作者candy79729 (candy79729)
站内NTU-Exam
标题[试题] 97上 陈逸聪 化学数学 期中考
时间Sun Dec 14 00:53:25 2008
课程名称︰化学数学
课程性质︰化学系系必修
课程教师︰陈逸聪
开课学院:理学院
开课系所︰化学系
考试日期(年月日)︰ 97 / 11 / 11
考试时限(分钟): 10 : 20 ~ 13 : 00 ,共 160 分钟
是否需发放奖励金: 是
试题 :
1. If a fossilized tree is claimed to be 4000 years old, what should be its
C14 content expressed as a percent of the ratio of C14 to C12 in a living
organism? (6%)
2. Test for exactness. If exact, solve. If not exact, find an integrating
factor and determind the corresponding particular solution. (10%)
( cos xy + x/y ) dx + ( 1 + x/y cos xy ) dy = 0
3. (a) Solve the following Bernouli equation. (5%)
y' = Ay - By^2
(b) Suppose that the population y(t) of a certain kind of fish is given by
the equation of (a), and fish are caught at a rate Hy propotional to y.
Solve this so-called Schaefer model. Find the equilibrium solutions y1
and y2 (>0) when H<A. The expression Y = Hy2 is called the equilibrium
harvest or sustainadle yield corresponding to H. Why? (5%)
4. Find the frequency of oscillation of a pendulum of length L, neglecting air
resistance and the weight of the rod, and assuming θ to be so small that
sin θ practically equals θ.
┬─
│\
│ \ L
│ \
│θ \
│ ○Body of mass m
5. (a) Find the solution for a forced oscillator of the following equation.
(6%)
y" + 25y = 99 cos 4.9t, y(0) = 2, y'(0) = 0
(b) How does the graph of the solution in (a) charge if you change
(i) y(0)
(ii) the frequency of the driving force? (4%)
6. Are cosh x = ( e^x + e^-x ) / 2 and sinh x = ( e^x - e^-x ) / 2 linearly
independent? Why? (6%)
7. Solve the nonhomogeneous ODE by variation of parameters or undermined
coefficients. Give a general solution. (10%)
Hint: To find y1, y2, set y = ux^-1/2
[ x^2*D^2 + xD + (x^2 - 1/4 ) I ] y = x^3/2 sin x
8. Find the current in the RCL-circuit when L=0.4H, R=40Ω, C=10^-4 F, and
E(t) = 220 sin 314t V (50 cycles/sec) (8%)
9. Find the steady-state solution of the damped forced oscillating system when
m=4, c=4, k=17 and the driving force is 202 cos 3t.
┬
ξ
k ξ Spring
ξ
m ■ Mass
│
c ︼ Dashpot
10. Solve the following initial value problem. Sketch or graph the solution.
(10%)
y" + 6y' + 18y = 0 y(0) = 5, y'(0) = 21
11. Solve the following initial value problem. (8%)
x^2 y" + 15xy' + 49y = 0 y(1) = 2, y'(1) = -11
12. Find the solutions of y'" - 3y" + 3y' - y = 0 and prove that your
solutions are linearly independent. (6%)
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◆ From: 118.166.10.7
1F:推 abacada :时间没有延长写得完吗? @@ 12/14 01:37
2F:推 eminemk10 :抱歉 我是他校的化学系学生 可以请问化数的教科书是? 12/14 09:17
3F:推 abacada :我之前修课是用Kri-开头那本厚厚的工程数学教科书 12/14 10:32
4F:推 abacada :不知道现在是? @@ 12/14 10:33
5F:推 Julibea :这次用Erwin Kreyszig的书 12/14 15:44
6F:→ Julibea :Advanced Engineering Mathematics 9e 12/14 15:45
7F:→ eminemk10 :Orz 感恩 12/14 18:06
※ 编辑: candy79729 来自: 118.166.12.194 (12/14 19:33)
8F:→ candy79729 :囧我忘了 有延长到1点...... 12/14 19:34
9F:推 abacada :哈 还是老样子 不过改版了XD 我用8e 12/14 20:19
10F:推 Julibea :上课也是有人拿8e来用啦 应该没差多少? 12/14 22:29
11F:推 abacada :应该是吧 12/14 23:45