathematics, vivid examples, colorful graphics, intuitive explanations, and extraordinary problem sets all work together to help students… More grasp a deeper understanding of calculus. Now Rogawski's Calculussuccess continues in a meticulously updated new edition. Revised in response to user feedback and classroom experiences, the new edition provides an even smoother teaching and learning experience.Less

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Book details

List price: $207.99 Edition: 2nd Copyright year: 2012 Publisher: W. H. Freeman & Company Publication date: 3/30/2011 Binding: Hardcover Pages: 1208 Size: 8.75" wide x 10.25" long x 1.50" tall Weight: 5.390 Language: English

AuthorTable of Contents

Precalculus Review

Real Numbers, Functions, and Graphs

Linear and Quadratic Functions

The Basic Classes of Functions

Trigonometric Functions

Inverse Functions

Exponential and Logarithmic Functions

Technology Calculators and Computers

Limits

Limits, Rates of Change, and Tangent Lines

Limits: A Numerical and Graphical Approach2.3 Basic Limit Laws

Limits and Continuity

Evaluating Limits Algebraically

Trigonometric Limits

Limits at Infinity

Intermediate Value Theorem

The Formal Definition of a Limit

Differentiation

Definition of the Derivative

The Derivative as a Function

Product and Quotient Rules

Rates of Change

Higher Derivatives

Trigonometric Functions

The Chain Rule

Derivatives of Inverse Functions

Derivatives of General Exponential and Logarithmic Functions

Implicit Differentiation

Related Rates

Applications of the Derivative

Linear Approximation and Applications

Extreme Values

The Mean Value Theorem and Monotonicity

The Shape of a Graph

L'Hopital's Rule

Graph Sketching and Asymptotes

Applied Optimization

Newton's Method

Antiderivatives

The Integral

Approximating and Computing Area

The Definite Integral

The Fundamental Theorem of Calculus, Part I

The Fundamental Theorem of Calculus, Part II

Net Change as the Integral of a Rate

Substitution Method

Further Transcendental Functions

Exponential Growth and Decay

Applications of the Integral

Area Between Two Curves

Setting Up Integrals: Volume, Density, Average Value

Volumes of Revolution

The Method of Cylindrical Shells

Work and Energy

Techniques of Integration

Integration by Parts

Trigonometric Integrals

Trigonometric Substitution

Integrals Involving Hyperbolic and Inverse Hyperbolic Functions

The Method of Partial Fractions

Improper Integrals

Probability and Integration

Numerical Integration

Further Applications of the Integral and Taylor Polynomials

Arc Length and Surface Area

Fluid Pressure and Force

Center of Mass

Taylor Polynomials

Introduction to Differential Equations

Solving Differential Equations

Models Involving y' = k (y-b)

Graphical and Numerical Methods

The Logistic Equation

First-Order Linear Equations

Infinite Series

Sequences

Summing an Infinite Series

Convergence of Series with Positive Terms

Absolute and Conditional Convergence

The Ratio and Root Tests

Power Series

Taylor Series

Parametric Equations, Polar Coordinates, and Conic Sections

Parametric Equations

Arc Length and Speed

Polar Coordinates

Area and Arc Length in Polar Coordinates

Conic Sections

Vector Geometry

Vectors in the Plane

Vectors in Three Dimensions

Dot Product and the Angle Between Two Vectors

The Cross Product

Planes in Three-Space

A Survey of Quadric Surfaces

Cylindrical and Spherical Coordinates

Calculus of Vector-Valued Functions

Vector-Valued Functions

Calculus of Vector-Valued Functions

Arc Length and Speed

Curvature

Motion in Three-Space

Planetary Motion According to Kepler and Newton

Differentiation in Several Variables

Functions of Two or More Variables

Limits and Continuity in Several Variables

Partial Derivatives

Differentiability and Tangent Planes

The Gradient and Directional Derivatives

The Chain Rule

Optimization in Several Variables

Lagrange Multipliers: Optimizing with a Constraint

Multiple Integration

Integration in Variables

Double Integrals over More General Regions

Triple Integrals

Integration in Polar, Cylindrical, and Spherical Coordinates

Applications of Multiplying Integrals

Change of Variables

Line and Surface Integrals

Vector Fields

Line Integrals

Conservative Vector Fields

Parametrized Surfaces and Surface Integrals

Surface Integrals of Vector Fields

Fundamental Theorems of Vector Analysis

Green's Theorem

Stokes' Theorem

Divergence Theorem

Appendices

The Language of Mathematics

Properties of Real Numbers

Mathematical Induction and the Binomial Theorem

Additional Proofs of Theorems

Taylor Polynomials

Answers to Odd-Numbered Exercises

References

Photo Credits

Index

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