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Calculus and Its Applications, 9/E
Marvin L. Bittinger, Indiana University Purdue University Indianapolis
David J. Ellenbogen, Community College of Vermont

ISBN-10: 0321395344
ISBN-13: 9780321395344

Publisher: Addison-Wesley
Copyright: 2008
Format: Cloth; 704 pp
Published: 02/15/2007

Suggested retail price: $128.00
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Calculus and Its Applications has, for years, been a best-selling text for one simple reason: it anticipates, then meets the needs of today's applied calculus student. Knowing that calculus is a course in which students typically struggle--both with algebra skills and visualizing new calculus concepts--Bittinger and Ellenbogen speak to students in a way they understand, taking great pains to provide clear and careful explanations. Since most students taking this course will go on to careers in the business world, large quantities of real data, especially as they apply to business, are included as well.

  • The text incorporates a careful, gradual introduction to differentiation, with relative and absolute maxima and minima covered in separate sections. Students will benefit by gradually building up these topics, as they consider graphing using calculus concepts.
  • Each chapter begins with a brief introduction to the material as well as an opening application to draw students into the concepts covered in the chapter.
  • At the beginning of each section, objectives are stated in the margin, providing a road map of each section for students and instructors.
  • The art program has been designed with a pedagogical, consistent use of color to make difficult concepts easier for students to understand and visualize. 
  • Throughout the text, Technology Connections give students advice on how to use their calculators and computers effectively in this course.
  • Extended Technology Applications at the end of each chapter use real applications and real data, and require a step-by-step analysis that lends itself well to group work.
  • The end-of-section exercises are designed to review conceptual understanding and basic skills through a variety of exercise types including traditional exercises, applications, synthesis problems, thinking/writing exercises, and technology connection exercises.
  • Applications are grouped by discipline within the exercise sets, using such headings as Life/Physical Science, Social Science, and General Interest, to show students the relevance of calculus to other disciplines.
  • The end-of-chapter material includes: Chapter Summary, Review Exercises including Chapter Comprehension, Review, Applications, Synthesis Exercises, and Thinking/Writing Exercises, a Chapter Test and an Extended Technology Application.

  • As a reminder that functions, graphs, and models should be review topics for most students taking this course, Chapter 1 has been renamed Chapter R. Highlighting the usefulness of this chapter, references throughout the book show students where to look to refresh and review their algebra skills.
  • Limits and Continuity: Numerically and Graphically, Section 2.1 in the prior edition, has been split into two sections in this edition, in order to more thoroughly develop the concept of limits before introducing continuity.  It also allows for a more intuitive development of limits in Section 1.1: Limits: A Numerical and Graphical Approach, saving the algebraic approach for Section 1.2: Algebraic Limits and Continuity, at which time it is used in the discussion of continuity. In addition, more exercises have been added on graphical limits to this new Section 1.1, especially appealing to more visually oriented students. 
  • In Chapter 2, the material in Section 2.6 has been rewritten (and retitled) so that marginal cost, revenue, and profit are the first concepts covered.  These topics are developed in a more business-centered and intuitive manner.  The material on differentials now comes last, and should be easier to cover since students will see it as a purely mathematical example of the business application that precedes it.
  • The material on instantaneous rates of change, previously covered in 2.6, has been moved up in the chapter, now in Section 1.4: Differentiation Using Limits of Difference Quotients. By doing so, the concept of instantaneous rate of change is located in the section that immediately follows the discussion of average rates of change.  The concept of instantaneous rate of change is reviewed a second time, later in the chapter, when velocity and acceleration are covered as part of the section on higher-order derivatives.
  • In Chapter 4, the first three sections have been completely revamped.  To better emphasize the link between area under a curve, Riemann sums, and antiderivatives, Chapter 4 now opens with a section entitled The Area Under a Graph (in which Riemann sums are introduced). Section 4.2: Area, Antiderivatives, and Integrals follows, in which the link between antiderivatives and the area under a curve is first developed, and then in Section 4.3: Area and Definite Integrals, the Fundamental Theorem of Calculus is explained and applications in business and science are developed.  Students and faculty will find this organization very intuitive and smooth- flowing.  Material on average value (formerly found in old section 5.3) now appears with other properties of the integral in Section 4.4. 
  • In this new edition, partial derivatives of all kinds are now covered in one section, 6.2: Partial Differentials in order to make this material easier to cover in one class period.
  • Extensive updates to the real data appear in examples and exercises throughout the book, with a special emphasis on applications from business, health, and science.
  • 20% of the exercises are new or revised, and exercise sets have been edited based on reviewer recommendations.
  • Every chapter now ends with a Chapter Summary in which highlights from each chapter along with appropriate examples and page references are listed in a format that is condensed, yet readable.  The Chapter Review Exercises that follow now begin with Chapter Comprehension Exercises to build student confidence and include matching, true/false, or fill-in-the-blank.  As an aid for instructors assigning exercises from the Chapter Review Exercises, each exercise is accompanied by a bracketed section reference that indicates the section in which that type of problem appears. 

    • R.        Functions, Graphs, and Models.

    R.1       Graphs and Equations.

    R.2       Functions and Models.

    R.3       Finding Domain and Range.

    R.4       Slope and Linear Functions.

    R.5       Nonlinear Functions and Models.

    R.6       Mathematical Modeling and Curve Fitting.

    Extended Technology Application: Payrolls of Professional Basketball Teams


    1.         Differentiation.

    1.1       Limits: A Numerical and Graphical Approach

    1.2       Algebraic Limits and Continuity

    1.3       Average Rates of Change

    1.4       Differentiation Using Limits of Difference Quotients.

    1.5       Differentiation Techniques: The Power and Sum-Difference Rules.

    1.6       Differentiation Techniques: The Product and Quotient Rules

    1.7       The Chain Rule

    1.8       Higher-Order Derivatives.

    Extended Technology Application: Path of a Baseball: The Tale of the Tape.


    2.         Applications of Differentiation.

    2.1       Using First Derivatives to Find Maximum and Minimum Values and Sketch Graphs.

    2.2       Using Second Derivatives to Find Maximum and Minimum Values and Sketch Graphs.

    2.3       Graph Sketching: Asymptotes and Rational Functions.

    2.4       Using Derivatives to Find Absolute Maximum and Minimum Values.

    2.5       Maximum-Minimum Problems: Business and Economics Applications.

    2.6       Marginals and Differentials.

    2.7       Implicit Differentiation and Related Rates.

    Extended Technology Application:  Maximum Sustainable Harvest


    3.         Exponential and Logarithmic Functions.

    3.1       Exponential Functions.

    3.2       Logarithmic Functions.

    3.3       Applications: The Uninhibited Growth Model, dP/dt = kP.

    3.4       Applications: Decay.

    3.5       The Derivatives of a x and logax.

    3.6       An Economics Application: Elasticity of Demand.

    Extended Technology Application: The Business of Motion Picture Box-Office Revenue.


    4.         Integration.

    4.1       The Area Under a Graph

    4.2       Area, Antiderivatives, and Integrals.

    4.3       Area and Definite Integrals.

    4.4       Properties of Definite Integrals.

    4.5       Integration Techniques: Substitution.

    4.6       Integration Techniques: Integration by Parts.

    4.7       Integration Techniques: Tables.

    Extended Technology Application: Financial Predictions for Starbucks, Lowes, The Gap, and Intel

    5.         Applications of Integration.

    5.1       An Economics Application: Consumer Surplus and Producer Surplus.

    5.2       Applications of the Models

    5.3       Improper Integrals.

    5.4       Probability.

    5.5       Probability: Expected Value; The Normal Distribution.

    5.6       Volume.

    5.7       Differential Equations.

    Extended Technology Application: Curve Fitting and the Volume of a Bottle of Soda.


    6.         Functions of Several Variables.

    6.1       Functions of Several Variables.

    6.2       Partial Derivatives.

    6.3       Maximum-Minimum Problems.

    6.4       An Application: The Least-Squares Technique.

    6.5       Constrained Maximum and Minimum Values: Lagrange Multipliers.

    6.6       Double Integrals

    Extended Technology Application: Minimizing Employees' Travel Time in a Building.


    Cumulative Review.
    Appendix A: Review of Basic Algebra.
    Tables.

    Integration Formulas.

    Areas for a Standard Normal Distribution.

     

      The Eighth Edition of Calculus and Its Applications builds on its reputation as one of the most student-oriented and clearly written Applied Calculus texts available. The exercises have been substantially updated to include additional relevant and current topics.

    • 0321166396Calculus and Its Applications, 8/E
      Bittinger
      © 2004 | Addison-Wesley | Cloth; 648 pages | Instock
      ISBN-10: 0321166396 | ISBN-13: 9780321166395
      Brief Description

    Marvin Bittinger For over thirty-eight years, Professor Marvin L. Bittinger has been teaching math at the university level. Since 1968, he has been employed  at Indiana University - Purdue University Indianapolis, and is now professor emeritus of mathematics education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. His hobbies include hiking in Utah, baseball, golf, and bowling. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters.

     

    David Ellenbogen    David Ellenbogen has taught math at the college level for twenty-two years, spending most of that time in the Massachusetts and Vermont community college systems, where he has served on both curriculum and developmental math committees.  He has also taught at St. Michael's College and The University of Vermont. Professor Ellenbogen has been active in the Mathematical Association of Two Year Colleges since 1985, having served on its Developmental Mathematics Committee and as a delegate, and has been a member of the Mathematical Association of America since 1979.  He has authored dozens of publications on topics ranging from prealgebra to calculus and has delivered lectures at numerous conferences on the use of language in mathematics.  Professor Ellenbogen received his BA in mathematics from Bates College and his MA in community college mathematics education from The University of Massachusetts at Amherst. A co-founder of the Colchester Vermont Recycling Program, Professor Ellenbogen has a deep love for the environment and the outdoors, especially in his home state of Vermont.  In his spare time, he enjoys playing keyboard in the band Soularium, volunteering as a community mentor, hiking, biking, and skiing.  He has two sons, Monroe and Zack.

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