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數學與統計 大學

大一公衛系微積分,求第二題解

公衛系 微積分期末考 (28/12/2018) 1. Use the Laplace transform to solve the differential equations. (1) j(t)+2y(t) = x(t), y(0)=1, x(t)=10, t20 (20) (2) Intravenous glucose is a treatment. Disposed at a fixed rate k grams per minute inputs into the blood, while blood glucose will be converted to other substances or moved to another place, at a rate proportional to the amount of glucose in the blood, the proportionality constant is a (a> 0), the initial amount of glucose in the blood is M. A. Find the variation in the amount of glucose in the blood (15) B. Determining the equilibrium, the amount of glucose in the blood. (5) = 2. SI Epidemic Model : The size of the population, n+1, remains fixed. Let i(t) be the number of infectives at time t, and let s(t) be the number of individuals who are susceptible. Given an initial number of infectives iO), we would like to know what will happen to i(t). SI Epidemic Model is described by the differential equation. di(t) = k·i(t).s(t) ......(5.1) dt i(t)+s(t)=n+1 i(0)=i, (1) Solve this differential equation of the SI Epidemic Model (5.1). (10 h) (2) What is the peak times t of the epidemic spread? (10) 3. Consider the Two-compartment physiological models and is shown in figure 1. C1 (t) represent the drug concentration in the first compartment and C2 (t) represents the drug concentration in the second compartment. Vi and V2 represent the compartment volume. Use the first order linear differential equation general solution to solve the C1 (t) (20 ) and use the Laplace transform to solve C2 (t). 【20 分). | 世」!()

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自然科學 大學

求解圖裡UICK quiz的第二小題

acit0r 1taneOuls CUrTent Differentiating Equation 27.22 with respectto time gives the inst: as afunction of time: 4 tt號 一Fe ptasafurc 主二 where Q;/有CC 三方 is the initial current. Figure 27.15b 5 in the resistor that we guessedin order to-apply Kirch Equations 27.15 and 27.21. Equation 27.23 shows that the ci ing capacitor is negative, indicating that the current 1s Figure 27.15c. Both the charge on the capacitor and the ct tially at a rate characterized by the time'constant7了三用C. 人 i 一 GOuicK ouiz 27.5 Considerthe circuitin Figure 27.17 and assume the battery has after the switch is closed, what is the currentin the Figure 27.17 no internal resistance. () 」 battery (a) 0 (b) &/2A(G 28/Z04 8/元(e) impossible to determine (ii) After a 有 eyerylong time, what is the Currentin the battery? Choose from the same choices. theswitch is CC (3 前:銜1加信介2放 IntermittentWindshield Wipers nobiles are equipped with windshield wipers that can operate intermittently during alight rainfall. How does ofsuch wipers depend on the charging and discharging ofacapacitor7 民 The wipers are part ofan 及C circuit whose time constant can be varied by selecting different values of及through amultipo- Sition sWitch. As the voltage across the capacitor increases, the capacitor reaches a point at which it discharges and Higgers the wipers. The circuit then begins another charging cycle. The time interval between the individual sweeps of the wiperS 1 determinedjby the value ofthe time constant.

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