University Calculus Early Transcendentals

For 3-semester or 4-quarter¿ courses covering single¿ variable and multivariable calculus, taken by students of mathematics, engineering, natural sciences, or economics.

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University Calculus: Early Transcendentals 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. 

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• 0135183715 / 9780135183717  MyLab Math with Pearson eText - Standalone Access Card - for University Calculus: Early Transcendentals

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 six widely used calculus texts as well as two 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, three-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 eight 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, to appear in 2019. 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. 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 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

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    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

16.     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 

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 AP-6

A.3 Lines and Circles AP-10

A.4 Conic Sections AP-16

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 at bit.ly/2IDDl8w )

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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