Applied Mathematics Courses Research Articles

Improvement of Mathematical Problem Solving Ability Through Problem Based Learning Model In Applied Mathematics Course II In Industrial Engineering Program of Polytechnic of South Aceh

This research is a quantitative research by true experimental design. Research design is random, pre test and post test. Sample is prepared randomly by two group; experiment and control group. Experiment group is prepared by problem based learning with 13 students in this group, while control group is taught by conventional method with 10 students in this group. Tests are applied in data collecting, then analyzed by t-test. Data analysis shows at a = 0,05 there was dan = 1,72 atau . It can be concluded that the increase in mathematical problem solving from experiment group is relatively better than those in control group in Applied mathematics II Course in Industry Technics Study Program, South Aceh Polytechnic.

Moving beyond the barriers: supporting meaningful teacher collaboration to improve secondary school mathematics

The Collaborative Teacher Inquiry Project was a professional development initiative that sought to improve the teaching and learning of Grade 9 Applied mathematics by encouraging teachers to work collaboratively. The project brought together Grade 9 Applied mathematics teachers from 11 schools across four neighboring public school boards in the same geographic area of a large urban city in Southern Ontario, Canada. Teachers formed learning communities as a result of the Collaborative Teacher Inquiry Project through active collaboration to further teachers’ knowledge about teaching the Grade 9 Applied mathematics course and in developing teaching materials. Although it was reported that there were barriers to collaboration, teachers described various strategies that were (or could be) implemented to overcome these barriers. Teachers were enthusiastic in continuing to creatively find solutions to combat barriers as they saw the overall benefits of collaboration to their professional growth and noticed an increase in student engagement and achievement.

A mechanical analog of the two-bounce resonance of solitary waves: Modeling and experiment.

We describe a simple mechanical system, a ball rolling along a specially-designed landscape, which mimics the well-known two-bounce resonance in solitary wave collisions, a phenomenon that has been seen in countless numerical simulations but never in the laboratory. We provide a brief history of the solitary wave problem, stressing the fundamental role collective-coordinate models played in understanding this phenomenon. We derive the equations governing the motion of a point particle confined to such a surface and then design a surface on which to roll the ball, such that its motion will evolve under the same equations that approximately govern solitary wave collisions. We report on physical experiments, carried out in an undergraduate applied mathematics course, that seem to exhibit the two-bounce resonance.

Analysis of experience in employing the networked teaching/learning method in the applied mathematics

This article describes the first experience with networked teaching/learning method Applied Mathematics course in teaching. Of networked teaching/learning method provides an active students and teacher use of online technologies and special software. The method of mathematics courses is not a trivial matter and requires a search for new didactic solutions.

WMI2, the student's on-line symbolic calculator

Student activities focused on discovering mathematics play an important role in the teaching and learning process. WebMathematics Interactive (WMI2) was developed to offer a fast and user-friendly on-line web interface to enhance the quality of both theoretical and applied mathematics courses. For the teacher, in the classroom, it provides immediate numerical computations, algebraic manipulations and graphical representations. For our students, WMI2 provides a unique classroom experience in their own Hungarian language that generates various mathematical representations. At home our students have a support system to help them explore mathematical concepts, test their mathematical knowledge and to assist them in their problem solving. WMI2 has been under continuous development since 2002 and has been in classroom use since 2007. It is freely available in 10 languages.

Learner-Centered Strategies and Advanced Mathematics: A Study of Students' Perspectives

A number of learner-centered strategies were implemented during a two-semester course in real analysis that is traditionally taught in lecture format. We seek to understand the role that these strategies can have in this proof-intensive theoretical mathematics classroom and the perceived benefits by the students. Although learner-centered strategies are a welcome addition in many applied mathematics courses and are known to be successful, the literature indicates that these remain largely absent from more advanced courses [9]. In an effort to correlate student resistance and acceptance of these strategies in different classroom settings we included an applied differential equations course in the study. Student feedback was obtained for two semesters of the real analysis course and compared to the feedback obtained during one semester of the differential equations course.

Assessing science students’ attitudes to mathematics: a case study on a modelling project with mathematical software

This article reports the attitudes of students towards mathematics after they had participated in an applied mathematical modelling project that was part of an Applied Mathematics course. The students were majoring in Earth Science at the National Taiwan Normal University. Twenty-six students took part in the project. It was the first time a mathematical modelling project had been incorporated into the Applied Mathematics course for such students at this University. This was also the first time the students experienced applied mathematical modelling and used the mathematical software. The main aim of this modelling project was to assess whether the students’ attitudes toward mathematics changed after participating in the project. We used two questionnaires and interviews to assess the students. The results were encouraging especially the attitude of enjoyment. Hence the approach of the modelling project seems to be an effective method for Earth Science students.

A unified approach for solving nonlinear regular perturbation problems

This aritcle describes a simple alternative unified method of solving nonlinear regular perturbation problems. The procedure is based upon the manipulation of Taylor's approximation for the expansion of the nonlinear term in the perturbed equation.An essential feature of this technique is the relative simplicity used and the associated unified computational procedure that is employed. As such it should be of interest to teachers of applied mathematics courses, particularly those courses which include perturbation methods.One of the merits of this approach is that it leads on naturally to a scheme based on Taylor's expansions and, consequently, allows the regular perturbation method to be introduced into a course much earlier than is currently common.The method is illustrated by implementing it to four perturbation problems, including two algebraic equations and two initial-value problems. The new approach is compared and contrasted with the traditional perturbation scheme in order to demonstrate its relative merit.

The Blasius Function: Computations Before Computers, the Value of Tricks, Undergraduate Projects, and Open Research Problems

The Blasius flow is the idealized flow of a viscous fluid past an infinitesimally thick, semi-infinite flat plate. The Blasius function is the solution to $2 f_{xxx} + f f_{xx} = 0$ on $x \in [0, \infty]$ subject to $f(0)=f_{x}(0)=0, f_{x}(\infty) = 1$. We use this famous problem to illustrate several themes. First, although the flow solves a nonlinear partial differential equation (PDE), Toepfer successfully computed highly accurate numerical solutions in 1912. His secret was to combine a Runge-Kutta method for integrating an ordinary differential equation (ODE) initial value problem with some symmetry principles and similarity reductions, which collapse the PDE system to the ODE shown above. This shows that PDE numerical studies were possible even in the precomputer age. The truth, both a hundred years ago and now, is that mathematical theorems and insights are an arithmurgist's best friend, and they can vastly reduce the computational burden. Second, we show that special tricks, applicable only to a given problem, can be as useful as the broad, general methods that are the fabric of most applied mathematics courses: the importance of “particularity.” In spite of these triumphs, many properties of the Blasius function $f(x)$ are unknown. We give a list of interesting projects for undergraduates and another list of challenging issues for the research mathematician.

Mechanics of Curved Composites. Solid Mechanics and its Applications, Vol. 78

9R28. Mechanics of Curved Composites. Solid Mechanics and its Applications, Vol 78. - SD Akbarov (Yildiz Tech Univ, Istanbul, Turkey) and AN Guz (Inst of Mech, Natl Acad of Sci, Kiev, Ukraine). Kluwer Acad Publ, Dordrecht, Netherlands. 2000. 441 pp. ISBN 0-7923-6477-5. $190.00. Reviewed by M-A Erki (Dept of Civil Eng, Royal Military Col of Canada, PO Box 17000 Station Forces, Kingston ON, K7K 7B4, Canada).This book is the 78th volume in the prestigious series Solid Mechanics and Its Applications edited by Professor GML Gladwell. The curve in the curved composites refers to fiber waviness. The composites are assumed to be composed of lower strength matrices reinforced with layers of high strength wavy fibers. Through the thickness of the composite, the fibers may be wavy all in the same way, that is in-phase (Plane-curved composites–Chapter 1), or the fiber waviness may be out-of-phase (Plane-strain state in periodically curved composites–Chapter 4). Additionally, the waviness of the fibers may be through two orthogonal planes (General curved composites–Chapter 2; Composites with spatially periodic curved layers–Chapter 5; Normalized modulus of elasticity–Chapter 9), the wavy fibers may be sandwiched between fiber layers that are composed of straight fibers (Chapter 4) or, finally, the composites may be composed of almost entirely straight fibers with only localized waviness (Locally-curved composites–Chapter 6). The most common occurrences of wavy fibers in composites are woven composites (2D and 3D weaves), which are composed of straight fibers rendered curved by their passing over and under fibers in the orthogonal direction. In civil engineering applications, where composites are replacing steel as concrete reinforcements, fiber composites that are made into bent bars have their fibers buckled nearest to the center of the bend. This latter example is but one of the fibers rendered wavy in a composite owing to a fabrication process. There are many others. Composites can also be unintentionally deformed during fabrication, transportation, or installation, resulting in local fiber waviness. A unique feature of the book is that it also tackles complicated fibrous composites (Chapter 9) based on the general formulations and solution methods presented for layered composites. What are the consequences of curved fibers in composites? Compared to composites with the same fiber volumes, but composed of straight fibers, wavy fibers in composites induce tangential and out-of-plane strains and stresses that result in lower ultimate strength and lower stiffness. Also, wavy fibers in a composite induce dynamic, stability, and fracture responses that differ from those of straight fiber composites. Quantifying the mechanical behavior of curved composites is a complex geometric problem that tracks the deformations of the curved fibers and their interaction with the surrounding matrix. All the preceding merely positions the subject and relevance of this outstanding book, with its elegant mathematical formulations. The formulations are based on continuum theories for piecewise homogenous bodies developed by the authors, using the exact equations of elasticity or viscoelasticity for anisotropic bodies. The linear and nonlinear numerical problems solved are applicable to a wide range of practical circumstances (Problems for curved composites–Chapter 3; Geometrically nonlinear problems–Chapter 8; Fracture problems–Chapter 10). The book is clearly and generously illustrated throughout the theoretical and problem-solving chapters. Professors Guz and Akbarov are among the foremost authorities in this field. The book refers to over 160 publications, nearly half of which were published by them. The references span 40 years of individual and collaborative work by Guz and Akbarov, with specific application to curved composites in the last 20 years. While, undergraduate applied mathematics courses may use the book as a reference text, Mechanics of Curved Composites is more likely applicable to graduate courses in aeronautical and mechanical engineering. Definitely, if you do numerical modeling of fiber composites for your work, this book will be very valuable to you. If you read books of mathematics for pleasure, as many do, this book will spoil you for any other for a long while.

Education

Entirely by coincidence, both Education papers in this issue have a decidedly historical bent, and they start in very similar styles. C. R. MacCluer's article, "The Many Proofs and Applications of Perron's Theorem," begins "A workhorse of much practical mathematics is the 1907 theorem of Oskar Perron...," while Antonio Garcia's paper "Orthogonal Sampling Formulas: A Unified Approach," starts with the words "In 1949 Claude Shannon published a remarkable result...." From there, both articles take readers on stimulating and well-written tours of two topics in applied mathematics, in both cases incorporating new proofs that should be helpful in understanding and teaching this material. MacCluer's article is concerned with positive and nonnegative matrices---matrices whose elements are all positive and all nonnegative, respectively---and the analysis of their eigenvalues. In vivid writing, MacCluer first conveys the applications of this area, which have an impressively wide span including differential equations, population models, Markov chains, economic models, and many others. He then presents a brief survey of the many proofs of Perron's theorem, including reference to work by Frobenius that is seminal for this topic. Finally, a proof derived by the author turns out to be a special case of a result of Karlin from 1959. This provides a nice module that can be added easily to courses in applied linear algebra and related topics. Garcia's paper addresses the topic of sampling theory, which is the reconstruction of functions or signals through their values at some appropriate set of points. It starts from the seminal work of Shannon, which along with independent work by Kotel'nikov and foundational research by Whittaker has provided the theoretical foundation for modern pulse code modulation communication systems. From these roots in the first half of the 20th century, this topic of sampling theory has grown to become a whole branch of applied mathematics. Garcia deals with the particular case of orthogonal sampling formulas, and he provides a new inductive procedure that can be used to derive various orthogonal formulas. The paper is not only very clearly written but also self-contained beyond a knowledge of Hilbert space theory. For this reason, it can serve as an introduction to the topic of sampling theory in a variety of signal processing and applied mathematics courses.

Humanists as Teachers of Science

culture, then surely science and its role in present and past societies must be part of it (Winchester 1989, iii). Furthermore, as I argue in this essay, at a time when the gap between the two cultures of the sci entist and of the humanist is increasing at a dizzying rate, the need has become pressing for nonscientists to play a greater role in teaching science in their liberal arts courses. I find it difficult to disagree with the sentiments of the engineer Henry Petros ki (1984): If a true liberal education means understanding the world in which one lives, then engineering, computer sci ence, and applied mathematics courses should certainly be required for a degree (14). For how can there be profitable philosophical or religious discussions of birth control or abortion without an understanding of biology? Can we mean ingfully study the aesthetics of art with out an understanding of sensory mecha nisms or, on the other hand, the actual

The Applied Mathematics Laboratory Introducing realism to an undergraduate, liberal arts environment

The demand by business and industry for college graduates with applied mathematics skills has recently encouraged mathematics departments to develop applied mathematics courses instructing students to solve realistic problems. The Mathematics Clinic, a course at the Claremont Colleges, has served as a model in this respect. The Applied Mathematics Laboratory, offered by the Mathematics Department at Towson State University, represents a similar endeavour to incorporate applied problem solving skills into the undergraduate curriculum, but at a liberal arts school which has no engineering college and no graduate mathematics programme. The special benefits of this course to the students and some of the projects that have been worked on are described, as well as particular difficulties encountered by an entirely undergraduate student team. Suggestions are made for other undergraduate schools which may be considering the addition of such a course to their mathematics curriculum.

Projects, problems and patience

Project work has become a major constituent of Applied Mathematics courses at most British polytechnics and universities. There is a general consensus among academics as to what constitutes a project, how to discover and vet suitable projects, what their value is as a teaching aid, and how a student’s project work should be assessed.

Some Changes in Shop Mathematics Due to Metrication

Some implications of conversion to the metric system for shop or applied mathematics courses.

An Applied Mathematics Course for Architects and Urban Designers

An Applied Mathematics Course for Architects and Urban Designers

An Applied Mathematics Course for Architects and Urban Designers

An Applied Mathematics Course for Architects and Urban Designers