Higher Education

Calculus, 1st Edition

  • Soo T. Tan Stonehill College
  • ISBN-10: 053446579X  |  ISBN-13: 9780534465797
  • 1456 Pages
  • © 2010 | Published
  • College Bookstore Wholesale Price = $161.50
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About

Overview

Known for accuracy, precision, and rigor, Soo Tan now brings those same qualities to the Calculus course. With his clear, concise writing style, and use of relevant, real world examples, Tan introduces abstract mathematical concepts with his intuitive approach that captures student interest without compromising mathematical rigor. In keeping with this emphasis on conceptual understanding, each exercise set begins with concept questions and each end-of-chapter review section includes fill-in-the-blank questions which help students master the definitions and theorems in each chapter. Additionally, many questions asking for the interpretation of graphical, numerical, and algebraic results are included among both the examples and the exercise sets.

Features and Benefits

  • Real-life, Relevant Applications: Soo Tan's intuitive approach to calculus links the abstract ideas of calculus with concrete, real-life examples. One such example—the maglev (magnetic levitation) train is used as a common thread from limits through integration, to show students the connection between all of these concepts.
  • Intuitive Presentation Style: By introducing the limit concept in the context of finding the rate of change of the maglev, Tan captures student interest from the very beginning – this approach demonstrates the relevance of calculus in the real world. Elsewhere in the text, this intuitive approach is again used to advantage to introduce and explain some of the fundamental theorems in calculus, such as the Intermediate Value Theorem and the Mean Value Theorem.
  • Guidance When Students Need It: Comments appear next to many of the steps and aid in student understanding. Notes found at the end of many examples further explain and clarify the example, and point out subtleties within them. Cautions advise students on how to avoid common mistakes and misunderstandings, addressing both student misconceptions and situations that often lead students down unproductive paths.
  • Emphasis on Concepts in the Exercise Sets: End of section Concept Questions are designed to test students' understanding and encourage students to explain these concepts in their own words. Beginning each end of chapter review, Concept Review Questions give students a chance to check their knowledge of the basic definitions and concepts.
  • Emphasis on Problem-Solving: Problem-Solving Techniques, at the end of selected chapters, teach students the tools they need to make seemingly complex problems easier to solve.

Table of Contents

0. PRELIMINARIES.
Lines. Functions and Their Graphs. The Trigonometric Functions. Combining Functions. Graphing Calculators and Computers. Mathematical Models. Chapter Review.
1. LIMITS.
An Intuitive Introduction to Limits. Techniques for Finding Limits. A Precise Definition of a Limit. Continuous Functions. Tangent Lines and Rates of Change. Chapter Review. Problem-Solving Techniques. Challenge Problems.
2. THE DERIVATIVE.
The Derivative. Basic Rules of Differentiation. The Product and Quotient Rules. The Role of the Derivative in the Real World. Derivatives of Trigonometric Functions. The Chain Rule. Implicit Differentiation. Related Rates. Differentials and Linear Approximations. Chapter Review. Problem-Solving Techniques. Challenge Problems.
3. APPLICATIONS OF THE DERIVATIVE.
Extrema of Functions. The Mean Value Theorem. Increasing and Decreasing Functions and the First. Derivative Test. Concavity and Inflection Points. Limits Involving Infinity; Asymptotes. Curve Sketching. Optimization Problems. Newton''s Method. Chapter Review. Problem-Solving Techniques. Challenge Problems.
4. INTEGRATION.
Indefinite Integrals. Integration by Substitution. Area. The Definite Integral. The Fundamental Theorem of Calculus. Numerical Integration. Chapter Review. Problem-Solving Techniques. Challenge Problems.
5. APPLICATIONS OF THE DEFINITE INTEGRAL.
Areas Between Curves. Volumes: Disks, Washers, and Cross Sections. Volumes Using Cylindrical Shells. Arc Length and Areas of Surfaces of Revolution. Work. Fluid Pressure and Force. Moments and Centers of Mass. Chapter Review. Problem-Solving Techniques. Challenge Problems.
6. THE TRANSCENDENTAL FUNCTIONS.
The Natural Logarithmic Function. Inverse Functions. Exponential Functions. General Exponential and Logarithmic Functions. Inverse Trigonometric Functions. Hyperbolic Functions. Indeterminate Forms and L''Hôpital''s Rule. Chapter Review. Challenge Problems.
7. TECHNIQUES OF INTEGRATION.
Integration by Parts. Trigonometric Integrals. Trigonometric Substitutions. The Method of Partial Fractions. Integration Using Tables of Integrals and CAS. Improper Integrals. Chapter Review. Problem-Solving Techniques. Challenge Problems.
8. DIFFERENTIAL EQUATIONS.
Differential Equations: Separable Equations. Direction Fields and Euler''s Method. The Logistic Equation. First-Order Linear Differential Equations. Chapter Review. Challenge Problems.
9. INFINITE SEQUENCES AND SERIES.
Sequences. Series. The Integral Test. The Comparison Tests. Alternating Series. Absolute Convergence; The Ratio and Root Tests. Power Series. Taylor and Maclaurin Series. Approximation by Taylor Polynomials. Chapter Review. Problem-Solving Techniques. Challenge Problems.
10. CONIC SECTIONS, PARAMETRIC EQUATIONS, AND POLAR COORDINATES.
Conic Sections. Plane Curves and Parametric Equations. The Calculus of Parametric Equations. Polar Coordinates. Areas and Arc Lengths in Polar Coordinates. Conic Sections in Polar Coordinates. Chapter Review. Challenge Problems.
11. VECTORS AND THE GEOMETRY OF SPACE.
Vectors in the Plane. Coordinate Systems and Vectors in Three-Space. The Dot Product. The Cross Product. Lines and Planes in Space. Surfaces in Space. Cylindrical and Spherical Coordinates. Chapter Review. Challenge Problems.
12. VECTOR-VALUED FUNCTIONS.
Vector-Valued Functions and Space Curves. Differentiation and Integration of Vector- Valued. Functions. Arc Length and Curvature. Velocity and Acceleration. Tangential and Normal Components of Acceleration. Chapter Review. Challenge Problems.
13. FUNCTIONS OF SEVERAL VARIABLES.
Functions of Two or More Variables. Limits and Continuity. Partial Derivatives. Differentials. The Chain Rule. Directional Derivatives and Gradient Vectors. Tangent Planes and Normal Lines. Extrema of Functions of Two Variables. Lagrange Multipliers. Chapter Review. Challenge Problems.
14. MULTIPLE INTEGRAL.S
Double Integrals. Iterated Integrals. Double Integrals in Polar Coordinates. Applications of Double Integrals. Surface Area. Triple Integrals. Triple Integrals in Cylindrical and Spherical Coordinates. Change of Variables in Multiple Integrals. Chapter Review. Challenge Problems.
15. VECTOR ANALYSIS.
Vector Fields. Divergence and Curl. Line Integrals. Independence of Path and Conservative Vector Fields. Green''s Theorem. Parametric Surfaces. Surface Integrals. The Divergence Theorem. Stoke''s Theorem. Chapter Review. Challenge Problems.
APPENDICES.
A. The Real Number Line, Inequalities, and Absolute Value. B. Proofs of Selected Theorems.

Alternate Formats

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  • Single Variable Calculus

    ISBN-10: 0534465668  | ISBN-13: 9780534465667

    List Price = $202.95  | College Bookstore Wholesale Price = $152.25

  • Multivariable Calculus

    ISBN-10:  0534465757 | ISBN-13:  9780534465759

    List Price = $179.95  | College Bookstore Wholesale Price = $135.50

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Bundle: Text + Maple Student Version 13.0

ISBN-10: 0495969001  | ISBN-13: 9780495969006

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Bundle: Text + Enhanced WebAssign with eBook Printed Access Card for Multi Term Math and Science

ISBN-10:  0538797185  | ISBN-13:  9780538797184

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Bundle: Text + Maple 12.0 for Calculus

ISBN-10:  0538774886  | ISBN-13:  9780538774888

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Bundle: Text + Student Solutions Manual (SV) + Student Solutions Manual (MV)

ISBN-10:  0538774908  | ISBN-13:  9780538774901

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Bundle: Text + Maple Student Version 14.0

ISBN-10:  1111498962  | ISBN-13:  9781111498962

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Supplements

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Instructor Supplements

Complete Solutions Manual  (ISBN-10: 0534465781 | ISBN-13: 9780534465780)

This manual includes worked-out solutions to every exercise in Multivariable Calculus (Chapters 10-15 of Calculus and Chapters 9-14 of Calculus: Early Transcendentals).

CalcLabs with Mathematica, SV Calc.  (ISBN-10: 0495560634 | ISBN-13: 9780495560630)

This comprehensive lab manual helps students learn to effectively use the technology tools that are available to them. Each lab contains clearly explained exercises and a variety of lab projects to accompany the text.

List Price = $126.95  | College Bookstore Wholesale Price = $95.75

Student Solutions Manual (Chapters 10-15)  (ISBN-10: 0534465773 | ISBN-13: 9780534465773)

This manual includes worked-out solutions to every odd-numbered exercise in Multivariable Calculus (Chapters 10-15 of Calculus and Chapters 9-14 of Calculus: Early Transcendentals).

List Price = $61.95  | CengageBrain Price = $61.95  | College Bookstore Wholesale Price = $46.75

CalcLabs with Maple for Multivariable Calculus  (ISBN-10: 0495560588 | ISBN-13: 9780495560586)

List Price = $74.95  | College Bookstore Wholesale Price = $56.50

Enhanced WebAssign Instant Access for Calculus, Multi-Term Courses  (ISBN-10: 1285858255 | ISBN-13: 9781285858258)

IMPORTANT: When purchasing this instant access code for Calculus, ensure that you are using it in a Calculus course. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If your students need to retake the course and you are using the same book AND edition then they will not need to buy a new code. This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your Cengage Learning Consultant.

List Price = $125.00  | CengageBrain Price = $125.00  | College Bookstore Wholesale Price = $125.00

CalcLabs with Maple for Single Variable Calculus  (ISBN-10: 0495560626 | ISBN-13: 9780495560623)

Maple is a powerful software tool for mathematical computations and visualization. The goal of this manual is to introduce Maple to students who are taking first year calculus. As such, Maple is a tool to solve problems that are too difficult to solve by hand. In addition, students will improve their understanding of the concepts of calculus. The order of the material is organized by computational topic and should be suitable for most texts on Single Variable calculus.

List Price = $122.95  | CengageBrain Price = $122.95  | College Bookstore Wholesale Price = $92.50

Enhanced WebAssign Printed Access Card for Calculus, Multi-Term Courses, Life of Edition  (ISBN-10: 1285858263 | ISBN-13: 9781285858265)

IMPORTANT: When purchasing this printed access card for Calculus, ensure that you are using it in a Calculus course. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If your students need to retake the course and you are using the same book AND edition then they will not need to buy a new code. If you are not certain this is the correct access code for your course, please contact your Cengage Learning Consultant.

List Price = $125.00  | College Bookstore Wholesale Price = $93.75

Student Supplements

CalcLabs with Mathematica, SV Calc.  (ISBN-10: 0495560634 | ISBN-13: 9780495560630)

This comprehensive lab manual helps students learn to effectively use the technology tools that are available to them. Each lab contains clearly explained exercises and a variety of lab projects to accompany the text.

List Price = $126.95  | College Bookstore Wholesale Price = $95.75

Student Solutions Manual (Chapters 10-15)  (ISBN-10: 0534465773 | ISBN-13: 9780534465773)

Prepare for exams and succeed in your mathematics course with this comprehensive solutions manual! Featuring worked out-solutions to the problems in MULTIVARIABLE CALCULUS, 1st Edition, this manual shows you how to approach and solve problems using the same step-by-step explanations found in your textbook examples.

List Price = $61.95  | CengageBrain Price = $61.95  | College Bookstore Wholesale Price = $46.75

CalcLabs with Maple for Multivariable Calculus  (ISBN-10: 0495560588 | ISBN-13: 9780495560586)

List Price = $74.95  | College Bookstore Wholesale Price = $56.50

Enhanced WebAssign Instant Access for Calculus, Multi-Term Courses  (ISBN-10: 1285858255 | ISBN-13: 9781285858258)

IMPORTANT: When purchasing this instant access code for Calculus, ensure that you are using it in a Calculus course. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If you need to retake the course and your instructor is using the same book AND edition then you will not need to buy a new code. This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your instructor.

List Price = $125.00  | CengageBrain Price = $125.00  | College Bookstore Wholesale Price = $125.00

CalcLabs with Maple for Single Variable Calculus  (ISBN-10: 0495560626 | ISBN-13: 9780495560623)

Maple is a powerful software tool for mathematical computations and visualization. The goal of this manual is to introduce Maple to students who are taking first year calculus. As such, Maple is a tool to solve problems that are too difficult to solve by hand. In addition, students will improve their understanding of the concepts of calculus. The order of the material is organized by computational topic and should be suitable for most texts on Single Variable calculus.

List Price = $122.95  | CengageBrain Price = $122.95  | College Bookstore Wholesale Price = $92.50

Bundle: Text + Enhanced WebAssign with eBook Printed Access Card for Multi Term Math and Science  (ISBN-10: 0538797185 | ISBN-13: 9780538797184)

Taking a fresh approach while retaining classic presentation, the Tan Calculus series utilizes a clear, concise writing style, and uses relevant, real world examples to introduce abstract mathematical concepts with an intuitive approach. In keeping with this emphasis on conceptual understanding, each exercise set in the three semester Calculus text begins with concept questions and each end-of-chapter review section includes fill-in-the-blank questions which are useful for mastering the definitions and theorems in each chapter. Additionally, many questions asking for the interpretation of graphical, numerical, and algebraic results are included among both the examples and the exercise sets. The Tan Calculus three semester text encourages a real world, application based, intuitive understanding of Calculus without comprising the mathematical rigor that is necessary in a Calculus text.

List Price = $240.95  | CengageBrain Price = $240.95  | College Bookstore Wholesale Price = $181.50

Enhanced WebAssign Printed Access Card for Calculus, Multi-Term Courses, Life of Edition  (ISBN-10: 1285858263 | ISBN-13: 9781285858265)

IMPORTANT: When purchasing this printed access card for Calculus, ensure that you are using it in a Calculus course. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If you need to retake the course and your instructor is using the same book AND edition then you will not need to buy a new code. If you are not certain this is the correct access code for your course, please contact your instructor.

List Price = $125.00  | College Bookstore Wholesale Price = $93.75

Meet the Author

Author Bio

Soo T. Tan

Soo T. Tan has published numerous papers in Optimal Control Theory and Numerical Analysis. He received his S.B. degree from Massachusetts Institute of Technology, his M.S. degree from the University of Wisconsin-Madison, and his Ph.D. from the University of California at Los Angeles. "One of the most important lessons I learned from my early experience teaching these courses is that many of the students come into these courses with some degree of apprehension. This awareness led to the intuitive approach I have adopted in all of my texts."

Author Q&A

Q: What is the benefit of using an intuitive approach in teaching calculus?
A: One of my goals in writing this text is to provide students with a book that motivates their interest and at the same time is easy for them to read. In my teaching experience, students coming to calculus for the first time respond best to an intuitive approach. Wherever appropriate, I try to use this approach by introducing abstract ideas with concrete, real-life examples that students can relate to. Often a simple real life illustration can serve as motivation for a more complex mathematical concept or theorem. For example, in Chapter 5, the area under a curve is precipitated by an example of two cars traveling along a highway. This type of illustration helps the student visualize the calculus, but at the same time does not compromise the mathematical rigor expected of an engineering calculus text.

Q: You use a unique approach to introduce the concept of limits. Why?
A: Many calculus textbooks introduce this concept via the slope of a tangent line to a curve, and then follow by relating the slope to the notion of the rate of change of one quantity with respect to another. In my text, I do precisely the opposite. I introduce the limit concept by looking at the rate of change of the maglev (magnetic levitation train). This approach is more intuitive and captures the interest of the student from the very beginning—it shows immediately the relevance of calculus to the real world. I might add that this approach has worked very well for me in the classroom.

Q: What techniques do you employ to help students grasp concepts and connect ideas across chapters?
A: In the previous question, I described my unique approach to introducing limits. My intent is to lead the student to the concept by exploring a real-world situation, and then applying it to the concept. I found it helpful to use a single application (the maglev train) to illustrate a number of connected and critical concepts. This visual approach (using the maglev as a vehicle) is carried into the introduction and explanation of some of the fundamental theorems in calculus, such as the intermediate value theorem and the mean value theorem. Consistently woven throughout, this idea permeates much of the text—from concepts in limits, to continuity, to integration, and even to inverse functions, showing students the connection between the important theorems and concepts presented.

Q: How does your text help students relate calculus to their lives?
A: Helping students make the connection between the mathematics of calculus and their lives has been a key goal for me in writing this book. I learned from my students that they have a much greater appreciation of the material if the applications are drawn from their fields of interest and from situations that occur in the real world. This is one reason why you will see so many examples and exercises in my texts that are drawn from various and diverse fields such as physics, chemistry, engineering, biology, business, and economics. There are also many exercises of general and current interest that are modeled from data gathered from newspapers, magazines, journals, and other media. Whether it be global warming, brain growth and IQs, projected U.S. gasoline usage, or finding the surface area of the Jacqueline Kennedy Onassis reservoir, I weave topics of current interest into my examples and exercises to keep the book relevant to all of my readers.

Q: How does technology help students in the course?
A: Practicing problems is always important in learning the mathematical concepts. Technology—in this case, Enhanced WebAssign®—smooths the pathway to success by incorporating interactive features that provide extra support as students practice solving problems online. This homework management system also provides instructors with the convenience of automatic grading. We have incorporated video tutorials into Enhanced WebAssign, giving students some extra help on how to attack a particular type of problem. One unique addition to my text is that we provide additional video lessons for the multivariable sections of the text that help students learn, step-by-step, how to draw the complex sketches required in multivariable calculus. Videos of these lessons will be available at the text’s companion website.

Q: In calculus, problem sets are vital to successful instruction and learning. What distinguishes your problem sets apart from those in other calculus texts?
A: As a mathematician and a professor, I understand the importance of good problem sets. To me, a “good” problem set has many characteristics. For instance, end-of-section or chapter problems should represent a variety of problem types, including conceptual questions, well-researched applications, problem-solving exercises, and graphing exercises. Additionally, it is just as important to provide problem sets that a professor can work out on the blackboard in class. I worked very hard to find interesting, engaging problems that will accurately reflect a calculus concept, and you will find many exercises of general and current interest that are modeled from data gathered from newspapers, magazines, journals, and other media. For example, global warming, projections for US gasoline usage, and the relationship between brain growth and IQ’s, which are topics that interest everyone. Also, I wrote the Solutions Manual to ensure consistency between the problems in the text and the worked out solutions.

Q: How have you ensured that your text is precise and accurate? Why did you choose to author the Solutions Manual yourself?
A: I try to introduce each abstract mathematical concept through an example drawn from a common, real-life experience. Once the idea has been conveyed, I then proceed to make it precise, thereby assuring that no mathematical rigor is lost in this intuitive treatment of the subject. As is the case with all of my projects, accuracy is of paramount importance. For this reason, I solved every problem myself and wrote the solutions for the Solutions Manual. Working with other instructors from around the country, we utilized a process that involved accuracy checking at each stage of production, a total of seven times!

Q: What special features result from your experience as both a textbook author and an instructor?
A: Over the years, I have gathered important feedback from professors that has served me well in developing and writing this book. I understand the importance of providing precise descriptions and explanations, the need for a variety of problems that test and reinforce conceptual knowledge, and the balance required to ensure mathematical rigor expected of a serious engineering calculus text. As a mathematician, I also understand the critical importance of being able to draw complex figures for multivariable calculus. To that end, I have worked to develop special video lessons to help students learn how to draw precise sketches required in the course.