Homework 1 Due Monday, September 17th at the beginning of class. Show your work. 1. Match the diﬀerential equation in (a)-(c) to a family of solutions in (d)-(f). The point of this exercise is not to solve the diﬀerential equations in a) - c). (a) y = y 2 (b) y = 1 + y 2 (c) yy = 3x (d) y = tan(x + C) (e) 3x2 − y 2 = C (f) y = −1/(x + C)

2. Find the value of k so that y = e3t + ke2t is a solution of y − 2y − 3y = 3e2t . 3. Solve the following diﬀerential equations and IVP’s. You may solve these equations implicitly. (a) y + 3x2 y = x2 (b) y ln t = y+1 t 2

dy dt

2 sin t dy = 0 y (d) y y − t = 0, y(1) = 2, y (1) = 1 (c) cos t dt + 1 + (e) y − y = et y 2 (f) cos(xy) − xy sin(xy) + 2xyex + (ex − 2y − x2 sin(xy))y = 0, y(1) = 0 dy x + 3y (g) = dx 3x + y 2 x sin x dy + (y cos3 x − 1) dx = 0, 0 < x < π (h) cos (i) (x + yey/x )dx − xey/x dy = 0, y(1) = 0 [Hint: Think homogeneous.] 4. Suppose the diﬀerential equation dP = (k cos t)P, dt is a model of the human population P (t) of a certain community, where k is a positive constant. Discuss a (non-morbid) interpretation for the solution of this equation. In other words, what kind of population do you think it describes? [Actually solving the equation is not helpful.] 5. Write down a diﬀerential equation for the velocity v(t) of a falling body of mass m if air resistance is proportional to the square of the instantaneous velocity. (Remarks: Consider the forces acting on a falling object, and what they must add up to by Newton’s Second Law. You do not need to solve the diﬀerential equation.) 2 2

6. The ﬂu makes its ﬁrst appearance in Pleasant Island (population 999) when Mrs. Smith’s niece arrives for a visit not feeling well. Let y(t) be the number of infected people. Suppose that apart from the initial visitor, no one enters or leaves the island for an indeﬁnite period of time. Suppose also that the number of islanders infected grows at a rate proportionate both to the number of people infected and the number...

...x)(a + x)(a + x)(a + x) = a4 +4a3x +6a2x2 +4ax3+ x4
Method 2 - PASCAL Triangle
Pascal's triangle is a triangular array of the binomial coefficients in a triangle. It is named after the French mathematician Blaise Pascal
Base on algebra method.
only using the coefficients of terms.
Power value Coefficient
n = 0 1
n = 1 1 1
n = 2...

...
Determination of Drag Coefficients for Various Sphere Types
Adriana Carbon, Jessica Lake, Jonathan Bessler
ChE 341 Experiment 1
March 6, 2015
Abstract
“A wind tunnel is a specially designed and protected space into which air is drawn, or blown, by mechanical means in order to achieve a specified speed and predetermined flow pattern at a given instant” . The flow over a specific object can be observed from outside the wind tunnel through transparent windows...

...the Pearson Correlation Coefficient (r)
The Pearson product-moment correlation coefficient (r) assesses the degree that quantitative variables are linearly related in a sample. Each individual or case must have scores on two quantitative variables (i.e., continuous variables measured on the interval or ratio scales). The significance test for r evaluates whether there is a linear relationship between the two variables in the population. The appropriate correlation...

...through a heat transfer coefficient. Heat is generated in the slab at the rate of 1.0 kW/m3. The thermal conductivity of the slab is 0.2 W/m-K. (a) Solve for the temperature distribution in the slab, noting any assumptions you must make. Be careful to clearly identify the boundary conditions. (b) Evaluate T at the front and back faces of the slab. (c) Show that your solution gives the expected heat fluxes at the back and front faces.
Q.2
Compute overall heat transfer...

...GINI COEFFICIENT
The Gini coefficient is a summary statistic that measures how equitably income is distributed in a population. It is derived from the Lorenz curve which plots the cumulative percentages of the income and the population against which it is distributed. The line at 45 degrees thus represents perfect equality of incomes. The Gini coefficient is the ratio of the area that lies between the line of equality and the Lorenz curve divided by...

...3/16
Chem 322 Friday
Partition Coefficient (Extraction) Lab for Benzoic Acid
Reaction Mechanism:
Purpose:
The purpose of this particular lab was to demonstrate the difference in separation of Benzoic acid in water and Dichloromethane. Also the difference in separation of Benzoic acid in bicarbonate and Dichloromethane. By calculating the partition coefficient for each of these separations, it became clear the differences in the separation of the...

...References..............................................................................................5
OBJECTIVE
This experiment was carried out to study the conduction of heat along a composite bar and evaluate the overall heat transfer coefficient.
INTRODUCTION
Conduction is defined as the transfer of energy from more energetic particles to adjacent less energetic particles as a result of interactions between the particles. In solids, conduction is the combined...

...
Coyne and Messina Articles, Part 3 Spearman Coefficient Review
Student Name
Instructor’s Name
Institution
Date
Coyne and Messina Articles, Part 3 Spearman Coefficient Review
The Spearman Correlation Coefficient remains one of the most important nonparametric measures of statistical dependence between two variables. The Spearman Correlation Coefficient facilitates the assessment of two variables using a monotonic...