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標題: 空間的尺度分析 (I)
Dimensional Analysis in Mathematics (I)
作者: 盧俊豪
Lu, Jun-Hao
關鍵字: Dimensional Analysis;尺度分析
出版社: 應用數學系所
引用: [1] Tom M. Apostol., Mathematical Analysis (2nd ed.), Addison-Wesley, 1974. [2] Richard L. Wheeden. and Antoni Zygmund., Measure and Integral: an introduction to Real Analysis, New York: Marcel Dekker, 1977. [3] H. L. Royden., Real Analysis (3rd ed.), New York: Macmillan, 1988. [4] Gerald B. Folland., Real Analysis: modern techniques and their applications, New York: Wiley, 1984. [5] Frank Jones., Lebesgue Integration on Eucliden spaces, Boston: Jones and Bartlett, 1993. [6] John B. Fraleigh., A first course in abstract algebra (4th ed.), Addison-Wesley, 1989. [7] P. W. Bridgman., Dimensional Analysis, New York: AMS Press, 1978. [8] Chi-Kun Lin., Applications of dimensional analysis to differential equations, inequalities and the related topics, Department of applied Mathematics National Chiao Tung University. [9] J. M. Marstrand., The dimension of Cartesian product sets, Proc. Cambridge Philos. Soc. 50, (1954). 198-202. [10] Donald L. Cohn., Measure theory, Boston: Birkhauser, 1980.
P. W. Bridgman 在其所著的Dimensional Analysis [7]書中提出以下物理觀點:
"物理上Dimensional Analysis 之目的在於能夠找出各種可測量物體或物理現象的相關

In this thesis, we introduce the dimensional analysis to mathematics from the concept in physics
which is “The purpose of dimensional analysis is to give certain information about the
relations which hold between the measurable quantities associated with various phenomena.”
(See P. W. Bridgman [7], p17.). Thus, the purpose of our study is to establish theoretic theory
of the dimensional analysis in mathematics.
其他識別: U0005-0106200910514900
Appears in Collections:應用數學系所

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