Matlab代写 - Math 370 – Mathematical Modeling

时间：2020-12-09

rning: Academic dishonesty includes such things as cheating, inventing false information or citations,
plagiarism, and helping someone commit an act of academic dishonesty. Students who violate university standards
of academic integrity are subject to disciplinary sanctions, including failure in the course and suspension from the
university. Since dishonesty in any form harms the individual, other students and the university, policies on
academic integrity are strictly enforced. You should familiarize yourself with the academic integrity guidelines
found in the current student handbook at http://www.fullerton.edu/handbook/.
I read, understood the above statements, and completed this exam without anyone’s help.
Name:
Student ID :
Signature:
1. Determine whether the following equation is dimensionally correct? (10 points)
, where
ρ u= wvu ∇= ⎣⎢⎢⎢⎢⎢⎡ 𝜕𝜕
𝜕𝜕𝜕𝜕
𝜕𝜕
𝜕𝜕𝑦𝑦
𝜕𝜕
𝜕𝜕𝑧𝑧⎦⎥⎥⎥⎥⎥⎤ t p 𝑇𝑇𝐷𝐷 f
Density 3D Velocity Vector gradient time pressure Stress tensor (pressure) force
2. Dimensional Analysis: Suppose V , the speed of a liquid
flowing through a horizontal pipe, depends on the pressure
drop ∆P , the length of the pipe l , the diameter D , density
of the liquid ρ , and the viscosity of the liquid µ . Show
that V can be modeled using the Buckingham Π theorem
as
( , ). 2 2 µρ ρ µ P D lD D V ∆ = ⋅Φ (10 points)
3. Similitude: Suppose the torque τ (N m) required to rotate a disk of diameter D (cm) submersed in a
fluid with density ρ (kg/m3
), and the bulk viscosity ν (kg/m/s) at the rotation rate ω (Radians/s) can
be modeled, using the Buckingham ∏-theorem as,
( ) 2 5 2 ν ω τ ρω D = D ⋅Φ [Do not show this!!].
If a scaled model, 50 times smaller, experiences a 5 N-m torque in water with the rotation rate
10 sec
3π rad
ω = and
the real-sized model is tested in oil. Assuming the two models are similar and water kinematic viscosity = 1.2
oil kinematic viscosity and water density = 3 oil density,
a) What is the rotation rate for the real-size model? (5 points)
b) At that rotation rate, what is the real-sized torque? (5 points)
4) Modeling with data: Given the data set populations versus the mean velocities over a 50-foot course for
15 locations on Table 4.5 of page138, find two non-polynomial models that can describe the relation between
P and V with 𝑅𝑅2 ≥ 92%. For each model, provided the mathematical equation with the parameters specified
along with the graph. You must include the R-square values. (10 pts for each model)
5) Prescribing Drug Dosage: Doctors may advise some patients to take a low dose of aspirin daily to
prevent blood clots and reduce the risk of stroke and heart attack. Suppose the concentration of a medication
administered in a patient follows the exponential decay model C(t) = C0e −kt , where C is the concentration ,
C0 is the initial dosage, k is the absorbing rate, and t is time.
a) Derive the concentration residual in the body after administering n consecutive dosages. (10 points)
b) Suppose aspirin is absorbed in the body at the rate k=0.075/hr and each dosage produces 2.5 mg/dl of
aspirin concentration in the body. With such prescription, what is the highest aspirin concentration in the
body? (2pts)
c) How many days does it take to get the aspirin concentration to reach 90% of the highest level? (3pts)
6) Given the differential equation 𝑑𝑑𝑑𝑑
𝑑𝑑𝑑𝑑 = (3 − 𝑢𝑢)(1 − 𝑢𝑢)2.
a) Find the equilibria (3 points)
b) Determine the stability at the equilibria (3 points),
c) Draw the solution trajectories in phase space (4 points)
d) Start with u(0)=0.99 and use the Euler method with ∆𝑡𝑡 = 0.1 to get and graph u(t) for the first 5
seconds. (5 points)
7) For each first order system of differential equations, find its equilibrium point(s), draw the phase space near
the equilibrium points, and describe the corresponding stability.
a)
x y dt
dy
y x
dt
dx
(3 2 ) (4 ) = − = − (10 points)
b)
x y dt
dy
y x
dt
dx
( 3 2 ) (4 ) = − + = − (10 points)

- 留学生代写
- Python代写
- Java代写
- c/c++代写
- 数据库代写
- 算法代写
- 机器学习代写
- 数据挖掘代写
- 数据分析代写
- android/ios代写
- web/html代写
- 计算机网络代写
- 操作系统代写
- 计算机体系结构代写
- R代写
- 数学代写
- Finance 金融作业代写
- Principles of Microeconomics 微观经济学代写
- Accounting 会计代写
- Statistics统计代写
- 生物代写
- 物理代写
- 机械代写
- Assignment代写
- sql数据库代写
- analysis代写
- Haskell代写
- Linux代写
- Shell代写
- SPSS, SAS, R 数据分析代写
- Principles of Macroeconomics 宏观经济学代写
- Economics 经济代写
- Econometrics 计量经济代写
- Money and Banking 货币银行学代写
- Financial statistics 金融统计代写
- Economic statistics 经济统计代写
- Probability theory 概率论代写
- Algebra 代数代写
- Engineering工程作业代写
- Mechanical and Automation Engineering 机械与自动化工程代写
- Actuarial Science 精算科学代写
- JavaScript代写
- Matlab代写
- Unity代写
- BigDate大数据代写
- 汇编代写
- stat代写
- scala代写
- OpenGL代写
- CS代写