ACADEMIC EDITION | August 2012 | Issue 8

Maple Helps Teach Calculus to 11-Year Old Students

For years, educators have been debating that use of technology in the classroom could radically change not just how we teach our children, but what we teach them, and when. The University of Tasmania in Australia set out to prove it. Because of their commitment to embracing the Digital Education Revolution, and to showcasing how big a transformation the use of computers can make in students’ learning, the University decided to take on the challenge of teaching integral calculus to 11-year-olds. While this age group is traditionally considered far too young for this topic, which is usually introduced at age 17 at the very earliest, the University wanted to see if computer software would make a difference in their learning. If students become comfortable with this complex topic at a young age, perhaps learning could become easier and more of them will gravitate to the scientific and technical fields as they get older.

The researchers used Maple as the software of choice for this project. They used Maple to teach fifth graders the Calculus curriculum used in the first year engineering program in Australian universities. The project team trained five classroom teachers who then worked with their students for two hours a week for six weeks. During this time, the students were introduced to a series of real-world problems and mathematical concepts, and learned how to solve these problems in Maple. Students used Maple to set up the solutions to word problems, calculate results, and graph functions.

For more information, click here to read the full user case study.


Maplesoft Events
9th International Modelica Conference 2012
September 3-5
Munich, Germany
MSO-Tools 2012
September 24-26
Berlin, Germany
Séminaire Maplesoft: Solutions Maplesoft pour l'éducation et la recherche
October 10
Université Lille 1, France
For further details about these events, click here.

Information Sheets
Maple Training Datasheet
Detailed course outline for Maple onsite training
MapleSim Training Datasheet
Detailed course outline for MapleSim onsite training

To access all Maplesoft Information sheets, click here.

Social Networks

Mathematics-Based Modeling of a Series-Hybrid Electric Vehicle
Thursday, September 27th at 10:00 am EDT

The automotive industry is in transformation. The complexity of the automobile has increased exponentially in the past decades and has triggered a design revolution that stresses detailed modeling and simulation steps prior to committing to metal and plastic. With new generation vehicles deploying hybrid (HEV), fully electric (EV), and fuel cell powerplants, the need for advanced physical modeling solutions is considerably greater due to increasing system complexity. This webcast covers new approaches to modeling and simulation for HEV and EV vehicle applications with emphasis on the development of high-fidelity physical models of automotive batteries. To speed up the design and prototyping processes of HEVs, a method that automatically generates mathematics equations governing the vehicle system response in an optimized symbolic form is desirable. To achieve this goal, the physical modeling tool MapleSim was employed to develop the multidomain model of a series-HEV, using the symbolic computing algorithms of the Maple software package to generate an optimized set of governing equations. The HEV model consists of a mean value internal-combustion engine, a Li-ion battery pack, and a multibody vehicle model. Simulations are then used to demonstrate the performance of the HEV system. Simulation results show that the model is viable and the number of governing equations is reduced significantly, resulting in a computationally efficient system. Webcast attendees will be invited to interact with the speakers during the program's live Q&A segment.


Dr. John McPhee, Professor, Systems Design Engineering, University of Waterloo, and NSERC/Toyota/Maplesoft Industrial Research Chair, Mathematics-based Modeling and Design
Dr. John McPhee's main area of research is multibody system dynamics, with principal application to the analysis and design of vehicles, mechatronic devices, and biomechanical systems. He has won many awards, including a Premier's Research Excellence Award and the I.W. Smith Award from the Canadian Society of Mechanical Engineers. He completed his term in 2009 as the Executive Director of the Waterloo Centre for Automotive Research, spending a sabbatical year at the Toyota Technical Center in Ann Arbor, Michigan. He holds a Ph.D. in mechanical engineering from the University of Waterloo, Canada.

Dr. Sam Dao, Application Engineer, Maplesoft
Dr. Sam Dao received his Ph.D. degree in mechatronics from the Department of Mechanical and Mechatronics Engineering at the University of Waterloo. He is currently an Application Engineer at Maplesoft. He has been involved in many research projects including multiple robot networking, hybrid electric vehicle modeling, and battery modeling.



Symbolic Computation Techniques for Multibody Model Development and Code Generation

Multibody models can generate large systems of differential algebraic equations (DAEs). These equations can take a significant amount of time to solve numerically and often the modeller needs to make difficult decisions between model fidelity and simulation speed.

This webinar presents some of the benefits of a general purpose symbolic computation environment when constructing and generating simulation code for multibody, multi-domain systems. Specifically, it considers how tools provided by these environments can be harnessed to generate highly efficient simulation code through coordinate selection, symbolic manipulation, and expression optimization.


Revamped MapleSim Model Gallery

The MapleSim Model Gallery has been dramatically revamped and now includes over 100 models. Discover the breadth and depth of MapleSim by browsing the real-world application examples from the MapleSim Model Gallery. The gallery currently contains examples from the following industries: Academic, Aerospace, Motion Control, Power Industries, Vehicle Engineering.

If your industry is not listed, or you want to discover more application examples, speak to our MapleSim experts for a personalized demonstration of how MapleSim can benefit you in your industry.

Video: Amir Khajepour talking about his rover project
  Dr. Amir Khajepour, Professor, University of Waterloo, describes his use of MapleSim and Maple in his research project with the Canadian Space Agency, in which he is designing models of autonomous space rovers for Mars exploration.
Ten new 'Teaching Concepts with Maple' examples added
  With the addition of ten new Clickable-Calculus examples to the Teaching Concepts with Maple section of the Maplesoft website, we've now posted 63 of the 154 solved problems in my data-base of syntax-free calculations.
Classroom Tips and Techniques: Best Taylor-Polynomial Approximations
Author: Dr. Robert Lopez
  This article applies Ecker's approach to the function f(x) = sinh(x)x e-3x, -1 ≤ x ≤ 3, then goes on to find other approximating quadratic polynomials.
Live Webinars
SAE Webinar: Mathematics-Based Modeling of a Series-Hybrid Electric Vehicle
Thursday, September 27 at 10:00 am EDT
Clickable Calculus Series - Part #3: Multivariate Calculus
Wednesday, September 5 at 2:00 pm EDT
Testing and Assessment with Maple T.A. 8
Thursday, September 6 at 2:00 pm EDT
Redefining Math Education with Clickable Math
Tuesday, September 11 at 10:00 am EDT
Challenges and solutions for STEM programs
Tuesday, September 25 at 2:00 pm EDT
Hollywood Math
Wednesday, September 26 at 2:00 pm EDT
Recorded Webinars
Présentation Maple 16
New Technology for Modelling HEVs and EVs
Space Equipment Gets in the Loop - MapleSim breaks new ground in HIL real-time simulation for planetary rovers
Desktop Engineering, August 7, 2012

“Dr. Amir Khajepour, Canada Research Chair in Mechatronic Vehicle Systems and a professor of engineering in the Mechanical and Mechatronics Engineering department at the University of Waterloo (UW), and his team worked with the Canadian Space Agency (CSA) and Maplesoft, to develop a hardware-in-the-loop (HIL) test platform for solar-powered planetary rovers... the main advantage of their approach is that it significantly reduces the overall development time in the project.”
Transmission modeling and simulation: key to reducing power loss
Automotive Engineering Online, July 18, 2012

“Over the last decade there has been a remarkable push toward acausal modeling environments, such as MapleSim from Maplesoft, which takes a different approach to modeling. Rather than representing mathematics directly, models use components that contain governing equations, and it is incumbent on the solver to perform the mathematical manipulation.”
Battery Design is Charging Ahead
Desktop Engineering, July 2, 2012

“...the industry is turning increasingly to math-based modeling techniques that allow engineers to accurately describe the behavior of the system--and the constraints on the system--in physical terms. These model equations are then used to develop, test and refine designs quickly, without building physical prototypes. Hence, having a good virtual model of the battery is essential so that both battery behavior and the physical interaction of the battery with all the other components are properly reflected in the model.”

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