請參閱論文PDF檔.

Please read the PDF file of my thesis.

Contents

1 Introduction 1
1.1 The mean value theorems ....................................1
1.2 Relationships among the mean value theorems ................4

2 Estimation of integral mean points and differential mean points 7
2.1 Integral mean points .......................................7
2.2 Differential mean points ...................................13

3 Converses of mean value theorems 18

Bibliography

[1] R.G. Bartle and D.R. Sherbert, An Introduction to Real Analysis, second
edition, Wiley, New York (1992).

[2] J.M. Borwein and Xianfu Wang, The converse of the mean value theorem may fail generically, Amer. Math. Monthly 105 (1998), 847-848.

[3] H.E. Campbell and P.F. Dierker, Calculus, second edition, Prindle, Weber
Schmidt (1978).

[4] B. Jacobson, On the mean value theorem for integrals, Amer. Math. Monthly
89 (1982), 300-301.

[5] W.J. Schwind, J. Ji, and D.E. Koditschek, A physically motivated further
note on the mean value theorem for integrals, Amer. Math. Monthly 106
(1999), 559-564.

[6] J. Tong and P.A. Braza, A converse of the mean value theorem, Amer. Math.
Monthly 104 (1997), 939-942.

[7] B. Zhang, A note on the mean value theorem for integrals, Amer. Math.
Monthly 104 (1997), 561-562.