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README.md

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[![View on File Exchange](https://www.mathworks.com/matlabcentral/images/matlab-file-exchange.svg)](https://www.mathworks.com/matlabcentral/fileexchange/XXXXX-PROJECTNAME) or [![Open in MATLAB Online](https://www.mathworks.com/images/responsive/global/open-in-matlab-online.svg)](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Multivariable-Space-and-Functions&project=Space.prj&file=README.m)
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[![View on File Exchange](https://www.mathworks.com/matlabcentral/images/matlab-file-exchange.svg)](https://www.mathworks.com/matlabcentral/fileexchange/XXXXX-PROJECTNAME) or [![Open in MATLAB Online](https://www.mathworks.com/images/responsive/global/open-in-matlab-online.svg)](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Multivariable-Space-and-Functions&project=Space.prj&file=README.mlx)
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[![MATLAB Versions Tested](https://img.shields.io/endpoint?url=https%3A%2F%2Fraw.githubusercontent.com%2FMathWorks-Teaching-Resources%2FMultivariable-Space-and-Functions%2Frelease%2FImages%2FTestedWith.json)](https://MathWorks-Teaching-Resources.github.io/Multivariable-Space-and-Functions)
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**Curriculum Module**
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_Created with R2025a. Compatible with R2025a and later releases._
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_Created with R2024a. Compatible with R2024a and later releases._
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# Information
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This curriculum module contains interactive [MATLAB® live scripts](https://www.mathworks.com/products/matlab/live-editor.html) that teach and apply standard concepts related to representing two and three dimensional space.
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This curriculum module contains interactive [MATLAB® live scripts](https://www.mathworks.com/products/matlab/live-editor.html) that teach and apply standard concepts related to representing two and three\-dimensional space.
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### **On Desktop:**
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Download or clone this repository. Open MATLAB, navigate to the folder containing these scripts and double\-click on [Space.prj](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Multivariable-Space-and-Functions&project=Space.prj&file=README.m). It will add the appropriate files to your MATLAB path and open an app that asks you where you would like to start.
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Download or clone this repository. Open MATLAB, navigate to the folder containing these scripts, and double\-click [Space.prj](<matlab: openProject("Space.prj")>). It will add the appropriate files to your MATLAB path and open an app asking where you would like to start.
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Ensure you have all the required products ([listed below](#H_E850B4FF)) installed. If you need to include a product, add it using the Add\-On Explorer. To install an add\-on, go to the **Home** tab and select <img src="Images/AddOnsIcon.png" width="16" alt="AddOnsIcon.png"> **Add-Ons** > **Get Add-Ons**.
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## Products
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MATLAB® and Symbolic Math Toolbox™ are used throughout. Tools from \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ *(list of other used toolboxes)* are used frequently as well. \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ *(function from following toolbox)* is used from \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ *(toolbox containing previously mentioned function).*
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*List of common products (not to be included in published README):*
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- Simulink®
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- Stateflow®
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- Simscape™
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- Statistics and Machine Learning Toolbox™
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- Curve Fitting Toolbox™
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- Optimization Toolbox™
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*If your module uses a product not on this list, you can find it* [*here*](https://www.mathworks.com/products.html)*.*
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MATLAB® and Symbolic Math Toolbox™ are used throughout. Tools from the Mapping Toolbox™ are used in the Further Exploration in the [CoordinateSystems](#M_0493) script.
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# Scripts
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## [**CoordinateSystems.m**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Multivariable-Space-and-Functions&project=Space.prj&file=Scripts/CoordinateSystems.m)
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## [**CoordinateSystems.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Multivariable-Space-and-Functions&project=Space.prj&file=Scripts/CoordinateSystems.mlx)
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| :-- | :-- | :-- |
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| <img src="Images/ShapesCard.png" width="159" alt="ShapesCard.png"> <br> | **In this script, students will...** <br> $\bullet$ Use polar, spherical, cartesian, and cylindrical coordinates to identify points, curves, surfaces, and volumes in space. <br> $\bullet$ Convert points, curves, surfaces, and volumes between different coordinate representations. <br> $\bullet$ Choose coordinate systems to describe given geometric objects and explain their choice. <br> | **Academic disciplines** <br> $\bullet$ Electrical Engineering <br> $\bullet$ Physics <br> $\bullet$ Navigation <br> $\bullet$ Mathematics <br> |
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| <img src="Images/ShapesCard.png" width="159" alt="ShapesCard.png"> <br> | **In this script, students will...** <br> $\bullet$ Use polar, spherical, cartesian, and cylindrical coordinates to identify points, curves, surfaces, and volumes in space. <br> $\bullet$ Convert points, curves, surfaces, and volumes between different coordinate representations. <br> $\bullet$ Choose coordinate systems to describe given geometric objects and explain their choice. <br> | **Academic disciplines** <br> $\bullet$ Electrical Engineering <br> $\bullet$ Mechanical Engineering <br> $\bullet$ Navigation <br> $\bullet$ Mathematics <br> |
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## [**VectorFields.m**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Multivariable-Space-and-Functions&project=Space.prj&file=Scripts/VectorFields.m)
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## **VectorFields** (planned)
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| :-- | :-- | :-- |
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| <img src="Images/VectorFieldCard.png" width="171" alt="VectorFieldCard.png"> <br> | **In this script, students will...** <br> $\bullet$ Visualize 2D and 3D vector fields <br> $\bullet$ Visualize 2D and 3D contour plots <br> $\bullet$ Define control surfaces and control volumes <br> | **Academic disciplines** <br> $\bullet$ Electrical Engineering <br> $\bullet$ Mechanical Engineering <br> $\bullet$ Physics <br> $\bullet$ Meteorology <br> $\bullet$ Mathematics <br> |
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## [**ParametricEquations.m**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Multivariable-Space-and-Functions&project=Space.prj&file=Scripts/ParametricEquations.m)
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## **ParametricEquations (planned)**
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| <img src="Images/ParametrizedFlower.png" width="171" alt="ParametrizedFlower.png"> <br> | **In this script, students will...** <br> $\bullet$ Identify a parametric expression for a given path in space. <br> $\bullet$ Visualize a path given as a parametric equation. <br> $\bullet$ Explore applications of parametric equations to represent space\-time data <br> | **Academic disciplines** <br> $\bullet$ Navigation <br> $\bullet$ Robotics <br> $\bullet$ Mathematics <br> |
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| **Courseware Module** <br> | **Sample Content** <br> | **Available on:** <br> |
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| [**Applied Partial Differential Equations**](https://www.mathworks.com/matlabcentral/fileexchange/172650-applied-partial-differential-equations) <br> | <img src="Images/AppliedPDEsCard.png" width="171" alt="AppliedPDEsCard.png"> <br> | [<img src="Images/OpenInFX.png" width="91" alt="OpenInFX.png">](https://www.mathworks.com/matlabcentral/fileexchange/172650-applied-partial-differential-equations) <br> [<img src="Images/OpenInMO.png" width="136" alt="OpenInMO.png">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Applied-PDEs&project=AppliedPDEs.prj&file=README.mlx) <br> [GitHub](https://github.com/MathWorks-Teaching-Resources/Applied-PDEs) <br> |
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| Multivariable: Derivatives <br> | <img src="Images/GradientCard.png" width="171" alt="GradientCard.png"> <br> | |
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| Multivariable: Integrals <br> | \[catchy image here\] <br> | |
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Or feel free to explore our other [modular courseware content](https://www.mathworks.com/matlabcentral/fileexchange/?q=tag%3A%22courseware+module%22&sort=downloads_desc_30d).

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