응용수치해석 2판 솔루션 (구매자 판매중지)

1

CHAPTER 1
1.1 You are given the following differential equation with the initial condition, v(t = 0) = 0,

c dv = g ? d v2 dt m
Multiply both sides by m/cd

m dv m = g ? v2 c d dt c d
Define a = mg / c d

m dv = a2 ? v2 c d dt
Integrate by separation of variables,

∫ a 2 ? v 2 = ∫ m dt
A table of integrals can be consulted to find that

dv

cd

∫a

2

1 dx x = tanh ?1 2 a a ?x

Therefore, the integration yields

1 v c tanh ?1 = d t + C a a m
If v = 0 at t = 0, then because tanh?1(0) = 0, the constant of integration C = 0 and the solution is

1 v c tanh ?1 = d t a a m
This result can then be rearranged to yield

v=

? gc d ? gm t? tanh? ? m ? cd ? ?

1.2 This is a transient computation. For the period from ending June 1:

Balance = Previous Balance + Deposits ? Withdrawals
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