Conference Session

Integrating Math, Science and Engineering

Collection

2008 Annual Conference & Exposition

Authors

Gregg Janowski, University of Alabama at Birmingham; Melinda Lalor, University of Alabama at Birmingham; Hassan Moore, University of Alabama at Birmingham

Tagged Divisions

Mathematics

; • Develop an innovative 200-level course that meets the needs of engineering students; • Ensure that problems related to engineering are emphasizedThe current manuscript will discuss the process and design of a four semester credit hour coursethat will include the key elements of multivariable calculus and differential equations with theprerequisites of traditional MA 125: Calculus I and MA 126: Calculus II courses.Needs of Engineering Students – Faculty InterviewsThe authors interviewed faculty from Biomedical Engineering, Electrical and ComputerEngineering and Mechanical Engineering who taught any course(s) that had/have either MA 227:Calculus III or MA 252: Introduction to Differential Equations as a prerequisite or had one ofthese courses

Conference Session

Mathematics Division Technical Session 4

Collection

2017 ASEE Annual Conference & Exposition

Authors

Paran Rebekah Norton, Clemson University; Karen A. High, Clemson University; William Bridges, Clemson University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

, since the impact of the policy changes in this preliminarystudy differed based on student group. The initial results of this study provide some insight intoinstructional policies that have a positive impact on reducing DFW proportions for Calculus I.These findings support the larger effort of addressing issues causing introductory calculus to be abarrier to success for many STEM majors.ReferencesBeichner, R. J., Saul, J. M., Abbott, D. S., Morse, J. J., Deardorff, D., Allain, R. J., … Risley, J. S. (2007). The student-centered activities for large enrollment undergraduate programs (SCALE-UP) project. Research-Based Reform of University Physics, 1(1), 2–39.Benson, L., Moss, W., Biggers, S., Schiff, S. D., Orr, M. K., & Ohland, M. W

Conference Session

The Use of Games and Unique Textbooks in Mathematics Education

Collection

2014 ASEE Annual Conference & Exposition

Authors

Erin Shaw, University of Southern California; Jihie Kim, University of Southern California; Zinan Xing, University of Southern California

Tagged Divisions

Mathematics

Mailman and board chair Beth Kennedy for supporting thestudy. A special thank you to PedGames server administrator Hao Xu and to all of the PedGamesstudent programmers for their creativity, dedication and hard work.Bibliography1. Shaw, S., Boehm, Z., Penwala, H., and Kim, J., GameMath! Embedding Secondary Mathematics into a Game- Making Curriculum Proceedings of the American Society of Engineering Education, 2012.2. van der Meulen, R. and Rivera, J. (2013) Gartner press release. Online at http://www.gartner.com/newsroom/id/2614915.3. Moskal, B. and Skokan, C. (2007). An innovative approach for attracting students to computing: A comprehensive proposal. Online at http://www.nsf.gov/awardsearch

Conference Session

Mathematics Division Technical Session 3

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Zeynep Akcay Ozkan, City University of New York, Queensborough Community College; Dona Boccio, City University of New York, Queensborough Community College ; Dugwon Seo, City University of New York, Queensborough Community College ; Sirin Budak, Univeristy of Wisconsin-Stevens Point

Tagged Divisions

Mathematics

over.References[1] A. C. Carius, “Teaching Practices in Mathematics During COVID-19 Pandemic: Challenges for Technological Inclusion in a Rural Brazilian School,” Am. Sci. Res. J. Eng. Technol. Sci., 2020.[2] A. Khirwadkar, S. Ibrahim Khan, J. Mgombelo, S. Ratkovic, and W. Forbes, “Reimagining Mathematics Education During the COVID-19 Pandemic,” Brock Educ. J., 2020, doi: 10.26522/brocked.v29i2.839.[3] E. M. Mulenga and J. M. Marbán, “Is covid-19 the gateway for digital learning in mathematics education?,” Contemp. Educ. Technol., 2020, doi: 10.30935/cedtech/7949.[4] J. König, D. J. Jäger-Biela, and N. Glutsch, “Adapting to online teaching during COVID- 19 school closure: teacher education and teacher

Collection

2016 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

-developed knowledge of conceptimage and concept definition of Riemann integrals. The use of absolute value with definite integralis an important aspect of the research question for the area calculations. In this work, the goal is toobserve graduate and senior undergraduate mathematics and engineering students’ ability tocombine integral and absolute value concepts by evaluating their responses to an integral question.____________________________________________________________________Special thanks to Drs. Deborah A. Trytten and Gizem S. Aydin for their valuable discussions andinput during the preparation of the IRB approved form.MethodologyIn pedagogy, researchers needed to observe students’ comprehension of the function concept. Thedefinitions in

Conference Session

Mathematics Division Technical Session 1

Collection

2018 ASEE Annual Conference & Exposition

Authors

Nancy Romance, Florida Atlantic University; Ali Zilouchian, Florida Atlantic University; Michael Vitale, East Carolina University; Lisa Greenberg, Florida Atlantic University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

Each CourseFaculty were divided into three math focus groups (leaving College Algebra for the end) wherethey specifically addressed main learning outcomes for the course, the core ideas upon whicheach course is grounded, and the supporting concepts that make up the core idea(s). Thisapproach builds upon a theoretical framework resulting from the work of numerous groups (i.e.,Mathematical Association of America - [MAA]) and individuals, such as Bransford et al., (2000)who, in his National Research Council commissioned book, How People Learn, providedrecommendations based on extensive work addressing learning and teaching in mathematics.Guiding their discussions were a series of questions such as (a) does the course outline reflect thedesired

Conference Session

Mathematics Division Technical Session 2

Collection

2013 ASEE Annual Conference & Exposition

Authors

Helen M Doerr, Syracuse University; Jonas Bergman Arleback, Syracuse University; AnnMarie H O'Neil, C.S. Driver Middle School

Tagged Divisions

Mathematics

form 𝑦 = 𝑎 ∙ 𝑏 ! that could be used to describe thedata; (b) give an interpretation of the constants a and b in (a); (c) find the point in time when thevoltage across the capacitor was 0.05 V; (d) compute the average rate of change over threesubintervals, from t = 5 to t = 10 seconds, t = 20 to t = 25 seconds, and t = 40 to t = 45 secondsrespectively; and (e) write two or three sentences interpreting the negative average rate of changedata in (d). 2.0529 − 4.2245 t = 5 to t = 10 : = −0.43 v/s 10 − 5 .27252

Conference Session

Mathematics Division Technical Session 1: Best Practices in Engineering Math Education

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

JaCoya Thompson, Northwestern University ; Sally P.W. Wu, Northwestern University; Jacob Mills, Evanston Township High School

Tagged Divisions

Mathematics

this study. This work wasmade possible through generous support from the National Science Foundation (grants CNS-1138461, CNS-1441041, DRL-1020101, DRL-1640201 and DRL-1842374) and the SpencerFoundation (Award #201600069). Any opinions, findings, or recommendations expressed in thismaterial are those of the author(s) and do not necessarily reflect the views of the fundingorganizations.References[1.] AP Statistics: AP Central - The College Board. (2019, August 1). Retrieved from https://apcentral.collegeboard.org/courses/ap-statistics?course=ap-statistics[2.] Barron, A. E., Ivers, K. S., Lilavois, N., & Wells, J. A. (2006). Technologies for education: A practical guide (5th ed.). Santa Barbara, CA: Libraries Unlimited[3.] Baumer

Conference Session

Engineering and Mathematics Potpourri

Collection

2009 Annual Conference & Exposition

Authors

Murray Teitell, DeVry University, Long Beach

Tagged Divisions

Mathematics

? Mechatronics4 is a subject that joinselectrical engineering with mechanical engineering. Energy systems are mechatronics systems inthat they are part mechanical and part electrical and electronic. The students’ challenge was tooptimize an energy plan for the U. S. for the next 50 years. The class divided themselves intodifferent factions. Since genetic algorithms lend themselves to systems that have indefinitefactors, this was the category of algorithm that was chosen for this investigation. A population of different energy resources was compiled. For each faction, a spreadsheet wascreated which contained a detailed summary of the energy plan components. Each faction thencreated and applied a genetic algorithm to their starting plans. Genetic

Conference Session

Mathematics Division Technical Session 4

Collection

2016 ASEE Annual Conference & Exposition

Authors

Sandra Nite, Texas A&M University; G. Donald Allen; Jim Morgan, Charles Sturt University; Ali Bicer, Texas A&M University; Robert M. Capraro, Texas A&M University

Tagged Divisions

Mathematics

interventions because of theimportance of mathematics knowledge and skills in science and engineering coursesrequired for successfully completing the coursework leading to a degree in engineering.Recruitment and retention of engineering students is vital to the progress of Americaneconomy and ability to solve problems to address the needs of an ever-changingtechnological world1, 2. College calculus success is highly correlated to engineeringretention3. Bridge programs designed to increase success for engineering majors werepopular in the 1990's but then waned to some degree. A thorough classification ofprograms in use was conducted in 2002, but insufficient data was reported for researchersto conduct a meta-analysis4. Several common characteristics of

Conference Session

Mathematics Division Technical Session 1

Collection

2018 ASEE Annual Conference & Exposition

Authors

Franziska Dorothea Wehner, Technische Universität Darmstadt

Tagged Divisions

Mathematics

Curriculum," Journal of Engineering Education, vol. 93, no. 3, pp. 253-257, 2004.[3] C. McLoughlin and B. Loch, "Building cognitive bridges in Mathematics: Exploring the role of screencasting in scaffolding flexible learning and engagement," in Show me the Learning. Proceedings ASCILITE 2016 Adelaide, ASCILITE 33rd International Conference of Innovation, Practice and Research in the Use of Educational Technologies in Tertiary Education 2016, Adelaide, Australia, November 27-30, 2016, S. Barker, S. Dawson, A. Pardo, C. Colvin, Eds. pp. 412-420.[4] M. Anastasakis, C. L. Robinson, and S. Lerman, "Links between students’ goals and their choice of educational resources in undergraduate mathematics

Conference Session

Mathematics Division Technical Session 3

Collection

2019 ASEE Annual Conference & Exposition

Authors

Maizey Benner, Purdue University; Daniel M. Ferguson, Purdue University; Matthew W. Ohland, Purdue University; Behzad Beigpourian, Purdue University

Tagged Divisions

Mathematics

on how to use the system. These videos were created for both the instructorand the students on how to operate the s Rater Practice system. The format of video instructionused is a sequential-step explanation and is a form of observational learning, which is learningthrough the behavior of others. Observational learning through video allows students to see a“flawless performance” of the task, and can be viewed repeatedly as needed [18]. Theinstructional videos on Rater Practice should be sufficient in learning how to operate thesimulation and can be viewed and practiced until the system is understood. If studentscomprehend the instructional videos, the barrier to many simulations - the instructions beingnon-intuitive - would be

Conference Session

The Transition from Secondary to College Mathematics

Collection

2012 ASEE Annual Conference & Exposition

Authors

Helen M. Doerr, Syracuse University; Andria Costello Staniec, Syracuse University; AnnMarie H. O'Neil, C.S. Driver Middle School

Tagged Divisions

Mathematics

in any complex human system, such as education, there is muchvariation present, most of which cannot be controlled in any meaningful sense. Hence, we havetaken a design-based approach that can yield improvements that can be measured locally andaggregated over time, while at the same time giving us insight into how to be effective inimplementing change.References[1] Gattis, C., Hill, B., & Lachowsky, A. (2007). A successful engineering peer mentoring program. In American Society for Engineering Education Annual Conference and Exposition, Conference Proceedings.[2] Jones, S., Rusch, K., Waggenspack, W., Seals, R., & Henderson, V. (2010). S-STEM: Eng^2 scholars for success engineering engagement. In American Society for

Conference Session

Bridging and Freshman Programs

Collection

2008 Annual Conference & Exposition

Authors

Wendy James, Oklahoma State University; Karen High, Oklahoma State University

Tagged Divisions

Mathematics

understanding the field.Some of the research questions would be best explored by a math-educator who can look throughtheir lens of expertise of common students’ K-12 experience based on current policies oncontent, the theories of semiotics, and theories of cognitive development in a social environment.Other questions are best tackled by engineering faculty, especially those which describe thenature of student misconceptions and lack of abilities in using mathematics in engineeringcourses. Page 13.627.16References1. Fink, L.D., Ambrose, S., & Wheeler, D. (2005). Becoming a professional engineering educator: A new role for a new era. Journal

Conference Session

Mathematics Division Technical Session 2

Collection

2018 ASEE Annual Conference & Exposition

Authors

Jose Roberto Portillo, Universidad Galileo; Alberth E Alvarado, Universidad Galileo; Jorge Samayoa Ranero, Universidad Galileo

Tagged Topics

Diversity

Tagged Divisions

Mathematics

instructor is incharge of presenting a clarification of the appeal during the next session.Multiple Application Activities: Besides tRAT, this part is considered the most important part ofthe session. Here, teams apply the gained knowledge to solve carefully designed applicationactivities. These activities are designed following the well-known 4-S Framework, i.e. SignificantProblem, Same Problem, Specific Choice and Simultaneous Report. Michaelsen [13] describesthe 4-S approach as follows: a. Address a significant problem that demonstrates a use of a particular concept. b. Make a specific choice among clear alternatives. c. Work on the same problem as other teams, so each team will care about the conclusions and rationales of the other

Conference Session

Mathematics Division Technical Session 1

Collection

2017 ASEE Annual Conference & Exposition

Authors

Sandra Nite, Texas A&M University; G. Donald Allen, Texas A&M University; Ali Bicer, Texas A&M University; Jim Morgan, Charles Sturt University; Vanessa Mae Warren, Texas A&M University; Luciana Barroso, Texas A&M University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

mathematical abilities [2]. Therefore, students who did not have the necessarymathematical abilities to be successful in engineering courses needed help to pursue theirengineering majors and complete their engineering degrees. In order to retain and supportengineering majors, many universities have offered bridge programs in mathematics for students[3][4]. Such programs were common in the 1990’s and have increased again recently as the needhas been recognized widely. Bridge programs aimed to increase engineering students’ retentionby strengthening their mathematical competencies. There are many types of bridge programs indifferent disciplines, especially science and mathematics. Bridge mathematics programs weremore common in mathematics than science

Conference Session

Mathematics Division Technical Session 1: Best Practices in Engineering Math Education

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Charles Lam, California State University, Bakersfield; Melissa Danforth, California State University, Bakersfield; Ronald Hughes, California State University, Bakersfield

Tagged Divisions

Mathematics

give sufficient time to refine products. 4. Any extra materials introduced should not be part of the graded curriculum. This makes the learning less stressful.AcknowledgmentThis paper is based upon work supported by the National Science Foundation under Grant No.1430398. Any opinions, findings, and conclusions or recommendations expressed in thismaterial are those of the author(s) and do not necessarily reflect the views of the NationalScience Foundation.References[1] US Census Bureau, Census Data for Kern County, CA, 2010 census and 2019 estimate.[2] V. L. Austin, "Teachers’ beliefs about co-teaching," Remedial and Special Education, vol. 22, pp. 245-256, 2001.[3] E. Cramer and A. Nevin, "A mixed methodology analysis of co-teacher

Conference Session

Mathematics Division Technical Session 3

Collection

2013 ASEE Annual Conference & Exposition

Authors

Jeremiah J. Neubert, University of North Dakota; Deborah Worley, University of North Dakota; Naima Kaabouch, University of North Dakota; Mohammad Khavanin, Professor of Mathematics at University of North Dakota

Tagged Divisions

Mathematics

the (b)curve. Figure 1: Unmanned Aerial Vehicles, such asThe plane can fly 15 miles of the spiral before it must return the one shown in (a), are playing anto refuel. increasing role in search and rescue. The desired search path is shown in (b).The distance travelled by the UAV for any given value ofis given as 1) Find the equation of the distance travelled by the UAV at any point . 2) What is the value of s when the plane has gone 15 miles? 3) Assuming the total range of the plane is 17.5 miles. Can the plane make it

Conference Session

The Transition from Secondary to College Mathematics

Collection

2012 ASEE Annual Conference & Exposition

Authors

Galen E. Turner III, Louisiana Tech University; Kelly B. Crittenden, Louisiana Tech University; James D. Nelson, Louisiana Tech University; Heath Tims, Louisiana Tech University

Tagged Divisions

Mathematics

schools for a particular college or university as well as the number ofstudents who enroll from those high schools are useful in evaluating future outreach programs.If we label the number of high schools who have graduates attending a university and the numberof students, Fs, from each school (s) attending the university, then we can characterize the usefuloutput of the feeder high schools through a single number, the f-index, for a given academic year.In any given year, an institution of higher education has index f if f of the number of feeder highschools, H, have at least f students each entering the institution where the other (H –f) schoolshave less than f students each. Cumulative f-indices can be easily created for periods of

Conference Session

Engineering and Math Potpouri

Collection

2008 Annual Conference & Exposition

Authors

Jeffrey Fong, National Institute of Standards and Technology; James Filliben, National Institute of Standards and Technology; Alan Heckert, National Institute of Standards and Technology; Roland deWit, National Institute of Standards and Technology

Tagged Divisions

Mathematics

To identify which factors/effects are important.Response Surface To maximize or minimize a response. designs To reduce variation by locating a region where it is easier to manage. To make a process robust (note: this objective may often be accomplished with screening designs rather than with response surface designs).Regression To estimate a precise model, quantifying the dependence of modeling response variable(s) on process inputs. Page 13.370.12© American Society for Engineering

Conference Session

Computers and Software in Teaching Mathemathetics

Collection

2009 Annual Conference & Exposition

Authors

Raymond Jacquot, University of Wyoming; Jeffrey Anderson, University of Wyoming; David Walrath, University of Wyoming

Tagged Divisions

Mathematics

Dimensionless Time, t/L Figure 2. Temperature as a Function of Time for Nine LocationsAnother way to present the solution is a 3-D plot of temperature as a function of location andtime as shown in Figure 3. Page 14.1044.4 Pres s En

Conference Session

The Use of Computers in Teaching Mathematics

Collection

2008 Annual Conference & Exposition

Authors

Janet Callahan, Boise State University; Seung Youn Chyung, Boise State University; Joanna Guild, Boise State University; William Clement, Boise State University; Joe Guarino, Boise State University; Doug Bullock, Boise State University; Cheryl Schrader, Boise State University

Tagged Divisions

Mathematics

DelineatorTM. The Style Delineatormeasures four qualities of concreteness, abstraction, sequence, and randomness in people’sperception toward, and ordering of, their world.9 As shown in Table 1, dominant learning stylesare identified with one of four style types: concrete-sequential (CS), abstract-sequential (AS),concrete-random (CR), and abstract-random (AR). Every individual has the ability to orienthimself or herself toward all four styles. However, people tend to have strong orientation towardone or two, or sometimes even three, dominant style(s). The Style Delineator reveals a score foreach style type, identifying the dominant learning style(s) among the 4 types. For example, aperson might score 39, 19, 26, and 16 for CS, AS, CR, and AR

Conference Session

Mathematics Division Technical Session 5: From Functions to Big Data–A Hands-on Challenge

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Rajendran Swamidurai, Alabama State University ; Cadavious M. Jones; Carl Pettis; Uma Kannan

Tagged Topics

Diversity

Tagged Divisions

Mathematics

from Auburn University in 2014. He is a contributor to the Australian Maths Trust, and member of the MASAMU international research group for mathematics.Dr. Carl Pettis Carl S. Pettis, Ph.D. Professor of Mathematics Department of Mathematics and Computer Science Al- abama State University Administrative role: Interim Associate Provost Office of Academic Affairs Alabama State UniversityDr. Uma Kannan Dr. Uma Kannan is Assistant Professor of Computer Information Systems in the College of Business Administration at Alabama State University, where she has taught since 2017. She received her Ph.D. degree in Cybersecurity from Auburn University in 2017. She specialized in Cybersecurity, particularly on

Collection

2016 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

: b n ∫ f ( x)dx = lim ∑ f (a + i∆x)∆x. a n→∞ i =1This definition will be called the limit definition of Riemann integral throughout this work. Thisdefinition of Riemann integral is taught at early stages of calculus education, therefore Riemannsum approximation needs to be known by the Numerical Methods/Analysis students to be able tosolve a question related to the Riemann integral’s limit definition.___________________________________________________________________________Special thanks to Drs. Deborah A. Trytten and Gizem S. Aydin for their valuable discussions and input during thepreparation of the IRB approved form.This definition

Conference Session

Mathematics Division Technical Session 2

Collection

2016 ASEE Annual Conference & Exposition

Authors

Aimee Cloutier, Texas Tech University; Jerry Dwyer, George Washington University; Sonya E. Sherrod, Texas Tech University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

, interested readers are welcome to contact the authorswho will be happy to share lesson plans and suggestions.References 1. National Math and Science Initiative. (2013). Increasing the achievement and presence of under- represented minorities in STEM fields. Report by the National Math and Science Initiative. 2. Crawford, M. Transformations: Women, Gender and Psychology. New York: McGraw-Hill: 2006. 3. Nassar-McMillan, S. C., Wyer, M., Oliver-Hoyo, M., Schneider, J. (2011). New tools for examining undergraduate students’ STEM stereotypes: Implications for women and other underrepresented groups. New Directions for Institutional Research, 2011(152), 87-98. 4. Blickenstaff, J. C. (2005). Women and science careers

Conference Session

Mathematics Division Technical Session 3

Collection

2015 ASEE Annual Conference & Exposition

Authors

Eliud Quintero, Tecnologico de Monterrey (ITESM); Patricia Salinas, Tecnologico de Monterrey (ITESM)

Tagged Topics

Diversity

Tagged Divisions

Mathematics

. Revista Latinoamericana de Investigación En Matemática Educativa, 12(3), 355– 382. 5. Noss, R., Hoyles, C., Mavrikis, M., Geraniou, E., Gutierrez-Santos, S., & Pearce, D. (2009). Broadening the sense of “dynamic”: A microworld to support students’ mathematical generalisation. ZDM—The International Journal on Mathematics Education, 41(4), 493–503. doi:10.1007/s11858-009-0182-8 6. Salinas, P., Quintero, E., & González-Mendívil, E. (2014). An environment to promote a visual learning of Calculus. In H. R. Arabnia, A. Bahrami, L. Deligiannidis, & G. Jandieri (Eds.), Proceedings of the International Conference on Frontiers in Education: Computer Science and Computer Engineering (pp. 425–429). Las

Conference Session

Computers and Software in Teaching Mathematics

Collection

2010 Annual Conference & Exposition

Authors

Cynthia Young, University of Central Florida; Michael Georgiopoulos, University of Central Florida; Tace Crouse, University of Central Florida; Alvaro Islas, University of Central Florida; Scott Hagen, University of Central Florida; Cherie Geiger, University of Central Florida; Melissa Dagley-Falls, University of Central Florida; Patricia Ramsey, University of Central Florida; Patrice Lancey, University of Central Florida

Tagged Divisions

Mathematics

AC 2010-171: EXCEL IN MATHEMATICS: APPLICATIONS OF CALCULUSCynthia Young, University of Central Florida Cynthia Young is a Professor in the Department of Mathematics in the UCF College of Sciences and a Co-PI of the NSF-funded S-STEM program at UCF entitled the "Young Entrepreneur and Scholar(YES) Scholarship Program" as well as the NSF-funded STEP program entitled "EXCEL:UCF-STEP Pathways to STEM: From Promise to Prominence." Dr. Young's research interests are in the mathematical modeling of atmospheric effects on laser beams. She currently has projects with the Office of Naval Research and the Naval Research Laboratory investigating atmospheric propagation in the marine

Conference Session

Mathematics Division Technical Session 1: Best Practices in Engineering Math Education

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Guenter Bischof, Joanneum University of Applied Sciences; Maximilian Brauchart, Joanneum University of Applied Sciences; Patrick Jenni, Joanneum University of Applied Sciences; Jeremias Pirker, Joanneum University of Applied Sciences; Julian Sachslehner, Joanneum University of Applied Sciences; Christian J. Steinmann, Joanneum University of Applied Sciences; Tobias Markus Zörweg, Joanneum University of Applied Sciences

Tagged Divisions

Mathematics

, dynamic vibration absorbers are frequently implemented with ahydraulic or frictional component in order to transform kinetic energy of vibration into heat.Figure 2 shows the frequency response s of the main mass m1 as a function of normalizedfrequency, i.e., the driving frequency divided by the resonance frequency (ω/ωc) of thedamped primary system. The blue curve shows the displacement of the primary systemwithout absorber. The red curve represents the response function of the main mass after thetuned dynamic absorber (m2 ≈ 0.14 m1) has been attached. Two new resonance frequencieshave been created, located above and below the original resonance frequency. Figure 2: Primary mass displacement (blue: without absorber, red: with absorber)The

Conference Session

Project and Model-Based Mathematics

Collection

2007 Annual Conference & Exposition

Authors

Sharlene Katz, California State University-Northridge; Bella Klass-Tsirulnikov, Sami Shamoon College of Engineering (formerly Negev Academic College of

Tagged Divisions

Mathematics

hardlims(x) = 4 5+1, x 2 0Thus the input of the single neuron is an R x 1 matrix p, and its final output is a scalar a =hardlims(Wp + b), depending upon whether the result n = Wp + b is positive or negative.A neural network can contain multiple neurons. Each neuron receives the same input vector, p,but produces a separate output. A network of S neurons has S outputs and can be represented ina manner similar to the single neuron network shown in figure 1. However, the weights are nowthe rows of a weight matrix W of size S x R. Accordingly, b, n, and a become column vectors oflength S, or S x 1 matrices. Thus, for an S neuron neural network with input p, we obtain Soutputs, which are contained in the S x 1 matrix

Conference Session

Applied Mathematics

Collection

2007 Annual Conference & Exposition

Authors

S.K. Sen, Florida Institute of Technology; Gholam Ali Shaykhian, NASA

Tagged Divisions

Mathematics

Page 12.1256.2sequences (stretches) of the same digit(s), say, 1, the overall sequence might be random though.Long sequences of the same digits, even though generated by a random process would reduce thelocal randomness of a sample. That is, a sample could only be globally random for sequences of,say, 100,000 digits while it might not appear at all random when a sequence of less than 500digits is considered. Usually in a statistical environment, the numeric sequence need to be a large one (30 or moreentries) before we could talk about whether the sequence is random or not. For example, in atossing of a coin denoting a head by 1 and a tail by 0, if we get 15 0’s successively, can we saythat the coin is biased statistically? The answer is no