University Calculus: Early Transcendentals, Global Edition

Joel Hass received his PhD from the University of California - Berkeley. He is currently a professor of mathematics at the University of California - Davis. He has coauthored 6 widely used calculus texts as well as 2 calculus study guides. He is currently on the editorial board of Geometriae Dedicata and Media-Enhanced Mathematics. He has been a member of the Institute for Advanced Study at Princeton University and of the Mathematical Sciences Research Institute, and he was a Sloan Research Fellow. Hass's current areas of research include the geometry of proteins, 3-dimensional manifolds, applied math and computational complexity. Christopher Heil received his PhD from the University of Maryland. He is currently a professor of mathematics at the Georgia Institute of Technology. He is the author of a graduate text on analysis and a number of highly cited research survey articles. He serves on the editorial boards of Applied and Computational Harmonic Analysis and The Journal of Fourier Analysis and Its Applications. Heil's current areas of research include redundant representations, operator theory and applied harmonic analysis.Maurice D. Weir holds a DA and MS from Carnegie-Mellon University and received his BS at Whitman College. He is a Professor Emeritus of the Department of Applied Mathematics at the Naval Postgraduate School in Monterey, California. Weir enjoys teaching Mathematical Modeling and Differential Equations. His current areas of research include modeling and simulation as well as mathematics education. Weir has been awarded the Outstanding Civilian Service Medal, the Superior Civilian Service Award, and the Schieffelin Award for Excellence in Teaching. He has coauthored 8 books, including the University Calculus series and Thomas' Calculus.Przemyslaw Bogacki is an Associate Professor of Mathematics and Statistics and a University Professor at Old Dominion University. He received his PhD in 1990 from Southern Methodist University. He is the author of a text on linear algebra. He is actively involved in applications of technology in collegiate mathematics. His areas of research include computer aided geometric design and numerical solution of initial value problems for ordinary differential equations.

• 1. Functions1.1    Functions and Their Graphs1.2    Combining Functions; Shifting and Scaling Graphs1.3    Trigonometric Functions1.4    Graphing with Software1.5    Exponential Functions1.6    Inverse Functions and Logarithms  2.    Limits and Continuity 2.1    Rates of Change and Tangent Lines to Curves2.2    Limit of a Function and Limit Laws2.3    The Precise Definition of a Limit2.4    One-Sided Limits2.5    Continuity2.6    Limits Involving Infinity; Asymptotes of GraphsQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced Exercises  3.    Derivatives3.1    Tangent Lines and the Derivative at a Point3.2    The Derivative as a Function3.3    Differentiation Rules3.4    The Derivative as a Rate of Change3.5    Derivatives of Trigonometric Functions3.6    The Chain Rule3.7    Implicit Differentiation3.8    Derivatives of Inverse Functions and Logarithms3.9    Inverse Trigonometric Functions3.10 Related Rates3.11 Linearization and DifferentialsQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced Exercises  4.    Applications of Derivatives4.1    Extreme Values of Functions on Closed Intervals4.2    The Mean Value Theorem4.3    Monotonic Functions and the First Derivative Test4.4    Concavity and Curve Sketching4.5    Indeterminate Forms and L’Hôpital’s Rule4.6    Applied Optimization4.7    Newton’s Method4.8    AntiderivativesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced Exercises  5.    Integrals5.1    Area and Estimating with Finite Sums5.2    Sigma Notation and Limits of Finite Sums5.3    The Definite Integral5.4    The Fundamental Theorem of Calculus5.5    Indefinite Integrals and the Substitution Method5.6   Definite Integral Substitutions and the Area Between CurvesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced Exercises  6.    Applications of Definite Integrals6.1    Volumes Using Cross-Sections6.2    Volumes Using Cylindrical Shells6.3    Arc Length6.4    Areas of Surfaces of Revolution6.5    Work6.6    Moments and Centers of MassQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced Exercises  7.    Integrals and Transcendental Functions7.1    The Logarithm Defined as an Integral7.2    Exponential Change and Separable Differential Equations7.3    Hyperbolic FunctionsQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced Exercises  8.    Techniques of Integration  8.1    Integration by Parts8.2    Trigonometric Integrals8.3    Trigonometric Substitutions8.4    Integration of Rational Functions by Partial Fractions