Overview

For 3-semester or 4-quarter courses covering single, variable and multivariable calculus University Calculus: Early Transcendentals helps students generalise and apply the key ideas of calculus through clear and precise explanations, thoughtfully chosen examples, meticulously crafted figures, and superior exercise sets. This text offers the right mix of basic, conceptual, and challenging exercises, along with meaningful applications. In the 4th Edition, new co-authors Chris Heil (Georgia Institute of Technology) and Przemyslaw Bogacki (Old Dominion University) partner with author Joel Hass to preserve the text's time-tested features while revisiting every word, figure, and MyLab question with today's students in mind.  

Full Product Details

Author:   Joel Hass ,  Christopher Heil ,  Maurice Weir ,  Przemyslaw Bogacki
Publisher:   Pearson Education (US)
Imprint:   Pearson
Edition:   4th edition
Dimensions:   Width: 22.70cm , Height: 5.40cm , Length: 28.30cm
Weight:   2.512kg
ISBN:  

9780134995540

ISBN 10:   0134995546
Pages:   1104
Publication Date:   01 January 2019
Audience:   College/higher education ,  Tertiary & Higher Education
Format:   Paperback
Publisher's Status:   Active
Availability:   Available To Order  
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Table of Contents

Functions 1.1 Functions and Their Graphs 1.2 Combining Functions; Shifting and Scaling Graphs 1.3 Trigonometric Functions 1.4 Graphing with Software 1.5 Exponential Functions 1.6 Inverse Functions and Logarithms Limits and Continuity 2.1 Rates of Change and Tangent Lines to Curves 2.2 Limit of a Function and Limit Laws 2.3 The Precise Definition of a Limit 2.4 One-Sided Limits 2.5 Continuity 2.6 Limits Involving Infinity; Asymptotes of Graphs Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Derivatives 3.1 Tangent Lines and the Derivative at a Point 3.2 The Derivative as a Function 3.3 Differentiation Rules 3.4 The Derivative as a Rate of Change 3.5 Derivatives of Trigonometric Functions 3.6 The Chain Rule 3.7 Implicit Differentiation 3.8 Derivatives of Inverse Functions and Logarithms 3.9 Inverse Trigonometric Functions 3.10 Related Rates 3.11 Linearization and Differentials Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Applications of Derivatives 4.1 Extreme Values of Functions on Closed Intervals 4.2 The Mean Value Theorem 4.3 Monotonic Functions and the First Derivative Test 4.4 Concavity and Curve Sketching 4.5 Indeterminate Forms and L’Hôpital’s Rule 4.6 Applied Optimization 4.7 Newton’s Method 4.8 Antiderivatives Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Integrals 5.1 Area and Estimating with Finite Sums 5.2 Sigma Notation and Limits of Finite Sums 5.3 The Definite Integral 5.4 The Fundamental Theorem of Calculus 5.5 Indefinite Integrals and the Substitution Method 5.6 Definite Integral Substitutions and the Area Between Curves Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Applications of Definite Integrals 6.1 Volumes Using Cross-Sections 6.2 Volumes Using Cylindrical Shells 6.3 Arc Length 6.4 Areas of Surfaces of Revolution 6.5 Work 6.6 Moments and Centers of Mass Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Integrals and Transcendental Functions 7.1 The Logarithm Defined as an Integral 7.2 Exponential Change and Separable Differential Equations 7.3 Hyperbolic Functions Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Techniques of Integration 8.1 Integration by Parts 8.2 Trigonometric Integrals 8.3 Trigonometric Substitutions 8.4 Integration of Rational Functions by Partial Fractions 8.5 Integral Tables and Computer Algebra Systems 8.6 Numerical Integration 8.7 Improper Integrals Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Infinite Sequences and Series 9.1 Sequences 9.2 Infinite Series 9.3 The Integral Test 9.4 Comparison Tests 9.5 Absolute Convergence; The Ratio and Root Tests 9.6 Alternating Series and Conditional Convergence 9.7 Power Series 9.8 Taylor and Maclaurin Series 9.9 Convergence of Taylor Series 9.10 Applications of Taylor Series Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Parametric Equations and Polar Coordinates 10.1 Parametrizations of Plane Curves 10.2 Calculus with Parametric Curves 10.3 Polar Coordinates 10.4 Graphing Polar Coordinate Equations 10.5 Areas and Lengths in Polar Coordinates Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Vectors and the Geometry of Space 11.1 Three-Dimensional Coordinate Systems 11.2 Vectors 11.3 The Dot Product 11.4 The Cross Product 11.5 Lines and Planes in Space 11.6 Cylinders and Quadric Surfaces Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Vector-Valued Functions and Motion in Space 12.1 Curves in Space and Their Tangents 12.2 Integrals of Vector Functions; Projectile Motion 12.3 Arc Length in Space 12.4 Curvature and Normal Vectors of a Curve 12.5 Tangential and Normal Components of Acceleration 12.6 Velocity and Acceleration in Polar Coordinates Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Partial Derivatives 13.1 Functions of Several Variables 13.2 Limits and Continuity in Higher Dimensions 13.3 Partial Derivatives 13.4 The Chain Rule 13.5 Directional Derivatives and Gradient Vectors 13.6 Tangent Planes and Differentials 13.7 Extreme Values and Saddle Points 13.8 Lagrange Multiplier Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Multiple Integrals 14.1 Double and Iterated Integrals over Rectangles 14.2 Double Integrals over General Regions 14.3 Area by Double Integration 14.4 Double Integrals in Polar Form 14.5 Triple Integrals in Rectangular Coordinates 14.6 Applications 14.7 Triple Integrals in Cylindrical and Spherical Coordinates 14.8 Substitutions in Multiple Integrals Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Integrals and Vector Fields 15.1 Line Integrals of Scalar Functions 15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux 15.3 Path Independence, Conservative Fields, and Potential Functions 15.4 Green’s Theorem in the Plane 15.5 Surfaces and Area 15.6 Surface Integrals 15.7 Stokes’ Theorem 15.8 The Divergence Theorem and a Unified Theory Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises First-Order Differential Equations (online at bit.ly/2pzYlEq) 16.1 Solutions, Slope Fields, and Euler’s Method 16.2 First-Order Linear Equations 16.3 Applications 16.4 Graphical Solutions of Autonomous Equations 16.5 Systems of Equations and Phase Planes Second-Order Differential Equations (online at bit.ly/2IHCJyE) 17.1 Second-Order Linear Equations 17.2 Non-homogeneous Linear Equations 17.3 Applications 17.4 Euler Equations 17.5 Power-Series Solutions Appendix A.1 Real Numbers and the Real Line A.2 Mathematical Induction A.3 Lines and Circles A.4 Conic Sections A.5 Proofs of Limit Theorems A.6 Commonly Occurring Limits A.7 Theory of the Real Numbers A.8 Complex Numbers A.9 The Distributive Law for Vector Cross Products A.10 The Mixed Derivative Theorem and the increment Theorem Additional Topics (online) B.1 Relative Rates of Growth B.2 Probability B.3 Conics in Polar Coordinates B.4 Taylor’s Formula for Two Variables B.5 Partial Derivatives with Constrained Variables Odd Answers

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Author Information

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.

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