Computer-Supported Calculus

1. Front Matter

   Pages i-xi

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2. Functions, limits, and continuity

   1. Front Matter

      Pages 1-1

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   2. Functions

      • Adi Ben-Israel, Robert Gilbert

      Pages 2-42

   3. Elementary functions used in calculus

      • Adi Ben-Israel, Robert Gilbert

      Pages 43-62

   4. Limits and continuity

      • Adi Ben-Israel, Robert Gilbert

      Pages 63-103

3. Derivatives

   1. Front Matter

      Pages 105-105

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   2. Differentiation

      • Adi Ben-Israel, Robert Gilbert

      Pages 106-147

   3. Differentiation rules

      • Adi Ben-Israel, Robert Gilbert

      Pages 148-178

   4. Extremum problems

      • Adi Ben-Israel, Robert Gilbert

      Pages 179-223

   5. Mean value theorem

      • Adi Ben-Israel, Robert Gilbert

      Pages 224-278

4. Integrals

   1. Front Matter

      Pages 279-279

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   2. Definite integrals

      • Adi Ben-Israel, Robert Gilbert

      Pages 280-321

   3. Fundamental theorem of calculus

      • Adi Ben-Israel, Robert Gilbert

      Pages 322-343

   4. Integration techniques

      • Adi Ben-Israel, Robert Gilbert

      Pages 344-383

   5. Applications of integrals

      • Adi Ben-Israel, Robert Gilbert

      Pages 384-425

5. Series and approximations

   1. Front Matter

      Pages 427-427

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   2. Sequences and series

      • Adi Ben-Israel, Robert Gilbert

      Pages 428-459

   3. Series expansions and approximations

      • Adi Ben-Israel, Robert Gilbert

      Pages 460-499

6. Back Matter

   Pages 501-612

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This is a new type of calculus book: Students who master this text will be well versed in calculus and, in addition, possess a useful working knowledge of one of the most important mathematical software systems, namely, MACSYMA. This will equip them with the mathematical competence they need for science and engi­ neering and the competitive workplace. The choice of MACSYMA is not essential for the didactic goal of the book. In fact, any of the other major mathematical software systems, e. g. , AXIOM, MATHEMATICA, MAPLE, DERIVE, or REDUCE, could have been taken for the examples and for acquiring the skill in using these systems for doing mathematics on computers. The symbolic and numerical calcu­ lations described in this book will be easily performed in any of these systems by slight modification of the syntax as soon as the student understands and masters the MACSYMA examples in this book. What is important, however, is that the student gets all the information necessary to design and execute the calculations in at least one concrete implementation language as this is done in this book and also that the use of the mathematical software system is completely integrated with the text. In these times of globalization, firms which are unable to hire adequately trained technology experts will not prosper. For corporations which depend heavily on sci­ ence and engineering, remaining competitive in the global economy will require hiring employees having had a traditionally rigorous mathematical education.

• Fundamental theorem of calculus
• Integralrechnung
• Macsyma
• Maple
• Mathematica
• algorithm
• algorithms
• approximation
• calculus
• derivative
• differential equation
• geometry
• linear optimization
• mathematics
• mean value theorem

• Rutgers Center for Operations Research and Department of Mathematics, Rutgers University, New Brunswick, USA

  Adi Ben-Israel

• Department of Mathematical Science and Computer and Informational Sciences, University of Delaware, Newark, USA

  Robert Gilbert

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