Roger B. Nelsen (Lewis and Portland Clark College)

Cameos for Calculus

Visualization in the First-Year Course

• Gebundenes Buch

Produktbeschreibung

Designed to aid teachers and students, Nelsen guides his readers through fifty short visual enhancements to the first-year calculus course.

Produktdetails

• Classroom Resource Materials
• Verlag: Mathematical Association of America
• Seitenzahl: 180
• Erscheinungstermin: 30. Dezember 2015
• Englisch
• Abmessung: 261mm x 177mm x 17mm
• Gewicht: 494g
• ISBN-13: 9780883857885
• ISBN-10: 088385788X
• Artikelnr.: 44827322

Autorenporträt

Roger B. Nelsen, Professor Emeritus of Mathematics, Lewis & Clark College, USA.

Inhaltsangabe

Preface
Part 1. Limits and Differentiation
1. The limit of (sin t)/t
2. Approximating π with the limit of (sin t)/t
3. Visualizing the derivative
4. The product rule
5. The quotient rule
6. The chain rule
7. The derivative of the sine
8. The derivative of the arctangent
9. The derivative of the arcsine
10. Means and the mean value theorem
11. Tangent line inequalities
12. A geometric illustration of the limit for e
13. Which is larger, π or πe? ab or ba?
14. Derivatives of area and volume
15. Means and optimization
Part 2. Integration
16. Combinatorial identities for Riemann sums
17. Summation by parts
18. Integration by parts
19. The world's sneakiest substitution
20. Symmetry and integration
21. Napier's inequality and the limit for e
22. The nth root of n! and another limit for e
23. Does shell volume equal disk volume?
24. Solids of revolution and the Cauchy-Schwarz inequality
25. The midpoint rule is better than the trapezoidal rule
26. Can the midpoint rule be improved?
27. Why is Simpson's rule exact for cubics?
28. Approximating π with integration
29. The Hermite-Hadamard inequality
30. Polar area and Cartesian area
31. Polar area as a source of antiderivatives
32. The prismoidal formula
Part 3. Infinite Series
33. The geometry of geometric series
34. Geometric differentiation of geometric series
35. Illustrating a telescoping series
36. Illustrating applications of the monotone sequence theorem
37. The harmonic series and the Euler-Mascheroni constant
38. The alternating harmonic series
39. The alternating series test
40. Approximating π with Maclaurin series
Part 4. Additional Topics
41. The hyperbolic functions I: Definitions
42. The hyperbolic functions II: Are they circular?
43. The conic sections
44. The conic sections revisited
45. The AM-GM inequality for n positive numbers
Part 5. Appendix: Some Precalculus Topics
46. Are all parabolas similar?
47. Basic trigonometric identities
48. The additional formulas for the sine and cosine
49. The double angle formulas
50. Completing the square
Solutions to the Exercises
References
Index
About the Author