Applied Calculus Projects

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Mathematics

Description

Your project should feature a practical problem from the field you are pursuing and require the use of calculus tools. Beyond that, problems might be either well-defined or open-ended.

Contents

1. Abstract

2. Motivation

3. Mathematical Description and Solution Approach

4. Discussion

5. Conclusions and Recommendations

6. Nomenclature

7. References Appendix (calculations, graphs, pictures, spreadsheet information …)

For more information see the – Guidelines for Students. Please follow the guidelines for each of them.

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Applied Calculus Projects – Guidelines for Students Nature of the Project Your project should feature a practical problem from the field you are pursuing and require the use of calculus tools. Beyond that, problems might be either well-defined or open-ended. All projects will have at least two advisors – a Subject Area Advisor and a Mathematics Advisor. Subject Area Advisor Your Subject Area Advisor will most likely be the person (e.g., work supervisor, faculty member, postdoc, etc.) who suggested the project to you. This person might simply hand you a project and say “Come back when you are done” or schedule meetings with you to discuss it. How you work with your Subject Area Advisor is between you and her/him. Math Advisor Your Calculus course Instructor will be your Mathematics Advisor. You may have more than one Mathematics Advisor (any Faculty or Graduate student in the Department of Mathematics & Statistics). How to Select a Project The problem for your project can come from a number of different sources. If you have a job or an internship, your work supervisor might have a problem that is important to the organization you work for. If you have an undergraduate research position, your research advisor can be a source of project ideas. Or, you might have already taken a class or two with faculty members in your major and they might be willing to suggest a problem for you to work on. The best source of a project might be you though. Consider the things you are interested in and look for an application of calculus to them. If you can find one, you can probably build a project around that. Publication in the Undergraduate Journal of Mathematical Modeling: One + Two Selected projects will be published in the open access electronic journal UJMM: One + Two http://scholarcommons.usf.edu/ujmm/ or http://ciim.usf.edu/ujmm under a Creative Commons Attribution Non-Commercial Share Alike 3.0 license. Submission of a project report will imply that you are giving the editors of UJMM: One + Two permission to publish your report in this journal, should it be selected. Page 1 Project Deadlines • The deadline for selecting a project will be given to you by your Calculus Instructor. • Your subject area advisor might wish to review your report and make suggestions before you submit it. You should ask her/him if this is the case and, if so, when the deadline for this is. • The official due date of the project (final submission) – the day that it must be uploaded – will be given to you by your Calculus Instructor. Project Submission Your project (equations, graphs, diagrams, pictures included) should be presented as a Microsoft WORD document. • • • • • Clarity of writing is important. At the very least, be sure to use your spell-checking and grammar-checking facilities. It is very important that you include the correct first and last names of your project advisors. Also be certain to include their correct USF Department or Company Affiliation. This information as well as your own correct first and last name is crucial for proper identification of your project upon online submission. You will need to prepare a Project Summary in advance. This is a concise abstract type description written in the third person. The Project Summary will be posted online so it should be understandable to a general audience. Therefore it should be focused on the subject matter rather than mathematical formulas and details. You should submit your project through the PROJECT SUBMISSION link provided by your Calculus Instructor. The check list of the required and optional data appears as the first page in the submission process. You may be required to provide your advisors with a hard copy of your project. Project Checklist 1. Find a Subject Area Advisor for your project, by ___________. 2. Meet with your chosen Subject Area Advisor and identify a problem, by ___________. 3. Check back with your Mathematics and Subject Area Advisors concerning your understanding of the problem and a mathematical approach to solve it. Consult with them about any difficulties or questions. 4. Show a draft of your report to all advisors no later than _______________. 5. Submit final copy online, by ___________. Report Format Project submissions must be in the following format: (a) Cover page and Problem statement. The cover page should use the following template, followed by the problem statement (see next page): Page 2 Your section MATHEMATICS – ENGINEERING PROJECT * (e.g., MAC2282.902) PROJECT TITLE Student: First Name Last Name ADVISORS Mathematics Advisor: First Name Last Name Affiliation** Subject Area Advisor: First Name Last Name Affiliation** Problem suggested by: First name Last name Affiliation** Current semester and year PROBLEM STATEMENT Provide an exact statement of the problem as suggested by its author. * or MATHEMATICS – MEDICINE PROJECT, MATHEMATICS – BIOLOGY PROJECT, MATHEMATICS-ENVIRONMENTAL SCIENCE PROJECT, etc. ** For instance, Electrical Engineering, University of South Florida, Tampa, FL. Research and Development, Raytheon Technology. St. Petersburg, FL. Department of Radiology, Tampa General Hospital, Tampa, FL. , etc. (b) Table of Contents. Include the following sections in the table and give the page numbers. Contents 1. Abstract 2. Motivation 3. Mathematical Description and Solution Approach 4. Discussion 5. Conclusions and Recommendations 6. Nomenclature 7. References Appendix (calculations, graphs, pictures, spreadsheet information …) Page 3 P A G E #’s (c) Abstract. The abstract is a short summary of your project report – it should not exceed one or two paragraphs. It should concisely state what you did, how you did it, and what conclusions you drew from the results. The abstract will be posted online so it should be well written. (d) Motivation. In this section you should give some background about why the problem is important to science or engineering. You should also describe the problem within its engineering or science context and provide the objective for the project. (e) Mathematical Description and Solution Approach. In this section, you should formulate the mathematical approach to solving the problem – providing the relevant equations, describing the mathematical tools you used and outline the procedure used. Do NOT simply list the equations – use text between them to provide a clear understanding of them to the reader. (f) Discussion. Here, you should provide the results and discuss them. Did you meet the objective of the project? Were they as expected, or were they counter-intuitive? What implications do your results have to the problem at hand and to the field in general? (g) Conclusions and Recommendations. Give the basic conclusions of your work. This will be somewhat similar to what is in the abstract but with a little more detail – for instance, including a summary of your interpretation of the results. You should also make a few recommendations – such as things a person doing the same project might do differently or ideas for a new study that is suggested by your results. (h) Nomenclature. List the symbols that you use in your report. For each symbol, provide a description of what it represents and its units. Example: P T v V Pressure Temperature Velocity Voltage kPa o C m/s V All units used should belong to the same measuring system: Standard (English) or Metric (SI). Carefully check whether the units agree and are balanced on both sides of each equation. (i) References. Any work or ideas that you have taken from someone else should be cited directly in the text of your report. This includes any figures that you might download from the web. Do your best to find and cite the original source of information rather than the secondhand source. At the end of the report should be a list of references that were cited. Book and scientific journal references are strongly preferable to webpages. (j) Appendices. You might have detailed calculations, spreadsheets or computer programs that were used to obtain your results but do not belong in the main report. If so, you should place these materials in appendices and refer to them as needed in the report. Page 4
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Hi,Find attached the completed work.Feel free to ask for any clarification or editing if need be.Looking forward to working with you in the future.Thank you.

Running head: HYDRAULIC ANALYSIS PROGRAMS

Hydraulic Analysis Programs
Student’s Name
Professor’s Name
Course Title
Date

HYDRAULIC ANALYSIS PROGRAMS

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Table of Contents
Abstract ...................................................................................................................................... 3
Motivation .................................................................................................................................. 4
Mathematical Description and Solution Approach .................................................................... 7
Sample case 1 ......................................................................................................................... 9
Sample case 2 ....................................................................................................................... 10
Discussion ................................................................................................................................ 12
Conclusions and Recommendations ........................................................................................ 14
Nomenclature ........................................................................................................................... 16
Summary .................................................................................................................................. 17
References ................................................................................................................................ 18
Appendices ............................................................................................................................... 21

HYDRAULIC ANALYSIS PROGRAMS

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Abstract

This project attempts to solve the numerous problems encountered during the flow of
water and water-saturated debris in open channel flow systems. Principles from Hydraulics,
which is a sub-branch of the civil engineering discipline, are used to come up with
conceptualized designs of open channel systems that may be consequently used in the
reduction of water and general fluid and debris overflow during the occurrence of natural
disasters such as earthquakes and landslides that always occur unplanned and are not easy to
control without the proper methods put in place beforehand.
A number of calculus tools like differentiation and integration have been used to show
that after a design is made by a hydraulic engineer through the use of hydraulic analysis
programs, these formulas are used in the analysis of the created design before its final
implementation stage. Any problems that may arise during the process are tacked early and
corrected. This report puts into use the equations of continuity and the equations of motion to
demonstrate how this process of analysis and interpretation is done in later sections. There
are various conclusions that were drawn while undertaking this investigation. One, the main
objective of the report was achieved as it was shown that it is indeed possible to reduce the
problems associated with earthflows, whether directly or indirectly, in open channel systems
through the examples calculated in the mathematical description and solution approach. Two,
it is now an almost established fact that the integration of mathematical formulas especially
calculus tools with the engineering discipline is a useful resource in coming up with solutions
that enhance the comfort of human life and make the world a better and a safer place.

HYDRAULIC ANALYSIS PROGRAMS

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Motivation
Open channel flow is a sub-section of Hydraulics, which is often referred to as the
study of the transference of liquids through various channels. The history of open channel
flow systems is traced way back to the ancient roman times but experimental trials began in
the17th century. During the 18th century, there was the invention of Hydrodynamics by Mr.
Bernoulli, which was later split into two disciplines; hydrodynamics and hydraulics. Over
time, each of these two disciplines has developed and evolved independently of the other.
Open channel flows refer to flows that are not exclusively bounded within fixed or
definite boundaries. The surface flow that is created in this case is therefore referred to as the
free surface because the boundaries deform freely, as opposed to the flowing of fluid that is
constrained within closed conduits. Earth flows, which move freely under the influence of
gravity, like rivers and other materials that have been saturated by rain water on the ground
are considered to be open channel flows.
For flow to be considered as taking place in an open channel there should be no
contact between the fluids present. However, water from sources like rivers or heavy rainfall
is considered to flow in open channel systems. This is because the difference in magnitude of
the density of the water in the channels and the atmosphere above is massive and therefore
the density of the atmosphere is considered negligible and ignored in any analyses.
Nevertheless, the techniques that are used in the analysis of boundary resistance and the
velocity profiles in open channels are similar to those used in closed conduit systems.
In the recent past, there have been many problems affecting open channel flow in
different earth flow systems. Some of these problems have been seen during occurrences such
as landslides, creeks, and floods in different parts of the world. Landslides can be triggered
by natural or human causes. The natural causes of landslides include the earthquakes and

HYDRAULIC ANALYSIS PROGRAMS

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heavy rainfall in steep areas like...


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