University Calculus: Early Transcendentals in SI Units

Series
Pearson
Author
Joel R. Hass / Maurice D. Weir / George B. Thomas  
Publisher
Pearson
Cover
Softcover
Edition
4
Language
English
Total pages
1104
Pub.-date
August 2019
ISBN13
9781292317304
ISBN
1292317302
Related Titles


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9781292317304
University Calculus: Early Transcendentals in SI Units
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Description

This title is a Pearson Global Edition. The Editorial team at Pearson has worked closely with educators around the world to include content which is especially relevant to students outside the United States.

 

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

 

Clear, precise, concise

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 SI 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 and figure with today’s students in mind. 

 

Pearson MyLab Math is not included. Students, if Pearson MyLab Math is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN. Pearson MyLab Math should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

 

Reach every student by pairing this text with Pearson MyLab Math

MyLab™ 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 personalizes the learning experience and improves results for each student.

 

Features

Teach calculus the way you want to teach it, and at a level that prepares students for their STEM majors

·    New co-author Chris Heil and co-author Joel Hass aim to develop students’ mathematical maturity and proficiency by going beyond memorization of formulas and routine procedures and showing how to generalize key concepts once they are introduced.

·    Key topics are presented both formally and informally. The distinction between the two is clearly stated as each is developed, including an explanation as to why a formal definition is needed. Ideas are introduced with examples and intuitive explanations that are then generalized so that students are not overwhelmed by abstraction.

·    Results are both carefully stated and proved throughout the book, and proofs are clearly explained and motivated. Students and instructors who proceed through the formal material will find it as carefully presented and explained as the informal development. If the instructor decides to downplay formality at any stage, it will not cause problems with later developments in the text. 

·    Expanded - PowerPoint® lecture slides now include examples as well as key theorems, definitions, and figures. The files are fully editable making them a robust and flexible teaching tool.

 

Assess student understanding of key concepts and skills through a wide range of time-tested exercises

·    Updated - Strong exercise sets feature a great breadth of problems — progressing from skills problems to applied and theoretical problems — to encourage students to think about and practice the concepts until they achieve mastery. In the 4th SI Edition, the authors added new exercises and exercise types throughout, many of which are geometric in nature.

·    Writing exercises throughout the text ask students to explore and explain a variety of calculus concepts and applications. 

·    Technology exercises (marked with a “T”) are included in each section, requiring students to use a graphing calculator or computer when solving. In addition, Computer Explorations give the option of assigning exercises that require a computer algebra system (CAS, such as Maple or Mathematica).

 

Support a complete understanding of calculus for students at varying levels

·    Each major topic is developed with both simple and more advanced examples to give the basic ideas and illustrate deeper concepts.

·    Updated - Figures are conceived and rendered to provide insight for students and support conceptual reasoning. In the 4th SI Edition, new figures are added to enhance understanding and graphics are revised throughout to emphasize clear visualization.

·    Enhanced - Annotations within examples (shown in blue type) guide students through the problem solution and emphasize that each step in a mathematical argument is rigorously justified. For the 4th SI Edition, many more annotations were added.

·    End-of-chapter materials include review questions, practice exercises covering the entire chapter, and a series of Additional and Advanced Exercises with more challenging or synthesizing problems. 

 

 

Pearson MyLab™ Math is not included. Students, if Pearson MyLab Math is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN. Pearson MyLab Math should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

 

Deliver trusted content

·    Updated - Assignable Exercises: New co-author Przemyslaw Bogacki analyzed aggregated student usage and performance data from MyLab™ Math for the previous edition of this text. The results of this analysis helped improve the quality and quantity of text and MyLab exercises and learning aids that matter the most to instructors and students.

·    Enhanced - Setup & Solve Exercises: These exercises require students to show how they set up a problem as well as the solution, better mirroring what is required on tests. This new exercise type was widely praised by users of the 3rd edition, so more were added to the 4th edition. Each Setup & Solve Exercise is also now available as a regular question where just the final answer is scored. 

·    New - Additional Conceptual Questions focus on deeper, theoretical understanding of the key concepts in calculus. These questions were written by faculty at Cornell University under an NSF grant and are also assignable through Learning Catalytics™.

·    New - A full suite of Interactive Figures has been added to support teaching and learning. The figures are designed to be used in lecture as well as by students independently. The figures are editable using the freely available GeoGebra software. Videos that use the Interactive Figures to explain key concepts are also included. The figures were created by Marc Renault (Shippensburg University), Steve Phelps (University of Cincinnati), Kevin Hopkins (Southwest Baptist University), and Tim Brzezinski (Berlin High School, CT).

·    Updated - Instructional videos: Numerous instructional videos augment the already robust collection within the course. These videos support the overall approach of the text by going beyond routine procedures to show students how to generalize and connect key concepts. The Guide to Video-Based Assignments makes it easy to assign videos for homework by showing which Pearson MyLab Math exercises correspond to each video.

 

Teach your course your way

·    Learning Catalytics: Now included in all Pearson MyLab Math courses, this student response tool uses students’ smartphones, tablets, or laptops to engage them in more interactive tasks and thinking during lecture. Learning Catalytics fosters student engagement and peer-to-peer learning with real-time analytics. Access pre-built exercises created specifically for calculus, including the additional conceptual questions.

 

Empower each learner

·    New - Enhanced Sample Assignments: These section-level assignments include just-in-time prerequisite review, help keep skills fresh with spaced practice of key concepts, and provide opportunities to work exercises without learning aids so students check their understanding.

New to this Edition

·    New co-author Chris Heil and co-author Joel Hass aim to develop students’ mathematical maturity and proficiency by going beyond memorization of formulas and routine procedures and showing how to generalize key concepts once they are introduced.

·    PowerPoint® lecture slides now include examples as well as key theorems, definitions, and figures. The files are fully editable making them a robust and flexible teaching tool.

·    Strong exercise sets feature a great breadth of problems — progressing from skills problems to applied and theoretical problems — to encourage students to think about and practice the concepts until they achieve mastery. In the 4th SI Edition, the authors added new exercises and exercise types throughout, many of which are geometric in nature.

·    Figures are conceived and rendered to provide insight for students and support conceptual reasoning. In the 4th SI Edition, new figures are added to enhance understanding and graphics are revised throughout to emphasize clear visualization.

·    Annotations within examples (shown in blue type) guide students through the problem solution and emphasize that each step in a mathematical argument is rigorously justified. For the 4th SI Edition, many more annotations were added.

 

 

Pearson MyLab™ Math is not included. Students, if Pearson MyLab Math is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN. Pearson MyLab Math should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

·    Assignable Exercises: New co-author Przemyslaw Bogacki analyzed aggregated student usage and performance data from MyLab™ Math for the previous edition of this text. The results of this analysis helped improve the quality and quantity of text and MyLab exercises and learning aids that matter the most to instructors and students.

·    Setup & Solve Exercises: These exercises require students to show how they set up a problem as well as the solution, better mirroring what is required on tests. This new exercise type was widely praised by users of the 3rd edition, so more were added to the 4th edition. Each Setup & Solve Exercise is also now available as a regular question where just the final answer is scored. 

·    Additional Conceptual Questions focus on deeper, theoretical understanding of the key concepts in calculus. These questions were written by faculty at Cornell University under an NSF grant and are also assignable through Learning Catalytics™.

·    A full suite of Interactive Figures has been added to support teaching and learning. The figures are designed to be used in lecture as well as by students independently. The figures are editable using the freely available GeoGebra software. Videos that use the Interactive Figures to explain key concepts are also included. The figures were created by Marc Renault (Shippensburg University), Steve Phelps (University of Cincinnati), Kevin Hopkins (Southwest Baptist University), and Tim Brzezinski (Berlin High School, CT).

·    Instructional videos: Numerous instructional videos augment the already robust collection within the course. These videos support the overall approach of the text by going beyond routine procedures to show students how to generalize and connect key concepts. The Guide to Video-Based Assignments makes it easy to assign videos for homework by showing which Pearson MyLab Math exercises correspond to each video.

Enhanced Sample Assignments: These section-level assignments include just-in-time prerequisite review, help keep skills fresh with spaced practice of key concepts, and provide opportunities to work exercises without learning aids so students check their understanding.

Table 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 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)

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)

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

 

Odd Answers