Multivariable: Space and Functions

or

Curriculum Module

Created with R2025a. Compatible with R2024a and later releases.

Information

This curriculum module contains interactive MATLAB® live scripts that teach and apply standard concepts related to representing two and three-dimensional space.

Background

You can use these live scripts as demonstrations in lectures, class activities, or interactive assignments outside class. This module covers coordinate systems, vector fields, and parametric equations. It also includes applications to electrical and gravitational attraction, electric and magnetic field diagrams, and robotic path planning.

The instructions inside the live scripts will guide you through the exercises and activities. Get started with each live script by running it one section at a time. To stop running the script or a section midway (for example, when an animation is in progress), use the Stop button in the RUN section of the Live Editor tab in the MATLAB Toolstrip.

Contact Us

Solutions are available upon instructor request. Contact the MathWorks teaching resources team if you would like to request solutions, provide feedback, or if you have a question.

Prerequisites

This module assumes knowledge of vector arithmetic, including the dot product and cross product, Cartesian coordinate systems, and trigonometry.

Courseware Module	Sample content	Available on:
Vector Arithmetic		GitHub

Getting Started

Accessing the Module

On MATLAB Online:

Use the link to download the module. You will be prompted to log in or create a MathWorks account. The project will be loaded, and you will see an app with several navigation options to get you started.

On Desktop:

Download or clone this repository. Open MATLAB, navigate to the folder containing these scripts, and double-click Space.prj. It will add the appropriate files to your MATLAB path and open an app asking where you would like to start.

Ensure you have all the required products (listed below) 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 Add-Ons > Get Add-Ons.

Products

MATLAB® and Symbolic Math Toolbox™ are used throughout. Tools from the Mapping Toolbox™ are used in the Further Exploration in the CoordinateSystems script.

Scripts

CoordinateSystems.mlx

	In this script, students will... $\bullet$ Use polar, spherical, cartesian, and cylindrical coordinates to identify points, curves, surfaces, and volumes in space. $\bullet$ Convert points, curves, surfaces, and volumes between different coordinate representations. $\bullet$ Choose coordinate systems to describe given geometric objects and explain their choice.	Academic disciplines $\bullet$ Electrical Engineering $\bullet$ Mechanical Engineering $\bullet$ Navigation $\bullet$ Mathematics

VectorFields (planned)

	In this script, students will... $\bullet$ Visualize 2D and 3D vector fields $\bullet$ Visualize 2D and 3D contour plots $\bullet$ Define control surfaces and control volumes	Academic disciplines $\bullet$ Electrical Engineering $\bullet$ Mechanical Engineering $\bullet$ Physics $\bullet$ Meteorology $\bullet$ Mathematics

ParametricEquations (planned)

	In this script, students will... $\bullet$ Identify a parametric expression for a given path in space. $\bullet$ Visualize a path given as a parametric equation. $\bullet$ Explore applications of parametric equations to represent space-time data	Academic disciplines $\bullet$ Navigation $\bullet$ Robotics $\bullet$ Mathematics

License

The license for this module is available in the LICENSE.md.

Related Courseware Modules

Courseware Module	Sample Content	Available on:
Applied Partial Differential Equations		GitHub

Or feel free to explore our other modular courseware content.

Educator Resources

• Educator Page

Contribute

Looking for more? Find an issue? Have a suggestion? Please contact the MathWorks teaching resources team. If you want to contribute directly to this project, you can find information about how to do so in the CONTRIBUTING.md page on GitHub.

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