Calculus: Early Transcendentals
Third Edition ©2015
"The clarity of examples, as well as their interconnectedness, remains a strong point. This fact alone goes a long way toward helping students better learn the concepts."
--Erik Tou, instructor, Carthage College
“It strikes the right balance between readability for the student and rigor for the instructor.”
--Debra Carney, instructor, Colorado School of Mines"It is refreshing to see that even in the chapter on limits, there are application problems from a variety of disciplines, including engineering, physics and biology. The applications feel realistic and relevant as opposed to constructed and stilted."
--Maria Siopsis, instructor, Maryville College"The strenghts are in the Conceptual and Graphical Insights. These are the kinds of comments that can make things 'click' and fall into place for the students."
--Berit Givens, instructor, California State Polytechnic University, Pomona"The notation is a strong point of this book. It is used consistently and the authors do not shy away from using math instead of excess prose. Those two features alone put these chapters well ahead of my present text.""It's an invitation to learn calculus the right way."
--Jonathan Pearsall, instructor, College of Southern Nevada
--Nadjib Bouzar, instructor, University of Indianapolis
Digital Options
Table of Contents
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 Review Exercises
2.1 Limits, Rates of Change, and Tangent Lines
2.2 Limits: A Numerical and Graphical Approach
2.3 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 Review Exercises
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 Implicit Differentiation
3.9 Derivatives of General Exponential and Logarithmic Functions
3.10 Related Rates
Chapter Review Exercises
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
Chapter Review Exercises
5.1 Approximating and Computing Area
5.2 The Definite Integral
5.3 The Indefinite Integral
5.4 The Fundamental Theorem of Calculus, Part I
5.5 The Fundamental Theorem of Calculus, Part II
5.6 Net Change as the Integral of a Rate
5.7 Substitution Method
5.8 Further Transcendental Functions
5.9 Exponential Growth and Decay
Chapter Review Exercises
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 Review Exercises
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 Strategies for Integration
7.7 Improper Integrals
7.8 Probability and Integration
7.9 Numerical Integration
Chapter Review Exercises
8.1 Arc Length and Surface Area
8.2 Fluid Pressure and Force
8.3 Center of Mass
8.4 Taylor Polynomials
Chapter Review Exercises
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 Review Exercises
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 Review Exercises
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 Review Exercises
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 Review Exercises
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 Review Exercises
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 Review Exercises
15.1 Integration in Two 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 Multiple Integrals
15.6 Change of Variables
Chapter Review Exercises
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 Review Exercises
17.1 Green’s Theorem
17.2 Stokes’ Theorem
17.3 Divergence Theorem
Chapter Review Exercises
A. The Language of Mathematics
B. Properties of Real Numbers
C. Induction and the Binomial Theorem
D. Additional Proofs
References
Index
Authors
Jon Rogawski
Jon Rogawski received his undergraduate and master’s degrees in mathematics simultaneously from Yale University, and he earned his PhD in mathematics from Princeton University, where he studied under Robert Langlands. Before joining the Department of Mathematics at UCLA in 1986, where he was a full professor, he held teaching and visiting positions at the Institute for Advanced Study, the University of Bonn, and the University of Paris at Jussieu and Orsay. Jon’s areas of interest were number theory, automorphic forms, and harmonic analysis on semisimple groups. He published numerous research articles in leading mathematics journals, including the research monograph Automorphic Representations of Unitary Groups in Three Variables (Princeton University Press). He was the recipient of a Sloan Fellowship and an editor of the Pacific Journal of Mathematics and the Transactions of the AMS. As a successful teacher for more than 30 years, Jon Rogawski listened and learned much from his own students. These valuable lessons made an impact on his thinking, his writing, and his shaping of a calculus text. Sadly, Jon Rogawski passed away in September 2011. Jon’s commitment to presenting the beauty of calculus and the important role it plays in students’ understanding of the wider world is the legacy that lives on in each new edition of Calculus.
Colin Adams
Colin Adams is the Thomas T. Read professor of Mathematics at Williams College, where he has taught since 1985. Colin received his undergraduate degree from MIT and his PhD from the University of Wisconsin. His research is in the area of knot theory and low-dimensional topology. He has held various grants to support his research, and written numerous research articles. Colin is the author or co-author of The Knot Book, How to Ace Calculus: The Streetwise Guide, How to Ace the Rest of Calculus: The Streetwise Guide, Riot at the Calc Exam and Other Mathematically Bent Stories, Why Knot?, Introduction to Topology: Pure and Applied, and Zombies & Calculus. He co-wrote and appears in the videos “The Great Pi vs. E Debate” and “Derivative vs. Integral: the Final Smackdown.” He is a recipient of the Haimo National Distinguished Teaching Award from the Mathematical Association of America (MAA) in 1998, an MAA Polya Lecturer for 1998-2000, a Sigma Xi Distinguished Lecturer for 2000-2002, and the recipient of the Robert Foster Cherry Teaching Award in 2003. Colin has two children and one slightly crazy dog, who is great at providing the entertainment.
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