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-1-1Exploring Multivariable Calculus
https://www.merlot.org/merlot/viewMaterial.htm?id=437177
<p>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.</p><p>To accomplish this goal, the project includes four parts:</p><p>· Creating a Multivariable Calculus Visualization applet using Java and publishing it on a website: web.monroecc.edu/calcNSF</p><p>· Creating a series of focused applets that demonstrate and explore particular 3D calculus concepts in a more dedicated way.</p><p>· Developing a series of guided exploration/assessments to be used by students to explore calculus concepts visually on their own.</p><p>· Dissemination of these materials through presentations and poster sessions at math conferences and through other publications.</p><p><strong>Intellectual Merit:</strong> 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:</p><p>- Instructors can use them to visually demonstrate concepts and verify results during lectures.</p><p>- Students can use them to explore the concepts visually outside of class, either using a guided activity or on their own.</p><p>- 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.</p><p>- 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.</p><p>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.</p><p>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 <a title="Exploration Applets" href="http://www.monroecc.edu/wusers/pseeburger/" target="_blank">www.monroecc.edu/wusers/pseeburger/</a>.</p><p><strong>Broader Impacts:</strong> 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.</p>Sun, 07 Mar 2010 20:17:32 GMTPaul Seeburger Monroe Community CollegeFlash Mathlets
https://www.merlot.org/merlot/viewMaterial.htm?id=87515
<p>"The Flash mathlets are divided into two sections.The For Students and Instructors section contains Flash applets which may be useful to instructors for classroom demonstrations, as well as to students for independent work and exploration. The For Developers section presents applets together with varied templates and the complete, object-oriented, easily-customizable source code that can be used by instructors for creating their own customized versions of the applets."</p>Wed, 19 Jul 2006 07:00:00 GMTBarbara Kaskosz University of Rhode IslandLeast Squares
https://www.merlot.org/merlot/viewMaterial.htm?id=89002
Visual explanation of the least squares procedure.Wed, 25 Apr 2001 07:00:00 GMTWilliam Finzer KCP TechnologiesPartial Derivative Geometrically Gallery
https://www.merlot.org/merlot/viewMaterial.htm?id=87575
A gallery of colorful and effective animations of partial derivatives for a small collection of functions of two variables.Fri, 28 Jul 2006 07:00:00 GMTDavid R. Hill Temple UniversityMultivariable Calculus
https://www.merlot.org/merlot/viewMaterial.htm?id=85558
This is an online textbook in Adobe PDF format. It begins with an introduction to Euclidian Three-Space and vector algebra and covers traditional calculus topics from derivatives up through Stoke's Theorem. Many nice exercises are included.Fri, 06 Jan 2006 08:00:00 GMTCain, George; Herod, JamesTutorial on Vectors and Vector Algebra
https://www.merlot.org/merlot/viewMaterial.htm?id=89590
A tutorial that uses a variety of applets, popup explanation and hint windows, images, and quiz tools. Covers the parallelogram, head-to-tail, and component method, as well as vector subtraction.Mon, 04 Jun 2001 07:00:00 GMTJohn Walkup Department of Physics, Oklahoma School of Science and MathematicsVector Fields Simulation
https://www.merlot.org/merlot/viewMaterial.htm?id=75572
<p>This applet demonstrates various properties of vector fields. You can select from a number of vector fields and see how particles move in the field if it is treated as either a velocity or a force field. This helps you visualize the field. Also you can see the values of the divergence and curl of the field. [From Author's Description]</p>Mon, 17 Sep 2001 07:00:00 GMTPaul FalstadA Parameterized Curve Applet
https://www.merlot.org/merlot/viewMaterial.htm?id=241454
This site contains an applet that allows the user to define a parametrized 2-dimensional curve and then create a three dimensional graph of this curve. Some additional properties of the curve can also be shown on the graph. This site is a member of the <a href="http://www.merlot.org/merlot/viewMaterial.htm?id=239777">Saint Louis University Calculus collection</a> .Thu, 15 Feb 2007 20:39:04 GMTMike May; Tom Banchoff Brown UniversityConnected Curriculum Project - Materials for Precalculus
https://www.merlot.org/merlot/viewMaterial.htm?id=84777
The CCP includes modules that combine the flexibility and connectivity of the Web with the power of computer algebra systems such as Maple, Mathematica, MatLab and MathCad. The single-topic units can be used for a two-hour lab, or for a shorter supervised period with follow-up on the student's own time, or for self-study. Modules are organized into areas of precalculus, differential calculus, integral calculus, multivariable calculus, linear algebra, differential equations and engineering mathematics. Applications include those in biology, chemistry, physics, engineering, economics and environmental science.Sun, 25 Sep 2005 07:00:00 GMTDavid Smith & Lawrence Moore, CCP Co-Directors Duke UniversityCross Section Applet
https://www.merlot.org/merlot/viewMaterial.htm?id=241424
This module is a part of the <a href="http://www.merlot.org/merlot/viewMaterial.htm?id=239777">Saint Louis University collection</a> of Calculus applets. The site contains an applet that is designed to show how the graph of a function in two variables can be constructed from the cross sections, which are each graphs of one variable.<br />Thu, 15 Feb 2007 17:03:49 GMTTom Banchoff; Mike May Brown UniversityLiveGraphics3D
https://www.merlot.org/merlot/viewMaterial.htm?id=86761
<p>LiveGraphics3D is a non-commercial Java 1.1 applet that enables users to put almost any three-dimensional graphics computed by Mathematica directly onto an HTML page. It can then be viewed and interactively rotated without any additional software. LiveGraphics3D also shows animations and supports parametrized graphics.</p>Fri, 02 Jun 2006 07:00:00 GMTMartin Kraus Universität StuttgartVector Field Applet
https://www.merlot.org/merlot/viewMaterial.htm?id=91106
<p>This applet draws a vector field and generates integral curves at the click of a mouse.</p>Sat, 29 Jul 2000 07:00:00 GMTSusan SchwarzAn Introduction to Lagrange Multipliers
https://www.merlot.org/merlot/viewMaterial.htm?id=1303017
<p>This is an exploration of Lagrange Multipliers that includes the definitions, applications, and motivation behind Lagrange Multipliers. Included in the page are two videos on the topic.</p>Fri, 26 May 2017 18:33:46 GMTSteuard Jensen Alma CollegeAPEX Calculus I
https://www.merlot.org/merlot/viewMaterial.htm?id=908754
<div class="summary">
<p>'This text is Part I of a three–text series on Calculus. This first part covers material taught in many “Calc 1” courses: limits, derivatives, and the basics of integration. The second text covers material often taught in “Calc 2:” integration and its applications, along with an introduction to sequences, series and Taylor Polynomials. The third text covers topics common in “Calc 3” or “multi-variable calc:” parametric equations, polar coordinates, vector–valued functions, and functions of more than one variable. All three are available for free at www.vmi.edu/APEX. These three texts are intended to work together and make one cohesive text, APEX Calculus, which can also be downloaded from the website.'</p>
<p>'A result of this spliƫng is that sometimes a concept is said to be explored in a “later section,” though that section does not actually appear in this particular text. Downloading the .pdf of APEX Calculus will ensure that you have all the content. This spliƫing of the material also results in unfortunate page/chapter numberings. Chapter 5 of this text is Chapter 1 of Calculus II. Apart from these numberings, page–for–page the content of the sections that appear in both Calculus I and Calculus II are idenƟcal.'</p>
</div>Thu, 13 Nov 2014 22:46:29 GMTGregory Hartman; Brian S. Heinhold; Troy Siemers; Dimplekumar Chalishajar Virginia Military Institute; Mount Saint Mary’s University; Virginia Military Institute; Virginia Military InstituteCALCULUS.ORG
https://www.merlot.org/merlot/viewMaterial.htm?id=789336
<p>Calculus.org compiled by U.C. Davis/Williams College, Department of Mathematics, provides site links/resources for the calculus student. Resources include calculus: online texts, applications, tutorials, exams, videos, software/aplets, calculators that compute derivatives, etc. </p>Wed, 11 Sep 2013 02:57:31 GMTDept. of Mathematics, U.C. Davis; Morgan Foundation; & Dept. of Mathematics, Williams College Calculus.orgJSP-Maple Applications for Multivariable Calculus
https://www.merlot.org/merlot/viewMaterial.htm?id=87554
This site contains several JSP-Maple applications to Multivariable Calculus. The applications are interactive and work under a MAPLE kernel on the USD server.Tue, 25 Jul 2006 07:00:00 GMTJose D. Flores The University of South DakotaLarry Green's Calculus Videos
https://www.merlot.org/merlot/viewMaterial.htm?id=443794
<p>This is a collection of 339 videos that work out typical exercises that first, second and third semester calculus students are asked to solve. The lengths of the videos range from a couple of minutes to up to seven minute depending on the complexity of the exercise. They are all closed captioned, and graphs and other diagrams accompany the words and equations when applicable.</p>Sun, 11 Apr 2010 06:37:08 GMTLarry Green Lake Tahoe Community CollegeLeast Squares Applet
https://www.merlot.org/merlot/viewMaterial.htm?id=314427
<p>Quoted from the site: This applet explores fitting a polynomial p(x) of degree n to a given set of data points. It computes the best least squares approximation to the data, "best" in the sense that SUM (p(xi) - yi)^2 is minimized. The applet provides controls for choosing the degree n, setting the precision of all displayed numbers, selecting and deselecting data points, and editing the data list. It also allows for entry of your own custom polynomial and computing its least squares error.</p>Wed, 04 Jun 2008 20:06:21 GMTDon Kreider; Dwight Lahr Department of Mathematics, Dartmouth College; Department of Mathematics, Dartmouth CollegeProject LINKS Module: The Gradient
https://www.merlot.org/merlot/viewMaterial.htm?id=76215
<p>This module provides a summary and motivation for the various properties of the gradient such as being the direction of steepest ascent and being the normal vector for level curves and surfaces.</p>Sun, 17 Feb 2002 08:00:00 GMTEdith Luchins, Tom Rousseau, Steven Irving, Sara Schubert Project LINKSThe Calculus of Functions of Several Variables
https://www.merlot.org/merlot/viewMaterial.htm?id=302300
Multivariable calculus text. Companion to Difference Equations to Differential Equations, by the same author.Sun, 13 Apr 2008 06:42:51 GMTDan Sloughter Furman UniversityTIG - A Scientific Calculator with Memory Variables and Complex Numbers Support
https://www.merlot.org/merlot/viewMaterial.htm?id=85479
A Complex Scientific Calculator with full support of Complex Functions of Complex Variables. Using the Memory Variables you can create Sessions to solve mathematical and scientific problems. A graphical visualisation of the Complex Numbers is provided.Mon, 02 Jan 2006 08:00:00 GMTTeodoru Gugoiu La Citadelle, Ontario, CanadaConnected Curriculum Project - Materials for Multivariable Calculus
https://www.merlot.org/merlot/viewMaterial.htm?id=85711
<p>The CCP includes modules that combine the flexibility and connectivity of the Web with the power of computer algebra systems such as Maple, Mathematica, MatLab and MathCad. This particular collection includes single-topic modules on Multivariable Calculus as well as applications in this subject.</p>Thu, 26 Jan 2006 08:00:00 GMTDavid Smith & Lawrence Moore, CCP Co-Directors Duke UniversityBridging the Vector Calculus Gap
https://www.merlot.org/merlot/viewMaterial.htm?id=77006
Collection of materials designed to bridge the gap between the way mathematicians typically teach vector calculus and way it is used by other scientists and engineers.<br/><br/>(These materials are not technology-based.)Thu, 13 Jun 2002 07:00:00 GMTTevian Dray Oregon State UniversityCalculus-Volume 3: OpenStax College
https://www.merlot.org/merlot/viewMaterial.htm?id=1138567
<p>Calculus-Volume 3, volume three of a three volume Calculus series, is an Open Textbook offered by OpenStax College. Calculus-Volume 3 is designed for a typical two or three semester Calculus course and it divided into three volumes to enhance student learning and offer instructors flexibility and efficiency. Calculus-Volume 3 covers parametric equations, polar coordinates, vectors, functions of several variables, and second-order differential equations. In addition, OpenStax College has compiled additional resources that directly coincide with your book from online homework and interactive study guides to faculty-only resources.</p>Wed, 16 Mar 2016 20:36:35 GMTGilbert Strang and Edwin "Jed" Herman (Senior Contributing Authors); and Contributing Authors OpenStax College (USA)