6,450 research outputs found
The design and use of macroeconomics simulation using maple software: A pilot study
No full textThe mathematical models used in intermediate macroeconomics have become increasingly more sophisticated and challenging for students to learn. This paper demonstrates how mathematics software, such as Maple, can be used to design a simulation as a pedagogical aid. The paper proceeds by developing a system of equations to model the economy, simulating the system with Maple, and illustrating the impacts of fiscal and monetary policy changes. A pilot test of the simulation was performed to see if higher levels of mathematical rigor could be introduced in a principles course. The results indicate that symbolic mathematics software can be an effective teaching and student learning tool.Economics instruction; macroeconomic simulation; Maple software
How to program with formulas in Maple: Formulas in Maple
No full textMaple's main strength is its ability to compute with mathematical formulasand not just with numbers. It can multiply and factor, differentiate and integrate, and simplify formulas. In this article, using differentiation as an example, I explain how to program with formulas in Maple. The key is the data representation that Maple uses for a formula and the operations Maple provides for operating on formulas. I will also discuss Automatic Differentiation as an alternative which differentiates programs
IMPACT OF THE 1998 ICE STORM ON THE EASTERN ONTARIO MAPLE SYRUP INDUSTRY: A CASE STUDY OF NATURAL DISASTER POLICY IN CANADA
No full textUnder Canada's Disaster Financial Assistance Arrangements (DFAA), the federal government can provide provinces with funds for emergency response and recovery in the event of a natural disaster. This assistance has historically been provided on an ad hoc basis. In recent years, the amount of DFAA assistance has significantly increased without any auditing to determine how effective and efficient these expenditures are in offsetting economic losses due to natural disasters. The goal of this paper is to examine the implications of natural disaster compensation and assistance programs for economic efficiency. A framework is developed to determine if government assistance expenditures have offset economic losses to a specific industry using a case study of the 1998 ice storm and the eastern Ontario maple syrup industry. Projections of damage recovery are used to measure the economic impact of the storm, and a comparison is then drawn between the change in producers' welfare and government assistance. The implications of the findings for the case study and for future natural disaster assistance programs in Canada are discussed.Environmental Economics and Policy, Resource /Energy Economics and Policy,
Maple Learn: An Exposition
No full textI present Maple Learn, one of Maplesoft’s educational products. I provide examples of documents created with it, list some of its capabilities, and share my experience using it in online mathematics tutoring. Overall, I recommend it to teachers and tutor
ميكانيكا الاهتزازات بواسطة تطبيقات برنامج (Maple) العملية
No full textThe book “Vibrational Mechanics by Maple Practical Applications” is designed to assist undergraduate and postgraduate students majoring in physics, mechanical engineering, electromechanical and aerospace engineering in acquiring a more thorough knowledge of vibrational mechanics using the Maple programming language. Maple® is a powerful mathematical software for solving complex problems in the field of vibration. This book contains all the Maple worksheets for problems and some animations for each chapter.
This book consists of five chapters, comprising all problems that are solved by the Maple programming language, preceded by an introduction to dynamics and Maple programming. In Chapters 1 and 2, vibrational systems with one degree of freedom for free vibration and force conditions are surveyed, respectively. In Chapter 3, vibrational systems in transient conditions are explored. Vibrational systems with more than one degree of freedom are discussed in Chapter 4, and in Chapter 5, vibration for continuous systems is studied.*_*This book is based on Maple 2016 Mathematical Programming Software. Users should have access to Maple 2016. For any further details, please contact Professor Mohammad Khoshnevisan, Affiliated Research Professor, Northeastern University, Physics Department, College of Science, USA at
[email protected]
or [email protected]يهدف كتاب "ميكانيكا الاهتزازات بواسطة تطبيقات برنامج (Maple) العملية" إلى مساعدة طلاب البكالوريوس والدراسات العليا المتخصصين في الفيزياء والهندسة الميكانيكية والهندسة الكهروميكانيكية وهندسة الفضاء في اكتساب معرفة أكثر شمولًا بميكانيكا الاهتزازات باستخدام برنامج لغة البرجمة (Maple). Maple® هو برنامج حاسوبي في علم الرياضيات يُستخدم لحل المشكلات المعقدة في مجال الاهتزازات. ويحتوي هذا الكتاب على جميع بيانات Maple الخاصة بالمشكلات، مضمنًا في كل فصل بعض الرسوم التوضيحية المتحركة.
يضم الكتاب خمسة فصول، تُلقي الضوء على جميع المشكلات التي تم حلها بواسطة لغة البرمجة Maple. يسبق هذه الفصول مقدمة تتناول ديناميات وبرمجة Maple. في الفصلين الأول والثاني، تمت دراسة الأنظمة الاهتزازية بدرجة واحدة من الحرية للاهتزاز الحر وظروف القوة. أما الفصل الثالث فقد ركز على استكشاف النظم الاهتزازية في الأوضاع سريعة الزوال. كما تمت مناقشة النظم الاهتزازية الأكثر حرية في الفصل الرابع، في حين تمت دراسة الاهتزاز للأنظمة المستمرة في الفصل الخامس والأخير
The utility of using sugar maple tree-ring data to reconstruct maple syrup production in New York
No full textMaple syrup production is both an economically and culturally important industry in the northeastern U.S., and the commercial harvest of the temperature-sensitive sap has occurred for several centuries. A significant decline in maple syrup yield has been associated with warming spring temperatures during the critical sugaring period, and increases in summer drought frequencies. What is unknown, however, is how this current decline compares within the range of variability expected for a broader range of crops. Few sugar maple tree-ring chronologies from the northeastern U.S. exist, yet the potential utility of this species is high. This project will be the first to incorporate and employ dendrochronological techniques to develop maple syrup yield reconstructions. This project is designed to investigate correlations between statewide tree growth and maple syrup production using data collected from multiple sites in New York State and determine if these relationships can be modeled to reconstruction historical yields. Thus, this project will help promote the effectiveness of using tree-ring data to predict agricultural yields, which will ultimately provide farmers additional information about crop yield cycles. This knowledge will in turn help determine appropriate management methods for sugarbush operators during less optimal climatological conditions
Dynamical systems with applications using Maple
No full text"The text treats a remarkable spectrum of topics and has a little for everyone. It can serve as an introduction to many of the topics of dynamical systems, and will help even the most jaded reader, such as this reviewer, enjoy some of the interactive aspects of studying dynamics using Maple." —UK Nonlinear News (Review of First Edition) "The book will be useful for all kinds of dynamical systems courses…. [It] shows the power of using a computer algebra program to study dynamical systems, and, by giving so many worked examples, provides ample opportunity for experiments. … [It] is well written and a pleasure to read, which is helped by its attention to historical background." —Mathematical Reviews (Review of First Edition) Since the first edition of this book was published in 2001, Maple™ has evolved from Maple V into Maple 13. Accordingly, this new edition has been thoroughly updated and expanded to include more applications, examples, and exercises, all with solutions; two new chapters on neural networks and simulation have also been added. There are also new sections on perturbation methods, normal forms, Gröbner bases, and chaos synchronization. The work provides an introduction to the theory of dynamical systems with the aid of Maple. The author has emphasized breadth of coverage rather than fine detail, and theorems with proof are kept to a minimum. Some of the topics treated are scarcely covered elsewhere. Common themes such as bifurcation, bistability, chaos, instability, multistability, and periodicity run through several chapters. The book has a hands-on approach, using Maple as a pedagogical tool throughout. Maple worksheet files are listed at the end of each chapter, and along with commands, programs, and output may be viewed in color at the author’s website. Additional applications and further links of interest may be found at Maplesoft’s Application Center. Dynamical Systems with Applications using Maple is aimed at senior undergraduates, graduate students, and working scientists in various branches of applied mathematics, the natural sciences, and engineering. ISBN 978-0-8176-4389-8 § Also by the author: Dynamical Systems with Applications using MATLAB®, ISBN 978-0-8176-4321-8 Dynamical Systems with Applications using Mathematica®, ISBN 978-0-8176-4482-
Applications of real number theorem proving in PVS
No full textThis work is supported by funding from the EPSRC under grants EP/H500162, EP/F02309X and GR/S31242Real number theorem proving has many uses, particularly for verification of safety critical systems and systems for which design errors may be costly. We discuss a chain of developments building on real number theorem proving in PVS. This leads from the verification of aspects of an air traffic control system, through work on the integration of computer algebra and automated theorem proving to a new tool, NRV, first presented here that builds on the capabilities of Maple and PVS to provide a verified and automatic analysis of Nichols plots. This automates a standard technique used by control engineers and greatly improves assurance compared with the traditional method of visual inspection of the Nichols plots.Peer reviewe
Construction of Recurrence Relations for the Jacobi Coefficients, Using Maple
No full textIntroduction In the field of numerical analysis, one frequently needs to determine the coefficients a (ff;fi) k [f ] in the expansion of a given function f into a uniformly convergent series of Jacobi polynomials, f(x) = 1 X k=0 a (ff;fi) k [f ] P (ff;fi) k (x) (\Gamma1 x 1); (1) where P (ff;fi) k (x) (ff; fi ? \Gamma1) is the usual notation for the kth Jacobi polynomial (cf. [2], Vol. II, x10.8, or [5], Vol. I, Ch. 8). The particular case of ff = fi = \Gamma 1 2 is c
Ten Tips for Successful Creation of Contextualized Problems for Secondary School Students with Maple
No full textStudents at all levels of schooling in all countries of the world need to practice mathematical problem solving to develop competencies that they will apply in real-life scenarios. On the other hand, concerning solving, problem posing refers to both the generation of new problems and the re-formulation of given problems. Teaching mathematics from a problem posing and problem-solving perspective entails more than solving non-routine problems or typical textbook types of problems. It is a way for students to exercise all aspects of problem solving: exploring, conjecturing, examining, testing, and generalizing. Tasks should be accessible and extend students’ knowledge. Even students should formulate problems from given situations and create new problems by modifying the conditions of a given problem. The quality of problems submitted to students is an issue that needs to be carefully considered. This work presents different ways to apply good practices when designing a problem-solving activity with students. It is based on the experience of Digital Math Training, a project whose aim is to develop and strengthen Mathematics and Computer Science skills through problem solving activities using the Advanced Computing Environment (ACE) Maple. After initial training in the laboratories of the schools, 3 students per class - the most skilled or motivated ones - participate in online training. They are asked to solve a problem every 10 days and to submit their solution. Meanwhile, students can participate in weekly synchronous tutoring on the use of Maple and collaborate with their colleagues through forum discussions. Students are selected in an intermediate competition and a final one. In this setting it is important to carefully plan and present the activity to the students, the text of the problem should be clear, and concise, with little storytelling to enter the setting of the problem. The problems should not be too theoretical, although they may inspect specific aspects of the related theory. They need to be solved by starting with simpler requests until the most difficult ones, close to the edge of students' knowledge, are reached. The solutions can make use of a calculator, in our case the ACE Maple. Precise design principles are based on both the adoption of suitable practice and the use of Maple. These principles can be adapted to different situations. The paper describes all these features with examples, according to the literature
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