Inside Calculus

1. Front Matter

   Pages i-xvii

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2. Limits

   Pages 1-18

3. Continuity

   Pages 19-30

4. The Language of Theorems

   Pages 31-38

5. Theorems about Continuous functions

   Pages 39-54

6. Limit Proofs

   Pages 55-69

7. Limit Theorems

   Pages 71-96

8. Which Functions are Continuous?

   Pages 97-116

9. Derivatives

   Pages 117-134

10. Theorems about the Derivative

    Pages 135-149

11. Other Limits

    Pages 151-180

12. Back Matter

    Pages 181-211

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The approach taken by this book is based on two beliefs. The first is that almost nobody understands calculus fully the first time around: multiple exposures are required. The second belief is that graphing calculators can be used to make the introduction of the theory of limits much easier for the students. This book presents the theoretical pieces of introductory calculus, using appropriate technology, in a style suitable to accompany almost any first calculus text. It offers a large range of increasingly sophisticated examples and problems to build understanding of the notion of limit and other theoretical concepts. It is aimed at students who will study fields in which the understanding of calculus as a tool is not sufficient. The text uses the "spiral approach" of teaching, returning again and again to difficult topics, anticipating such returns across the calculus courses in preparation for the first analysis course. The book may be used as the "content" text for a transition to upper level mathematics course.

• Calc
• boundary element method
• calculus
• derivative
• function
• functions
• language
• mathematics
• proof
• technology
• theorem
• time
• tool

• Department of Mathematics, Bucknell University, Lewisburg, USA

  George R. Exner

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