application of secant method
April 16, 2013
MCS 1st sem
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ROLL # 31 to 40

SECANT METHOD
* The Secant command numerically approximates the roots of an algebraic function, f, using a technique similar to Newton's method but without the need to evaluate the derivative of function. * Given an expression f and an initial approximate a, the Secant command computes a sequence, =, of approximations to a root of f, where is the number of iterations taken to reach a stopping criterion. * The Secant command is a shortcut for calling the Roots command with the method=secant option

Advantages of secant method
* It converges at faster than a linear rate, so that it is more rapidly convergent than the bisection method. * It does not require use of the derivative of the function, something that is not available in a number of applications. * It requires only one function evaluation per iteration, as compared with Newton’s method which requires two Disadvantages of secant method

* It may not converge.
* There is no guaranteed error bound for the computed iterates. * It is likely to have difficulty if f′(α) = 0. This means the x-axis is tangent to the graph of y = f (x) at x = α. * Newton’s method generalizes more easily to new methods for solving simultaneous systems of nonlinear equations.

APPLICATION OF SECANT METHOD

1. You are working for a start-up computer assembly company and have been asked to determine the minimum number of computers that the shop will have to sell to make a profit. The equation that gives the minimum number of computers to be sold after considering the total costs and the total sales is

2. Use the secant method of finding roots of equations to find the minimum number of computers that need to be sold to make a profit. Conduct three...

...Numerical Methods Questions
1 f(x) = x3 – 2x – 5
a) Show that there is a root β of f(x) = 0 in the interval [2,3]. The root β is to be estimated using the iterative formula
,2 5 2 0 2 1 1 = =++ x x x n n
b) Calculate the values of x1, x2, x3, and x4, giving your answers to 4 sig fig.
c) Prove that, to 5 significant figures, β is 2.0946
2 Use the iterative formula
n
n n cox x x − =+ 1 1 With x1 = 0.5 to find the limit of the sequence x1, x2, x3,……. Correct to 2 decimal places.
3 Starting with x0 = 1, use the iterative formula
( ) 5lnln1 =++ xx n
To find, to 2 decimal places, the value of x1, x2, x3, and x4.
4 The equation 2x = x3 has two roots. Show that the intervals are [1,2] and [9,10].
5 f( x ) = x 3 – 2 –
x 1
, x ≠ 0.
(a) Show that the equation f( x ) = 0 has a root between 1 and 2.
An approximation for this root is found using the iteration formula
x n + 1 =
3 1
nx 1 2
+ , with 0 x = 1.5.
(b) By calculating the values of x 1, x 2, x 3 and x 4, find an approximation to this root, giving your answer to 3 decimal places.
(c) By considering the change of sign of f( x ) in a suitable interval, verify that your answer to part (b) is correct to 3 decimal places.
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished...

...is cooled
by radiation and convection to its surroundings.
I decided to use 4th order Runge Kutta method to
solve the problem.
Objective
To solve the first order nonlinear ordinary
differential equations using numerical
method.
To understand the 4th order Runge Kutta
method and its applications.
Problem statement
Steel ball bearing radius 0.02m, ρ =
dT
7800kg/m3
A T 4 Ta4 mC
dt
The radiation equation is
The convection equation is
Assumed T0= 1200K and Ambient
temperature,
Assumed that all heat transfer in
radiation and convection only.
Mathematical model
Combining both convection and radiation
equation to form a new rate of heat lost
equation:
After subsitution of the constants, the
equation reduced to:
Preliminary Solution
Rewrite the equations:
=(((-2.20673*(10^-13))*(T^4))-((1.60256*(10^-2))*(T))
+(4.8095))
f(t,T)=(((-2.20673*(10^-13))*(T^4))-((1.60256*(10^-2))*(T))
+(4.8095))
Set
Runge Kutta 4th Order Solution
1
Ti 1 Ti k1 2k 2 2k3 k 4 h
6
k1 f (ti , Ti )
1
1
k 2 f (ti h, Ti k1h)
2
2
1
1
k3 f (ti h, Ti k 2 h)
2
2
k 4 f (ti h, Ti k3 h)
MATLAB IMPLEMENTATION
Result
Discussion and conclusion
The steel ball bearing will reach temperature
1000K at 15.3 seconds
The time taken for the ball bearing to cool from
1200K to 1000K is obtained by using the 4 th
order Runge Kutta method to analyze the rate
of...

...Lyceum of the Philippines University-Batangas
Capitol Site, Batangas City
School of Advanced Studies and Research
SUBJECT: Enrollment System
TOPIC: Problems met by the CITHM Students in the Sectioning and Encoding process during enrollment period
DISCUSSANTS: Patricia Isabel P. Maghirang
Joy S. Macatangay
PROFESSOR: Mrs. Jessica Cabaces
I. INTRODUCTION
This research activity focused on the slow processing of transactions in enrollment period, to know the problems, to recognize the reason, to give possible solutions.
II. Related Literature/Presentation
1. To know the problems met by the CITHM students in the Sectioning and Encoding process during enrollment period.
Processing of transactions was most difficult during the enrollment period. Some of the major problems encountered, particularly as concerns the enrollment are; Slow processing of transactions, tedious enrollment procedures, too much paper works, not enough rooms, settle financial obligations in the university, submit requested documents, comply with admission provisions, students have to go back and forth in different offices for evaluation and validation.
2. To recognize the reasons on the slow processing of transactions during enrollment period; Poor marketing/admissions, poor leadership, inaccessibility or unavailability of data/system that were needed immediately, and unorganized steps for enrollment, lack of enrollment personnel.
3. The possible solutions to the slow...

...Methods of Research
Jennifer Whitehead
CJ490
8/12/14
Professor Price
Methods of Research
Scientist conducts research on a daily basis. The purpose of this research is exploration, description, explanation, and application. In the area of criminal justice things are getting researched all of the time. Take murder for example, the police have to explore to find out what actually happened. They have to describe the events leading up the the murder. They have to explain the facts to try and come up with a suspect. Finally, they have to use the process of application to put it all together so they can make an arrest. When using the different purposes of research it is important to examine each purpose by itself because each purpose has its own different aspect when it comes to research design.
The exploration stage is the first stage that researchers begin with when using research methods. “This stage is typically done for three purposes: to satisfy the researcher does curiosity and desires for better understand, to test the feasibility of undertaking a more extensive study, and to develop the methods to be employed in any subsequent studies.” (Crossman, 2014) A researcher will use the exploration stage of research when they want to find out about something that there is little known about. Take drugs for example; let’s say a researcher wants to find out how bad the drug problem is...

...references to relevant items in the category frame, per chosen unit of content.
- Express the results as an overall distribution of the chosen content sample in terms of the frequency of occurrence of the sought-for referents.
This procedure is based on two main assumptions: first, that the link between the external object of reference and the reference to it in the text will be reasonably clear and unambiguous, and second, that the frequency of occurrence of chosen references will validly express the predominant “meaning” of the text in an objective way. The method produces a statistical summary of a much larger media reality, it has been used especially for comparing media content with a known frequency distribution in “social reality”.
LIMITs 362
ARTHUR ASA BERGER: Media Research Techniques !!!!???? Missing!!!!
“ Media Analysis Techniques
97 C.A. is a standard sociological technique that uses statistical methods to make inferences about what is found in the media (:97).
-Historical frame of ref to make comparisons between earlier samples, is there more or less X? if so, what does it mean?
Topic: the representation of young men in Irish advertising.
The topic only addresses age and gender: young men, it does not specify any research questions or context, which leaves the analyst not being certain about which are the variables or measurable elements of interest (Hornig:87). The field is advertising, regarding representations, no context...

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Personal Essay
* Answer Required
Use the space below to compose an essay including the following information:
• Your career goals
• Why you believe getting a college education is important
• How you will contribute back to your community
• Why you believe Ivy Tech Community College can assist you in achieving these goals
•
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Personal Essay
* Answer Required
Use the space below to compose an essay including the following information:
• Your career goals
• Why you believe getting a college education...

...Assignment in Research Methods
1) Overview of various research methods
When writing a Research Paper it is important to know different research methods. These methods help to gather and systemize the information and data in order to scientifically prove the validity of the work. Further will be explained ways how to collect the data.
Research methods are divided in two big blocks: quantitative and qualitative. Quantitative methods are those where results are explained in numbers, whereas qualitative methods define outcomes by what respondents answer. It is more subjective and more open, as results are not described by numbers, but rather as observations. To put both methods differences together: quantitative look more for statistical explanation, but qualitative are more in-depth. 1 Further will be in more detail explained methods that lay under quantitative and qualitative.
There are many ways how to collect data for the research. One of them is doing experiments. It usually involves small amount of people who are doing some tests, for example, detecting how fast people read, what affects their reading skills and other objectives. This method is very in-depth and counted as qualitative as the behaviour people is investigated in order to conclude some outcomes. One of the minuses of such methods is that it...

...sUnit 3: Concepts
By: Tiffany Linville
Kaplan University
CJ490: Research Methods in Criminal Justice
Professor: Elycia Daniel
3/24/2013
Abstract
Problem statement: Wayne County data indicates that 25% of the population has used illicit drugs at some point in their life (Wayne County, Indiana Strategic Prevention Framework, 2005).
Briefly summarize from at least 4 journal articles, government reports, or databases on your topic. Summarize statistical data where appropriate. Present the important information from each of the sources. (It is not a summary if you simply list what kind of information can be found in the article). What did these data sources and/or information reveal to you? Be sure to support your findings.
Journal Articles, Government Reports, or Databases
The following is a summary of information gathered from various sources regarding drug use in Wayne County, IN.
The report for Wayne County's Strategic Prevention Framework ~ State Incentive Grant is a valuable resource with a great deal of information about drug use in Wayne County. This information is pulled from multiple sources, including surveys of drug use, economic comparisons, different demographic factors, and information regarding school suspension and expulsion rates. Statistics are broken down by age, gender, and other categories (SPF-SIG Local Epidemiological Report - Wayne County, IN).
The Indiana National Prevention Resource Center survey of...