University Calculus: Early Transcendentals, Single Variable

For 2-semester or 3-quarter courses in single-variable calculus for math, science, and engineering majors.

Clear, precise, concise
University Calculus: Early Transcendentals, Single Variable helps students generalize 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. 

Also available with MyLab Math 
MyLab Math is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. Learn more about MyLab Math.

List of contents

1. 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
2. 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
3. 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
4. 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 LHôpitals Rule
   • 4.6 Applied Optimization
   • 4.7 Newtons Method
   • 4.8 Antiderivatives
   • Questions to Guide Your Review
   • Practice Exercises
   • Additional and Advanced Exercises
5. 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
6. 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
7. 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
8. 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
9. 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
10. 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
11. 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
12. 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
13. 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
14. 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
15. 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 Greens 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
16. First-Order Differential Equations (online at bit.ly/2pzYlEq)
    • 16.1 Solutions, Slope Fields, and Eulers 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
17. 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 Taylors Formula for Two Variables
• B.5 Partial Derivatives with Constrained Variables

Odd Answers

About the author

About our authors

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 ofGeometriae 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. In his free time, Hass enjoys kayaking.
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. In his spare time, Heil pursues his hobby of astronomy.
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.

Summary

For 2-semester or 3-quarter courses in single-variable calculus for math, science, and engineering majors.

Clear, precise, concise

University Calculus: Early Transcendentals, Single Variable helps students generalize 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. 

Also available with MyLab Math 

By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. 

Note: You are purchasing a standalone product; MyLab Math does not come packaged with this content. Students, if interested in purchasing this title with MyLab Math, ask your instructor to confirm the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information.

If you would like to purchase both the physical text and MyLab Math, search for:

0135308046 / 9780135308042 University Calculus, Single Variable plus MyLab Math with Pearson eText - Access Card Package

Package consists of:

• 0135164842 / 9780135164846 University Calculus: Early Transcendentals, Single Variable
• 0135183715 / 9780135183717 MyLab Math with Pearson eText - Standalone Access Card - for University Calculus: Early Transcendentals

Product details

• Authors: Przemyslaw Bogacki, Joel Hass, Joel R. Hass, Christopher Heil, Christopher E. Heil, George Thomas, George B. Thomas, Maurice Weir, Maurice D. Weir
• Publisher: Pearson Academic
• Languages: English
• Product format: Paperback / Softback
• Released: 28.09.2024
• EAN: 9780135164846
• ISBN: 978-0-13-516484-6
• No. of pages: 752
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Analysis