Conference Session

Improving the Mathematical Preparation of Students

Collection

2006 Annual Conference & Exposition

Authors

Shuki Aroshas, Technion-Israel Institute of Technology; Igor Verner, Technion-Israel Institute of Technology; Avi Berman, Technion - Israel Institute of Technology

Tagged Divisions

Mathematics

1A). With development of the Technion Mathematics Web tutoringsystem the classes were reduced to one hour a week (Figure 1B). A. Lectures 4 h Classes 2 h B. Lectures 4 h Classes 1 h Web tutorials C. Lectures 4 h Classes 1 h Web tutorials Supplementary applications classes 1-2 h Figure 1. Multivariable Calculus outlines: A. Conventional; Page 11.779.4 B. Computerized; C. Applications integratedIn our study the course

Conference Session

Mathematics in Transition

Collection

2006 Annual Conference & Exposition

Authors

Dale Buechler, University of Wisconsin-Milwaukee; Christopher Papadopoulos

Tagged Divisions

Mathematics

m x 0.2m). (b) Areas approximated by using common shapes.3. Measuring and predicting the behavior of beamsTwo basic experiments were prepared, each involving three aluminum cantilevered beams. Thefirst experiment tested the effect of varied beam depth (Figure 2a); these beams had commonwidths and lengths. The second experiment tested the effect of varied beam width (Figure 2b);these beams had common depths and lengths. For each beam, increasing weights weresuccessively hung from the free end. A dial gage was positioned (using a magnetic mounts) tomeasure the deflection of the free end. Because the gage itself exerts a force on the end of thebeam, for each specified applied weight, the effect of the gage was eliminated by manuallylifting

Conference Session

Integrating Math, Science, & Engineering

Collection

2006 Annual Conference & Exposition

Authors

Phillip Smith, New Mexico State University

Tagged Divisions

Mathematics

×(∇×V )+ ] = B−∇p+∇{µ(∇·V )−∇×[µ(∇×V )]+∇[(ζ + µ)∇·V ]}, (1) 2 ∂t 3which is the Navier-Stokes equation for a compressible fluid flow in vector notation and in whichρ is the density of the fluid, V is the vector velocity of the fluid, µ is the coefficient of dynamicviscosity of the fluid, ζ is the second coefficient of viscosity, p is the pressure, t is the time, andB is the body force (e.g. the gravitational vector); Dh Dp ρ = + ∇ · (k∇T ) + Φ, (2) Dt Dtis the energy equation for a compressible fluid flow in vector notation and in

Conference Session

Mathematics in Transition

Collection

2006 Annual Conference & Exposition

Authors

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

Tagged Divisions

Mathematics

this kind are called infinite.2. Bijection. Next we define the notion of bijection. Given two arbitrary sets, A and B, afunction f is a rule that associates a unique element b=f(a) of B to each element a of A. Instead ofsaying "a function", we may use the term: "mapping f: A 1 B" between A and B, or from A toB. A mapping f: A 1 B is said to be one-to-one if different elements of A are mapped intodifferent elements of B. A mapping f: A 1 B is said to be onto B if for each element b of B thereis an element a of A such that b=f(a). Informally speaking, a mapping f: A 1 B is onto B, if Bcan be covered by the elements of A, using the rule b=f(a). A mapping that is not onto B, is saidto be into B. Finally, a mapping f: A 1 B is called bijective (or

Conference Session

Mathematics in Transition

Collection

2006 Annual Conference & Exposition

Authors

Josue Njock-Libii, Indiana University-Purdue University Fort Wayne

Tagged Divisions

Mathematics

∞ ( a ) r ( b) r ( x k )2 F1 ([ a , b],[ c], x ) ≡ ∑ k , (1) r=0 ( c) r r !where ( a ) r is the Pochhammer symbol 4, for which Γ (a + r )( a ) r = a (a + 1)(a + 2)...(a + r − 1) = , (2) Γ (a )and Γ denotes the gamma function given by the Euler Integral of the second kind 3.Hypergeometric functions are solutions to the hypergeometric differential equationz(1 − z) y ′′ + [c − (a + b + 1) z] y ′ − aby = 0 . (3)Using the Froebenius method, the complete solution to this

Conference Session

Use of Technology in Teaching Mathematics

Collection

2006 Annual Conference & Exposition

Authors

Arthur Snider, University of South Florida; Sami Kadamani, Hillsborough Community College

Tagged Divisions

Mathematics

. κ x 2 +κ y 2 ZThis example illustrates the straightforward extension of the procedure to three dimensions andthe transcendental equation that the Robin boundary condition invokes for the eigenvalues.Example 3. Steady state heat flow in a cylindrical sector with facial heat sources (homogenousLaplace equation in the three dimensions inside a partial cylinder, nonhomogenous Dirichletcondition on the top and one flat side, homogenous Dirichlet conditions on the bottom and thecurved wall, and a homogenous Neumann condition on the other flat side): 2∇ Ψ =0Ψ ( ρ ,θ , 0 ) = Ψ ( b,θ , z ) = 0,∂Ψ ( ρ , 0, z ) = 0, Ψ ( ρ , Θ, z ) = f θ = Θ ( z, ρ ) ,∂θΨ ( ρ , θ , Z ) = f z = Z (θ , ρ )The USFKAD solution:Ψ = Ψ1 + Ψ 2Ψ = ∑ κ z ∫ ∞0 d κ ρ : z sin

Conference Session

Integrating Math, Science, & Engineering

Collection

2006 Annual Conference & Exposition

Authors

Leslie Keiser, University of Tulsa; William Hamill, University of Tulsa; Bryan Tapp, University of Tulsa; William Potter, University of Tulsa; Jerry McCoy, University of Tulsa; Peter LoPresti, University of Tulsa; Donna Farrior, University of Tulsa; Shirley Pomeranz, University of Tulsa

Tagged Divisions

Mathematics

6 . L e a rn in g a s m e m o r iz in g in ta c t L e a r n i n g a s c o n s tr u c t i n g a n d u n d e r s t a n d i n g k n o w le d g e I V . U s e f u ln e ss o f M a th e m a tic s F a ll: 5 .3 4 S p r in g : 4 .7 1 7 . M a th e m a tic s a s a s c h o o l s u b je c t w ith M a th e m a tic s a s a u s e fu l e n d e a v o r little v a lu e in e v e ry d a y life o r fu tu re w o rkFor example, with respect to Dimension 1: The Nature of Mathematical Knowledge -Composition of Mathematical Knowledge, a response of 1 indicates that a student feels thatmathematical knowledge

Conference Session

Mathematics in Transition

Collection

2006 Annual Conference & Exposition

Authors

Andrew Grossfield, Vaughn College of Aeronautics

Tagged Divisions

Mathematics

measure equal to zerowhile the measure of the set of transcendental numbers is one. Transcendental numbers are notrare. The transcendental numbers are not observed in common use because it is impossible towrite them exactly. Like π and e, they must be approximated with rational numbers.Properties of numbersIn textbooks, the properties of numbers are described in the laws. The properties of numbersinvolving the operations of addition, multiplication and powers and the inverses of theseoperations are called the algebraic properties. The properties of numbers concerning therelations >, ≥, b and b > c, then a > c Distance d( x , x ) = 0 if x ≠ y then d( x , y ) > 0

Conference Session

Integrating Math, Science, & Engineering

Collection

2006 Annual Conference & Exposition

Authors

Sarah Maor, Technion-Israel Institute of Technology; Igor Verner, Technion-Israel Institute of Technology

Tagged Divisions

Mathematics

Learning activities1. Tessellations A. Mathematical Understanding harmonic Seminar presentations on golden (16 hours) concepts of dimensions and their use in section, Fibonacci sequence, tessellations design art, music, and architecture logarithmic spiral, and applications. B. Practice in solving Acquiring basic skills in Drawing logarithmic spirals and mathematical analysis of proportions, tessellation fragments, analyzing problems related to symmetry, and drawing basic geometrical figures and their tessellations tessellations

Conference Session

Improving the Mathematical Preparation of Students

Collection

2006 Annual Conference & Exposition

Authors

Jenna Carpenter, Louisiana Tech University; Ruth Ellen Hanna, Louisiana Tech University

Tagged Divisions

Mathematics

(Assessment and LEarning inKnowledge Spaces)1 in an effort to provide a more effective mathematics tutoring program forour students. The goals were to 1) increase student retention and success in freshman andsophomore-level mathematics courses (such as calculus, which all engineering majors take), and2) increase the willingness of students to utilize the available tutorial services. Note that “studentsuccess” is defined as “making an “A”, “B” or “C” in the course” (since all engineering andscience majors are required to earn a grade of “C” or higher in all math courses which areprerequisites for other courses).ALEKS is a web-based system (versus software-based) that can be accessed from any computerwith web access and a java-enabled web browser. The

Conference Session

Integrating Math, Science, & Engineering

Collection

2006 Annual Conference & Exposition

Authors

Stephen Pennell, University of Massachusetts-Lowell; Peter Avitabile, University of Massachusetts-Lowell; John White, University of Massachusetts-Lowell

Tagged Divisions

Mathematics

voltage E = E0.)b) Show that q approaches a constant value as t → ∞.c) How long does it take q to reach 95% of its limiting value?d) What fraction of its limiting value does q reach after one time constant (t = 1)?4. Response to sinusoidal input.a. Solve the IVP (2) for ε = cos (ω t ) (which corresponds to an input voltageE = E0 cos (ωT / RC ) ).b. Show that the response q from part a contains a transient term qtr that approaches 0 as t → ∞and a steady-state term qss that does not approach 0.c. Express qss in the form qss = D cos (ω t − α ) . (See pages 184 and 185 of the textbook. Yourexpressions for D and α will contain ω .)d. Plot D vs. ω on a loglog plot for 0.01 ≤ ω ≤ 1000 . (Notice that the amplitude of the responsedecreases as ω increases

Conference Session

Use of Technology in Teaching Mathematics

Collection

2006 Annual Conference & Exposition

Authors

Peter Avitabile, University of Massachusetts-Lowell; Jeffrey Hodgkins, University of Massachusetts-Lowell; Tracy Van Zandt, University of Massachusetts-Lowell

Tagged Divisions

Mathematics

. “Employers Demand New Skills”, Machine Design, Sept 199210 Knight,C.V., McDonald,G.H., “Modernization of a Mechanical Engineering Laboratory using Data Acquisition with LABVIEW”, ASEE Session 226611 Onaral,B., “A Road Less Traveled”, ASEE Prism, September 199212 Wankat,P., Oreovicz,F., “Learning Outside the Classroom”, ASEE Prism, p32, Jan 200013 McConnaughay,K., Welsford,I., Stabenau,E., “Inquiry, Investigation, and Integration in Undergraduate Science Curricula”, Council on Undergraduate Research Quartley, pp14-18, September 199914 Course Webpage for Mechanical Engineering Laboratory I – 22.302 http://faculty.uml.edu/pavitabile/22.302/web_download/Mech_lab_PDF_downloads.htm15 Specific Course Webpage Tags to PDF File and

Conference Session

Use of Technology in Teaching Mathematics

Collection

2006 Annual Conference & Exposition

Authors

Sabina Jeschke, Technische Universitat Berlin, Inst. f. Mathematik; Lars Knipping, Technische Universitat Berlin; Raul Rojas, Freie Universitat Berlin; Ruedi Seiler, Technische Universitat Berlin

Tagged Divisions

Mathematics

Engineering Systems: 9th International Conference (KES 2005), Proceeding, Part I, volume 3681 of Lecture Notes in Computer Sciences, pages 744–750. Springer Verlag, September 2005.9. Gerald Friedland, Lars Knipping, Raúl Rojas, Joachim Schulte, and Christian Zick. Evaluationsergebnisse zum Einsatz des E-Kreide Systems im Wintersemester 2003/2004. Technical Report B-04-06, Fachbereich Mathematik und Informatik, Freie Universität Berlin, June 2004.10. Gerald Friedland, Lars Knipping, Joachim Schulte, and Ernesto Tapia. E-Chalk: A lecture recording system using the chalkboard metaphor. Interactive Technology and Smart Education (ITSE), 1(1):9–20, February 2004.11. Gerald Friedland, Lars Knipping, and Ernesto Tapia. Web based lectures

Conference Session

Use of Technology in Teaching Mathematics

Collection

2006 Annual Conference & Exposition

Authors

Melinda Z. Kalainoff, U.S. Military Academy; Dawn E. Riegner, U.S. Military Academy; Matthew Deloia, U.S. Military Academy; Russ Lachance, U.S. Military Academy; Andrew Biaglow, U.S. Military Academy

Tagged Divisions

Mathematics

± standarddeviation (sample size). Cadets were asked to rank their response on a scale from 1 to 5,with 1 being the least favorable response and 5 being most favorable. Page 11.589.9Instructor / Question Instructor’s test Instructor’s standard hour hours A / 9a1 82.4 ± 39.3 (17) 55.6 ± 50.2 (54) B / 9a1 35.3 ± 49.3 (17) 23.6 ± 42.9 (55) C / 9a1 100.0 ± 0.0 (19) 100.0 ± 0.0 (20) A / 9b2 82.4 ± 39.3 (17) 70.4 ± 46.1 (54) B / 9b2 29.4 ± 47.0 (17) 29.1 ± 45.8 (55

Conference Session

Innovative Instruction Strategies

Collection

2006 Annual Conference & Exposition

Authors

Jonathan Lambright, Savannah State University

Tagged Divisions

Mathematics

equations.Students must be taught the fundamentals of developing and solving these numericalapproximations by hand. However, theory must be combined with technology and hands onpractice to emphasize the need for tools such as Matlab and Excel in solving engineeringproblems through numerical approximations. By implementing such tools in the classroom,students sharpen their programming and analytical thinking skills. In addition, students canexperience the need for and the power of these tools in solving real world problems and use theexperience to creatively think of newer ways to solve engineering problems.References[1] Hanselman, D., and Littlefield, B., “Mastering MATLAB 7: A Comprehensive Tutorial andReference”, Prentice Hall Publishers.[2] Chapra, S.C

Conference Session

Use of Technology in Teaching Mathematics

Collection

2006 Annual Conference & Exposition

Authors

Paul Wlodkowski, Maine Maritime Academy

Tagged Divisions

Mathematics

-disciplinary interaction among engineering, physics, and mathematics. In addition, he holds an appointment with the Academy’s Loeb-Sullivan School, a graduate program in International Business and Logistics. He has sixteen years of industrial, manufacturing and academic experience that encompasses the fields of materials engineering, applied physics, reliability engineering, acoustics, applied statistics, shock and vibration, sensor design, radiation effects, and technical marketing. As the Principal Staff Engineer and Program Manager at Wilcoxon Research, Inc., he led several of the Company's high technology programs in the research, development, and commercialization of directional, acoustic

Conference Session

Integrating Math, Science, & Engineering

Collection

2006 Annual Conference & Exposition

Authors

Bruno Osorno, California State University-Northridge

Tagged Divisions

Mathematics

2006-783: STUDENT ENGAGEMENT THROUGH MATHEMATICALAPPLICATIONS IN ELECTRICAL POWER SYSTEMSBruno Osorno, California State University-Northridge Bruno Osorno has been teaching for over 20 years. He has written over 20 technical papers all related to electrical engineering. His interests are reasearch in engineering education, application of new technologies into the curriculum and computer applications in electric power systems. He received an MSEE from the University of Colorado, Boulder and continued studies towards a PHD degree resulting in ABD. He has a great deal of industrial and consulting experience, more recently he was involved in consulting for NASA-JPL in the analysis of an electrical

Conference Session

Innovative Instruction Strategies

Collection

2006 Annual Conference & Exposition

Authors

John Schmeelk, Virginia Commonwealth University

Tagged Divisions

Mathematics

applications in allareas of research including medical research. A patient can be diagnosed as having ananeurysm by studying an angiogram. An angiogram is the visual view of the bloodvessels whereby the edges are highlighted through the implementation of edge detectors.This process is completed through convolution, wavelets and matrix techniques. Someillustrations included will be vertical, horizontal, Sobel and wavelet edge detectors.I. IntroductionTo help motivate this paper, we provide an introduction to some interesting problems inimage processing implementing matrix techniques, partial derivatives and convolutions.Section (2) provides an introduction to matrix and partial derivatives and how they areapplied to the pixels to obtain the gray level

Conference Session

Improving the Mathematical Preparation of Students

Collection

2006 Annual Conference & Exposition

Authors

Mark Inlow, Rose-Hulman Institute of Technology

Tagged Divisions

Mathematics

violations and IID violations are much more difficult to handle, theIID assumption is the more crucial of the two.In spite of this fact, we believe introductory statistics courses for engineers, and thecorresponding texts, neither adequately stress the importance of the IID assumption nor provideadequate tools for assessing it. Our belief is based on observing students in upper level statisticscourses unthinkingly apply IID analysis methods to data which is blatantly non-IID. We becameaware of the extent of this problem when students in an advanced statistics course, after spendinga week on time series analysis, blithely computed a confidence interval for the mean of thefollowing nonstationary data using the IID formula

Conference Session

Improving the Mathematical Preparation of Students

Collection

2006 Annual Conference & Exposition

Authors

Elton Graves, Rose-Hulman Institute of Technology

Tagged Divisions

Mathematics

school with advanced placement credits in mathematics to take additional mathematicscourses beyond the courses required for their major.Creating courses and tracts of interestOver the past few years the Rose-Hulman Mathematics Department has made several changes toencourage students to take upper level mathematics courses. One of the major changes was tochange the courses required to get a degree in mathematics. Until the late 1900’s Rose had onlyone tract for a degree or major in mathematics. We have now split this into four different tracts.Our first tract is for the traditional mathematics major who wants to go to graduate school andearn and masters degree or doctorate in mathematics. This tract is not a tract that would interestmost