Multivariable Calculus: Integrals

or

Curriculum Module

Created with R2025a. Compatible with R2025a and later releases.

Information

This curriculum module contains interactive MATLAB® live scripts that teach and apply standard concepts in integral multivariable calculus.

Background

You can use these live scripts as demonstrations in lectures, class activities, or interactive assignments outside class. The first script released in this collection is It also includes examples of computing work and area.

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 single variable calculus and vectors, including vector fields, as covered in the courseware listed here:

Courseware Module	Sample content	Available on:
Vector Arithmetic		GitHub
Multivariable: Space and Functions		GitHub
Calculus: Integrals		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 on Integrals.prj. It will add the appropriate files to your MATLAB path and open an app that asks you 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, and Statistics and Machine Learning Toolbox™ is used in AddArrow.m.

Scripts

LineIntegrals.m

	In this script, students will... $\bullet$ Compute line integrals given a path and vector field $\bullet$ Identify conservative vector fields and use this to compute line integrals $\bullet$ Apply Green's Theorem to compute area	Academic disciplines $\bullet$ Electrical Engineering $\bullet$ Physics $\bullet$ Mathematics

MultipleIntegrals.m (planned)

	In this script, students will... $\bullet$ Compute and visualize double and triple integrals $\bullet$ Use change of variables to simplify and evaluate multiple integrals	Academic disciplines $\bullet$ Physics $\bullet$ Mathematics

SurfaceIntegrals.m (planned)

	In this script, students will... $\bullet$ Explore the concepts of control surfaces and control volumes $\bullet$ Use the divergence theorem	Academic disciplines $\bullet$ Electrical Engineering $\bullet$ Physics $\bullet$ 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
Multivariable: Space and Functions		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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