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4434Exploring Multivariable Calculus
http://www.merlot.org/merlot/viewMaterial.htm?id=437177
The main goal of this project is to improve student understanding of the geometric nature of multivariable calculus concepts, i.e., to help them develop accurate geometric intuition about multivariable calculus concepts and the various relationships among them.To accomplish this goal, the project includes four parts:· Creating a Multivariable Calculus Visualization applet using Java and publishing it on a website: web.monroecc.edu/calcNSF· Creating a series of focused applets that demonstrate and explore particular 3D calculus concepts in a more dedicated way.· Developing a series of guided exploration/assessments to be used by students to explore calculus concepts visually on their own.· Dissemination of these materials through presentations and poster sessions at math conferences and through other publications.Intellectual Merit: This project provides dynamic visualization tools that enhance the teaching and learning of multivariable calculus. The visualization applets can be used in a number of ways:- Instructors can use them to visually demonstrate concepts and verify results during lectures.- Students can use them to explore the concepts visually outside of class, either using a guided activity or on their own.- Instructors can use the main applet (CalcPlot3D) to create colorful graphs for visual aids (color overheads), worksheets, notes/handouts, or tests. 3D graphs or 2D contour plots can be copied from the applet and pasted into a word processor like Microsoft Word.- Instructors will be able to use CalcPlot3D to create lecture demonstrations containing particular functions they specify and/or guided explorations for their own students using a scripting feature that is being integrated with this applet.The guided activities created for this project will provide a means for instructors to get their students to use these applets to actively explore and “play” with the calculus concepts.Paul Seeburger, the Principal Investigator (PI) for this grant project, has a lot of experience developing applets to bring calculus concepts to life. He has created 100+ Java applets supporting 5 major calculus textbooks (Anton, Thomas, Varberg, Salas, Hughes-Hallett). These applets essentially make textbook figures come to life. See examples of these applets at www.monroecc.edu/wusers/pseeburger/.Broader Impacts: This project will provide reliable visualization tools for educators to use to enhance their teaching in calculus and also in various Physics/Engineering classes. It is designed to promote student exploration and discovery, providing a way to truly “see” how the concepts work in motion and living color. The applets and support materials will be published and widely disseminated through the web and conference presentations.Med-Calc Tutorial
http://www.merlot.org/merlot/viewMaterial.htm?id=84322
An interactive multimedia tutorial for healthcare professionals wishing to refresh math skills and learn how to calculate medication dosages and intravenous (IV) rates. The tutorial has three modules. Each module has includes a quiz. The first module covers information about fractions, decimals, ratios, proportions, and percentage. The second module covers information about conversions, medication administration, and dosage calculation. The third module covers information about intraveneous infusions including tubing calculation and intraveneous flow rates. Key words: Medication calculation; Intravenous flow rate calculation; Mathematics principlesShodor Educational Foundation
http://www.merlot.org/merlot/viewMaterial.htm?id=78540
This is a series of online interactive activities designed for use in middle school mathematics.Crump Institute for Biological Imaging
http://www.merlot.org/merlot/viewMaterial.htm?id=78800
From the website: "The Crump Institute for Molecular Imaging brings together faculty, students, and staff with a variety of backgrounds - physics, mathematics, engineering, biology, chemistry, and medicine - to pursue innovative technologies and science to accelerate our understanding of biology and medicine.״Instructor-Made Videos as a Scaffolding Tool
http://www.merlot.org/merlot/viewMaterial.htm?id=768947
Abstract: Instructors have frequently found that some content, such as mathematical formulae, chemistry laboratory experiments, and business practices, are unusually difficult for students to comprehend through text-centered approaches, and that this is especially so for online students. In response, instructor-made videos (IMVs) of three to 10 minutes in length on problematic topics or subject matter areas were produced for business, chemistry, and mathematics courses. The IMVs were intended to scaffold student learning. Initial findings revealed that multimodal IMVs involving the demonstration, illustration, and presentation of key terms, knowledge, skills, and resources can help students understand important procedures, structures, or mechanisms in previously problematic content. Simply stated, IMVs can have a positive impact on student learning.Volume 8, No. 4, December 2012, pp. 298-311HTML / PDFSpectroscopic Simulator
http://www.merlot.org/merlot/viewMaterial.htm?id=74659
We chose to develop this applet first since it covers an aspect of the course that is based on relatively simple mathematics, but which students seem to find very confusing. At this point in the course, students have learned the basic aspects of quantum mechanics, namely, that the energy associated with the motions of molecules can not be assigned arbitrarily but must take on specific values.Escher and the Droste Effect
http://www.merlot.org/merlot/viewMaterial.htm?id=83200
The goal of this site is to visualize the mathematical structure behind M.C. Escher's picture called "Print Gallery" (1956). The visualization itself is largely non-mathematical and is accomplished through many still images and animations. The actual mathematics, involving conformal mappings of the complex plane, is contained in a pdf copy of the original AMS publication. The Droste Effect refers to any image that contains itself on a smaller scale.Flash Animations for Physics
http://www.merlot.org/merlot/viewMaterial.htm?id=85267
The resource contains many Flash physics animations covering topics such as chaos, mechanics, vectors, waves, relativity; includes a tutorial on using Flash with mathematical equations to create controlled animations.Graphical representation of complex eigenvectors
http://www.merlot.org/merlot/viewMaterial.htm?id=821153
The Graphical representation of complex eigenvectors simulation aims to help students make connections between graphical and mathematical representations of complex eigenvectors and eigenvalues. The simulation depicts two components of a complex vector in the complex plane, and the same vector under several transformations that can be chosen by the user. A slider allows students to change the second component of the initial vector. The simulation shows whether or not the vector is an eigenvector, and if so displays the associated eigenvalue. The simulation includes a small challenge in asking the student to find the elements of one of the transformation matrices. An accompanying activity for this simulation is available at http://quantumphysics.iop.org and at www.st-andrews.ac.uk/physics/quvis. The simulation can be downloaded from the QuVis website www.st-andrews.ac.uk/physics/quvis.This simulation is part of the UK Institute of Physics New Quantum Curriculum, see http://quantumphysics.iop.org. Simulations and accompanying activities can be accessed from the IOP site and from www.st-andrews.ac.uk/physics/quvis. Sharing of these resources is encouraged, with all usage under the Creative Commons CC BY-NC-ND licence. Instructors can email quantumphysics@iop.org for activity solutions and to request to modify materials.Graphical representation of eigenvectors
http://www.merlot.org/merlot/viewMaterial.htm?id=821150
The Graphical representation of eigenvectors simulation aims to help students make connections between graphical and mathematical representations of eigenvectors and eigenvalues. The simulation depicts the two components of a unit vector in the xy-plane, and the same vector under several different transformations that can be chosen by the user. A slider allows students to change the orientation of the initial vector. The simulation shows whether or not the vector is an eigenvector, and if so displays the associated eigenvalue. The simulation includes a small challenge in asking students to find the elements of one of the transformation matrices 4. An accompanying activity for this simulation is available at http://quantumphysics.iop.org and at www.st-andrews.ac.uk/physics/quvis. The simulation can be downloaded from the QuVis website www.st-andrews.ac.uk/physics/quvis.This simulation is part of the UK Institute of Physics New Quantum Curriculum, see http://quantumphysics.iop.org. Simulations and accompanying activities can be accessed from the IOP site and from www.st-andrews.ac.uk/physics/quvis. Sharing of these resources is encouraged, with all usage under the Creative Commons CC BY-NC-ND licence. Instructors can email quantumphysics@iop.org for activity solutions and to request to modify materials.