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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

求解答案是否正確

Multiple-choice questions: (70 points) write the letter of statement that is not true: 1. A.B.U The Drude Model: (a) It is a classical approach using concepts from the kinetic theory of gases. (b) A relaxation-time approximation is used where the probability of collision is l/t. (c) No forces act on the electrons in between collisions. (d) It predicts accurately the electronic heat capacity of metals. 2. The Sommerfeld Model: (a) The crystal potential is replaced by an average Coulomb potential. (b) The separation of states is so close that a continuum model can be applied. (c) The electrons are highly localized due to a strong crystal potential. (Q) The energy of the highest occupied state at 0 K is the Fermi energy. 3. Density of states in k-space, N(k): (a) N(k) is determined by the boundary value conditions. (b) For lattices in any dimensions, N(k) is constant in k-space. (C) N(k) depends on the direction and magnitude of k. (d) It is directly proportional to the volume of the crystal. E影響, c 4. The Fermi surface of a metal: (a) is responsible for many of the transport properties of the metal, (b) depends on the nature of the chemical bonds, (c) is always a sphere, (d) can involve mixing of electron orbitals. ✓ 5. The conductivity of a material () increases with the mobility of its carriers, (b) increases with the density of carriers, (C) it is inversely proportional to the energy gap. cogu changes with temperature. 6. BID Plasmons: (a) They are an important characteristic of the Sommerfeld electron gas model. (b) Plasmons occur spontaneously in metals. (c) They are related to charge density oscillations. (d) The Plasmon energy is typically of the order of 10 eV. The Fermi energy Ef in intrinsic semiconductors 8) is usually close to y E, at OK (b) it ACiD. can increase or decrease with temperature depending on the ratio of hole and electron effective masses, (c) it represents the point at which the probability of occupation is 12, even though there may not been any states with that energy, (d) its value relative to the electronic bands must remain unaffected in the presence of defects or interfaces.

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