Dedication

pp vii-viii

Preface

pp ix-x

Contents

pp xi-xiv

I - Limits and Differentiation

pp 1-2

1 - The limit of (sin t)/t

pp 3-4

2 - Approximating π with the limit of (sin t)/t

pp 5-6

3 - Visualizing the derivative

pp 7-8

4 - The product rule

pp 9-10

5 - The quotient rule

pp 11-12

6 - The chain rule

pp 13-14

7 - The derivative of the sine

pp 15-16

8 - The derivative of the arctangent

pp 17-18

9 - The derivative of the arcsine

pp 19-20

10 - Means and the mean value theorem

pp 21-22

11 - Tangent line inequalities

pp 23-26

12 - A geometric illustration of the limit for e

pp 27-28

13 - Which is larger, eπ or πe? ab or ba?

pp 29-30

14 - Derivatives of area and volume

pp 31-32

15 - Means and optimization

pp 33-38

II - Integration

pp 39-40

16 - Combinatorial identities for Riemann sums

pp 41-46

17 - Summation by parts

pp 47-50

18 - Integration by parts

pp 51-52

19 - The world's sneakiest substitution

pp 53-56

20 - Symmetry and integration

pp 57-60

21 - Napier's inequality and the limit for e

pp 61-64

22 - The nth root of n! and another limit for e

pp 65-66

23 - Does shell volume equal disk volume?

pp 67-70

24 - Solids of revolution and the Cauchy-Schwarz inequality

pp 71-74