Student Solutions Manual for University Calculus

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Student Solutions Manual for University Calculus

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Description

  • 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 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 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 Edition, many more annotations were added.

Check out the preface for a complete list of features and what’s new in this edition.

Also available with MyLab Math 

  • 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. There are approximately 8550 assignable exercises in MyLab Math, 490 of which are new to this edition.
  • 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: Over 200 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 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.

This manual provides detailed solutions to odd-numbered exercises in the text.

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.

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 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 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 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.

Check out the preface for a complete list of features and what’s new in this edition.

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.

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. There are approximately 8550 assignable exercises in MyLab Math, 490 of which are new to this edition.
  • 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: Over 200 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 MyLab Math exercises correspond to each video.

Teach your course your way

  • Learning Catalytics: Now included in all 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

  • Integrated Review: This MyLab course features pre-made, assignable (and editable) quizzes to assess the prerequisite skills needed for each chapter, plus personalized remediation for any gaps in skills that are identified. Each student, therefore, receives just the help that he or she needs–no more, no less.
  • 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.

This manual provides detailed solutions to odd-numbered exercises in the text.

 
0135166136 / 9780135166130 STUDENT SOLUTIONS MANUAL SINGLE VARIABLE FOR UNIVERSITY CALCULUS: EARLY TRANSCENDENTALS, 4/e
  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
  • 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

Additional information

Dimensions 0.90 × 8.60 × 10.80 in
Imprint

Format

ISBN-13

ISBN-10

Author

, , ,

Subjects

mathematics, calculus, higher education, Calculus, Applied & Advanced Math