Calculus

1. Front Matter

   Pages i-xi

   PDF

2. Functions and Graphs

   • Harley Flanders

   Pages 1-37

3. Limits

   • Harley Flanders

   Pages 38-60

4. The Derivative

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   Pages 61-93

5. Applications of Derivatives

   • Harley Flanders

   Pages 94-141

6. Integration

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   Pages 142-180

7. Applications of Integration

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   Pages 181-207

8. Functions and Integrals

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   Pages 208-246

9. Approximation

   • Harley Flanders

   Pages 247-299

10. Power Series

    • Harley Flanders

    Pages 300-319

11. Back Matter

    Pages 320-332

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Preface Objectives of This Book • To teach calculus as a laboratory science, with the computer and software as the lab, and to use this lab as an essential tool in learning and using calculus. • To present calculus and elementary differential equations with a minimum of fuss-through practice, not theory. • To stress ideas of calculus, applications, and problem solving, rather than definitions, theorems, and proofs. • Toemphasize numerical aspects: approximations, order of magnitude, concrete answers to problems. • To organize the topics consistent with the needs of students in their concurrent science and engineering courses. The subject matter of calculus courses has developed over many years, much by negotiation with the disciplines calculus serves, particularly engineering. This text covers the standard topics in their conventional order. Mostly because of commercial pressures, calculus texts have grown larger and larger, trying to include everything that anyone conceivably would cover. Calculus texts have also added more and more expensive pizzazz, up to four colors now. This text is lean; it eliminates most of the "fat" of recent calculus texts; it has a simple physical black/white format; it ignores much of current calculus "culture". The computer has forced basic changes in emphasis and how to teach calculus.

• calculus
• derivative
• integral
• integration

• University of Michigan, Ann Arbor, USA

  Harley Flanders

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