a - Ch.1 PHYS 2041 Problems in Quantitative Methods for...

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Ch.1 PHYS 2041 Problems in Quantitative Methods for Basic Physics (1 st Term 10/11) 1 Chapter 1 Elementary Functions and Complex Numbers 1.1 Exponential and Logarithmic Functions The exponential function of x is denoted as x e or   exp x and the inverse function of x e is  ln x or log e x , i.e.   ln ln xx ee x  . ( 1 . 1 . 1 ) Some identities of the exponential and logarithmic functions : (i) x yx y e  , (ii) ln ln ln x y  . The power series of x e and   ln x : 23 1 2! 3! x ex     ( 1 . 1 . 2 ) and ln 1   ( 1 . 1 . 3 ) Exponential Change Consider the Input-Output Principle : Increase = Input - Output , during the short period h ,
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Ch.1 PHYS 2041 Problems in Quantitative Methods for Basic Physics (1 st Term 10/11) 2    Pt h Pt BPth CPth  ,    Pt B CPth  , ( 1 . 1 . 4 ) where B and C are constants. When 0 h , equation (1.1.4) becomes the differential equation: dP t B CPt dt  , ( 1 . 1 . 5 ) which has the solution of exponential form: BCt A e . ( 1 . 1 . 6 ) If B - C > 0, the change of the magnitude of   is exponential growth . If B - C < 0, the change of the magnitude of   is exponential decay .
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This note was uploaded on 10/14/2010 for the course PHYS 2051 taught by Professor Drkwong during the Spring '10 term at CUHK.

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a - Ch.1 PHYS 2041 Problems in Quantitative Methods for...

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