- Explain differential costs, differential revenue, incremental cost, and avoidable cost. Give examples for each concept.
- Explain opportunity costs and examine how opportunity costs are used in decision making. Give examples of opportunity costs in decision making.
- Examine the concept of the time value of money and how the concept is used in capital investment decision making.
- Compare and contrast between net present value and internal rate of return methods
Tag: differential
Department of Mathematics and Philosophy of Engineering
MHZ3531 Engineering Mathematics IA
Assignment No: 2
Academic Year: 2020/2021 Due Date: Will be notify later
Instructions
• Answer all the questions.
• Attach the cover page with your answer scripts.
• Use both sides of papers when you are answering the assignment.
• Please send the answer scripts of your assignment on or before the due date to the following address.
Course Coordinator – MHZ3531,
Dept. of Mathematics & Philosophy of Engineering,
Faculty of Engineering Technology,
The Open University of Sri Lanka,
P.O. Box 21,
Nawala,
Nugegoda.
MHZ3531-Engineering Mathematics IA
Assignment 2
Q1 (a) Write down the order and the degree of the following differential equations.
i) ???? ???? + (???? + sin ??) = 0 ii) ??2?? 3 ???? 4 3
iii) ??3?? 5 ??2?? iv) ??2?? 3
v)
(b) Using the method of variable separation, solve the following differential equations
i) (???? + ??)???? = (??2??2 + ??2+??2 + 1)????
ii)
iii)
iv) ??????2?? ???? = ??????2?? ????
v)
Q2 (a) Solve the following homogeneous differential equations.
i) ???? ???? ii)
iii) ???? iv)
b) Show that the following differential equations are exact and solve them.
i)
ii) (?? + sin ??)???? + (?? cos ?? – 2??)???? = 0 iii) 2?? + ?? cos ????)???? + ?? cos ???? ???? = 0
(c) Using an integrating factor, solve the following differential equations.
i) (??2 + ??2 + ??)???? + ???? ???? = 0
ii)
.
Q3
?? = ??????, then show that ?? has two distinct real values. Further, if the values of ?? are ??1 and ??2, then show that ?? = ??1????1?? + ??2????2?? is the complete primitive of the given differential equation, where ??1 and ??2 are arbitrary constants.
?? = ??????, then show that ?? has two distinct imaginary values. Further, show that the complete primitive of the above differential can be expressed of the form
?? = ??????(??1 cos ???? + ??2 sin ????), where ??1 and ??2 are arbitrary constants.
Q4 (a) Let ??(??) = ??2 – 3. Show that the equation ??(??) = 0 has a root between 1 and 2.
i) By using the bisection method, find a solution for the above equation correct to nine decimal places.
ii) By applying Newton Raphson’s method, find a solution for above equation correct to nine decimal places taking ??0 = 1.5.
(b) Using Newton’s interpolation divided difference formula and the following table calculate an approximation value for ??(1.5).
???? -2 0 1 4 5
??(????) -8 0 1 64 125
(c) Using Lagrange’s interpolation formula and the following table, calculate an approximation value for ??(10).
???? 5 6 9 11
??(????) 12 13 14 16
where ?? interpolates ?? at these points.
Q5 (a) Write down Trapezoidal Rule and Simpson’s rule to approximate the finite
.
i) Using the Trapezoidal Rule with ?? = 6 subintervals, approximate the integral
approximation.
ii) Using Simpson’s Rule with ?? = 4 subintervals, approximate the
integral ? ?? ?? ???? to 3 decimal places. Estimate the relative percent
-2
error of the approximation.
(b) Using the Jacobi’s iteration method, find the sixth iteration of the solution of the following system of equations.
3?? + 10?? – ?? = -8
2?? – 3?? + 10?? = 15
10?? + ?? – 2?? = 7
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Think back to high school and the “cliques†you encountered in that environment.
Write an essay of 500-750 words considering differential association theory, using your memories from high school or other regularly scheduled social gatherings.
Describe the groups (or cliques) present in that environment and the relative propensity to involvement in crime. Does differential association theory explain the behaviors of groups at that age? Why or why not?
Use the GCU Library to locate three to five relevant, scholarly sources in support of your content, no older than 5 years.
Prepare this assignment according to the guidelines found in the GCU Style Guide, located in the Student Success Center. An abstract is not required.
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Name of Student
Course Title
Name of Instructor
Groups and Their Relative Propensity to Involvement in Crime
Growing within one’s local community provides an opportunity to develop relationships with family members and neighbors. This is true in community settings where one gets to go to local schools within the reach of the family members. However, there is another added element of developing social bonds with the other children during school hours. In my time during high school, I had an opportunity to develop and enhance relationships with different students from different races. Although I developed close relationships with others, other relationships were strictly academic. The main reason for these differences in the kinds of relationships that I developed was the clash in individual values, beliefs, and norms. As I grew I had an opportunity to learn about different behaviors among the different groups of students. Some later became closer and turned to be helpful, while others turned out delinquent and eventually turning into criminal activities. Such group behaviors can be explained through the differential association theory.
Social learning theories have become popular in criminology is developing an understanding of crime and criminal tendencies. Walters (2020) asserts that the differential association theory is one of the basic premises behind the social learning theories. The author points out that youth learn the attitudes and criminal techniques from the individuals they associate with. The influences of association on enhancing criminal tendencies among individuals have also been examined extensively. In their study, Harris et al. (2017) showed that inmates who were kept with more experienced criminals tend to develop increased criminal tendencies once out of prison. The authors indicate that the differential association theory serves to show that association determines the nature of trajectory that a delinquent individual can assume in their life. This is consistent with what I observed during my high school, where the friends who associated with students with delinquent behavior later turned into criminal activities. Boonstoppel and Thompson (2017) points out that the differential association theory considers crime as a learned behavior. According to the authors, individuals acquire their values and definitions of their groups through intense, frequent, and regular interactions. My high school experience allowed me to observe how individuals and groups interacted. I developed associations with students whom I felt had better morals and great work ethics. This later determined who I wanted to be and what I am today. The groups that I avoided included those who showed truancy and other disciplinary issues. Just as outlined in differential association theory, the associations that were developed by the different groups yielded different personalities. A majority of those who developed
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Pick one of the following terms for your research: Moral philosophy, justice, white-collar crime, differential association, or power.
definition
summary
discussion
references
minimum 450 words
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