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Calculus: Early Transcendentals / Edition 2

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Overview

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 teaching—supported by Rogawski’s Calculus Second Edition—the most successful new calculus text in 25 years!
 
Widely adopted in its first edition, Rogawski’s Calculus worked 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 grasp a deeper understanding of calculus.
 
Now Rogawski’s Calculus success 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.

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Product Details

  • ISBN-13: 9781429208383
  • Publisher: Freeman, W. H. & Company
  • Publication date: 3/30/2011
  • Edition description: Second Edition
  • Edition number: 2
  • Pages: 1050
  • Sales rank: 58,285
  • Product dimensions: 8.90 (w) x 10.10 (h) x 1.80 (d)

Meet the Author

About Jon Rogawski
Jon Rogawski received his undergraduate degree (and simultaneously a master's degree in mathematics) at Yale, and a Ph.D. in mathematics from Princeton University, where he studied under Robert Langlands. Prior to joining the Department of Mathematics at UCLA, where he is currently Full Professor, he held teaching positions at Yale and the University of Chicago, and research positions at the Institute for Advanced Study and University of Bonn.

Jon's areas of interest are number theory, automorphic forms, and harmonic analysis on semisimple groups. He has published numerous research articles in leading mathematical journals, including a research monograph entitled "Automorphic Representations of Unitary Groups in Three Variables" (Princeton University Press). He is the recipient of a Sloan Fellowship and an editor of The Pacific Journal of Mathematics.

Jon and his wife Julie, a physician in family practice, have four children. They run a busy household and, whenever possible, enjoy family vacations in the mountains of California. Jon is a passionate classical music lover and plays the violin and classical guitar.

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Table of Contents

Chapter 1:  Precalculus Review
1.1 Real Numbers, Functions, and Graphs
1.2 Linear and Quadratic Functions
1.3 The Basic Classes of Functions
1.4 Trigonometric Functions
1.5 Inverse Functions
1.6 Exponential and Logarithmic Functions
1.7 Technology Calculators and Computers

Chapter 2:  Limits2.1 Limits, Rates of Change, and Tangent Lines
2.2 Limits:  A Numerical and Graphical Approach2.3 Basic Limit Laws
2.4 Limits and Continuity
2.5 Evaluating Limits Algebraically
2.6 Trigonometric Limits
2.7 Limits at Infinity
2.8 Intermediate Value Theorem
2.9 The Formal Definition of a Limit

Chapter 3:  Differentiation
3.1 Definition of the Derivative
3.2 The Derivative as a Function
3.3 Product and Quotient Rules
3.4 Rates of Change
3.5 Higher Derivatives
3.6 Trigonometric Functions
3.7 The Chain Rule
3.8 Derivatives of Inverse Functions
3.9 Derivatives of General Exponential and Logarithmic Functions
3.10 Implicit Differentiation
3.11 Related Rates

Chapter 4: Applications of the Derivative
4.1 Linear Approximation and Applications
4.2 Extreme Values
4.3 The Mean Value Theorem and Monotonicity
4.4 The Shape of a Graph
4.5 L’Hopital’s Rule
4.6 Graph Sketching and Asymptotes
4.7 Applied Optimization
4.8 Newton’s Method
4.9 Antiderivatives

Chapter 5:  The Integral
5.1 Approximating and Computing Area
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus, Part I
5.4 The Fundamental Theorem of Calculus, Part II
5.5 Net Change as the Integral of a Rate
5.6 Substitution Method
5.7 Further Transcendental Functions
5.8 Exponential Growth and Decay

Chapter 6:  Applications of the Integral
6.1 Area Between Two Curves
6.2 Setting Up Integrals:  Volume, Density, Average Value
6.3 Volumes of Revolution
6.4 The Method of Cylindrical Shells
6.5  Work and Energy

Chapter 7:  Techniques of Integration
7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution
7.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions
7.5 The Method of Partial Fractions
7.6 Improper Integrals
7.7 Probability and Integration
7.8 Numerical Integration

Chapter 8:  Further Applications of the Integral and Taylor Polynomials
8.1 Arc Length and Surface Area
8.2 Fluid Pressure and Force
8.3 Center of Mass
8.4 Taylor Polynomials

Chapter 9:  Introduction to Differential Equations
9.1 Solving Differential Equations
9.2 Models Involving y’ = k (y-b)
9.3 Graphical and Numerical Methods
9.4 The Logistic Equation
9.5 First-Order Linear Equations

Chapter 10:  Infinite Series
10.1 Sequences
10.2 Summing an Infinite Series
10.3 Convergence of Series with Positive Terms
10.4 Absolute and Conditional Convergence
10.5 The Ratio and Root Tests
10.6 Power Series
10.7 Taylor Series

Chapter 11:  Parametric Equations, Polar Coordinates, and Conic Sections
11.1 Parametric Equations
11.2 Arc Length and Speed
11.3 Polar Coordinates
11.4 Area and Arc Length in Polar Coordinates
11.5 Conic Sections

Chapter 12:  Vector Geometry
12.1 Vectors in the Plane
12.2 Vectors in Three Dimensions
12.3 Dot Product and the Angle Between Two Vectors
12.4 The Cross Product
12.5 Planes in Three-Space
12.6 A Survey of Quadric Surfaces
12.7 Cylindrical and Spherical Coordinates

Chapter 13:  Calculus of Vector-Valued Functions
13.1 Vector-Valued Functions
13.2 Calculus of Vector-Valued Functions
13.3 Arc Length and Speed
13.4 Curvature
13.5 Motion in Three-Space
13.6 Planetary Motion According to Kepler and Newton

Chapter 14:  Differentiation in Several Variables
14.1 Functions of Two or More Variables
14.2 Limits and Continuity in Several Variables
14.3 Partial Derivatives
14.4 Differentiability and Tangent Planes
14.5 The Gradient and Directional Derivatives
14.6 The Chain Rule
14.7 Optimization in Several Variables
14.8 Lagrange Multipliers:  Optimizing with a Constraint

Chapter 15: Multiple Integration
15.1 Integration in Variables
15.2 Double Integrals over More General Regions
15.3 Triple Integrals
15.4 Integration in Polar, Cylindrical, and Spherical Coordinates
15.5 Applications of Multiplying Integrals
15.6 Change of Variables

Chapter 16: Line and Surface Integrals
16.1 Vector Fields
16.2 Line Integrals
16.3 Conservative Vector Fields
16.4 Parametrized Surfaces and Surface Integrals
16.5 Surface Integrals of Vector Fields

Chapter 17: Fundamental Theorems of Vector Analysis
17.1 Green’s Theorem
17.2 Stokes’ Theorem
17.3 Divergence Theorem

Appendices
A. The Language of Mathematics
B. Properties of Real Numbers
C. Mathematical Induction and the Binomial Theorem
D. Additional Proofs of Theorems
E. Taylor Polynomials

Answers to Odd-Numbered Exercises
References
Photo Credits
Index

For a complete table of contents and additional information, visit: www.whfreeman.com/rogawski2epreview

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