Calculus, Second Edition

Deborah Hughes-Hallett, Harvard University

Andrew M. Gleason, Harvard University

ISBN: 0-471-16443-7, 704 Pages, Cloth, 1998
ISBN: 0-471-16442-9, 704 Pages, Paper, 1998

• New thread of honors sections, called Focus on Theory, that build upon the student's geometric intuition. These sections present case studies in the formulation of axioms, definitions, and proof, including the completeness axiom, the definition of limit, the Extreme Value Theorem, and the Mean Value Theorem.
• New section on limits and continuity in Chapter 1.
• New section on limits, l'Hopital's Rule, and relative growth rates in Chapter 4.
• New section on hyperbolic functions in Chapter 5.
• New appendix on parameterized curves.
• Reorganization of some material: properties of the definite integral have been moved to Chapter 3, refocussing Chapter 6 on reconstructing functions from their derivatives.
• Chapter 9 (formerly Chapter 10) on Approximations and Series has been expanded to include more discussion of series of constants. New section on ratio test and the interval of convergence of a power series, including a discussion of the harmonic series and alternating series. Differential equations is now Chapter 10.
• Inclusion of more easy and medium level problems in each section of the text, and a battery of practice problems at the end of Chapter 4 (differentiation) and Chapter 7 (integration).
• Answers are included in the back of the book to those odd numbered problems that have them.
• Each chapter includes a summary of the main points.
• Selected projects are included in the text as well as more in the Instructors' Manual.

• A problem driven text in which the student starts with a practical problem and derives general results from it.
• The topical coverage was determined after discussion with mathematicians and client disciplines to focus on students'calculus needs. Emphasis is on depth of understanding and not breadth of coverage.
• Equal weight is given to describing functions graphically, numerically, symbollically, and verbally in order to provide alternate avenues through which students can understand the material.
• Many of the real world problems are open-ended, meaning that there may be more than one approach and more than one solution, depending on the student's analysis. Solving a problem usually relies on the use of common sense and critical thinking skills. Students are encouraged to develop estimating and approximating skills.
• The book contains the main ideas of calculus in plain English to improve the students' understanding and to encourage them to read it.
• Worked out examples are not entirely like the problem sets in the text. The result is that students cannot simply mimic techniques from the examples, without actually learning the concepts.
• Technology is used as a tool to help students visualize the concepts. It is recommended that a graphing calculator, graphing software, or computer algebra system be used with this book but the emphasis is on the calculus concepts and not the technology.

Solutions Manual: 0-471-23910-0. Contains complete solutions to all problems. Instructors'Manual: 0-47123909-7. Includes teaching tips by section, test questions by section, calculator programs, additional projects by section, and overhead transparency masters. Student Solutions Manual: 0-471-24260-8. Contains complete solutions to all odd-numbered problems. Instructors' Resource CD: 0-471-24292-6. Contains all print supplements on CD-ROM. On-Line Testing: Pending. Web based on-line tutorial testing system for algebraic skill building in integration and differentiation available on CD to be used on schools' Intranet. Hughes-Hallett Interactive: Pending. Highly interactive full-text version of Hughes-Hallett driven by a Mathematica engine on CD-ROM. Provides a user-friendly front end that requires no knowledge of Mathematica syntax for imputing functions.

Table of Contents: 1. A Library of Functions 2. Key Concept: The Derivative 3. Key Concept: The Definite Integral 4. Short-Cuts to Differentiation 5. Using the Derivative 6. Constructing Antiderivatives 7. Integration 8. Using the Definite Integral 9. Approximations and Series 10. Differential Equations Appendices A. Roots and Accuracy B. Notes on Compound Interest C. Polar Coordinates D. Complex Numbers E. Newton's Method F. Parametric Curves