{"id":16042845,"url":"https://github.com/MathWorks-Teaching-Resources/Numerical-Integration","last_synced_at":"2025-10-22T04:31:02.230Z","repository":{"id":109700974,"uuid":"381055961","full_name":"MathWorks-Teaching-Resources/Numerical-Integration","owner":"MathWorks-Teaching-Resources","description":"Interactive courseware module that addresses the fundamentals of numerical integration taught in mathematics courses.","archived":false,"fork":false,"pushed_at":"2024-04-30T16:28:07.000Z","size":1062,"stargazers_count":4,"open_issues_count":0,"forks_count":4,"subscribers_count":3,"default_branch":"release","last_synced_at":"2024-04-30T17:43:26.904Z","etag":null,"topics":["mathematics-education","matlab-live-script","numerical-integration"],"latest_commit_sha":null,"homepage":null,"language":"MATLAB","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"bsd-3-clause","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/MathWorks-Teaching-Resources.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":"CONTRIBUTING.md","funding":null,"license":"LICENSE.md","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":"SECURITY.md","support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2021-06-28T14:15:29.000Z","updated_at":"2024-04-30T16:28:12.000Z","dependencies_parsed_at":"2024-05-07T02:00:23.082Z","dependency_job_id":null,"html_url":"https://github.com/MathWorks-Teaching-Resources/Numerical-Integration","commit_stats":null,"previous_names":[],"tags_count":4,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/MathWorks-Teaching-Resources%2FNumerical-Integration","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/MathWorks-Teaching-Resources%2FNumerical-Integration/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/MathWorks-Teaching-Resources%2FNumerical-Integration/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/MathWorks-Teaching-Resources%2FNumerical-Integration/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/MathWorks-Teaching-Resources","download_url":"https://codeload.github.com/MathWorks-Teaching-Resources/Numerical-Integration/tar.gz/refs/heads/release","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":219868597,"owners_count":16555717,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["mathematics-education","matlab-live-script","numerical-integration"],"created_at":"2024-10-09T00:03:02.688Z","updated_at":"2025-10-22T04:31:02.212Z","avatar_url":"https://github.com/MathWorks-Teaching-Resources.png","language":"MATLAB","funding_links":[],"categories":["Numerical integration and quadrature"],"sub_categories":[],"readme":"\n\u003ca name=\"T_DEF03274\"\u003e\u003c/a\u003e\n# \u003cspan style=\"color:rgb(213,80,0)\"\u003eNumerical Integration\u003c/span\u003e\n\u003ca name=\"H_053613DF\"\u003e\u003c/a\u003e\n\nLearn the Trapezoid Rule and Simpson's Rule methods of numerical integration.\n\n[![View on File Exchange](https://www.mathworks.com/matlabcentral/images/matlab-file-exchange.svg)](https://www.mathworks.com/matlabcentral/fileexchange/94963-numerical-integration) 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/Numerical-Integration\u0026project=NumericalIntegration.prj\u0026file=README.mlx)\n\n[![MATLAB Versions Tested](https://img.shields.io/endpoint?url=https%3A%2F%2Fraw.githubusercontent.com%2FMathWorks-Teaching-Resources%2FNumerical-Integration%2Frelease%2FImages%2FTestedWith.json)](https://MathWorks-Teaching-Resources.github.io/Numerical-Integration)\n\n**Curriculum Module**\n\n_Created with R2020b. Compatible with R2020b and later releases._\n\n# Information\n\nThis curriculum module contains interactive [MATLAB® live scripts](https://www.mathworks.com/products/matlab/live-editor.html) that teach two fundamental techniques for approximating definite integrals: the trapezoid and Simpson’s rules. These rules are derived from Lagrange interpolating polynomials and explored through interactive visualizations.\n\n\u003ca name=\"H_F00D98E4\"\u003e\u003c/a\u003e\n## Background\n\nYou can use these live scripts as demonstrations in lectures, class activities, or interactive assignments outside class. This module covers the derivation and implementation of the trapezoid rule and the 1/3 and 3/8 Simpson's rules. \n\n\nThe 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 \u003cimg src=\"Images/EndIcon.png\" width=\"19\" alt=\"EndIcon.png\"\u003e Stop button in the **RUN** section of the **Live Editor** tab in the MATLAB Toolstrip.\n\n## Contact Us\n\nContact the [MathWorks Educator Content Development Team](mailto:onlineteaching@mathworks.com) if you would like to request assistance, provide feedback, or if you have a question.\n\n\u003ca name=\"H_30BC7141\"\u003e\u003c/a\u003e\n## Prerequisites\n\nThis module assumes knowledge of [MATLAB Onramp](https://matlabacademy.mathworks.com/details/matlab-onramp/gettingstarted) – a free two-hour introductory tutorial that teaches the essentials of MATLAB.\n\n\u003ca name=\"H_330E72C3\"\u003e\u003c/a\u003e\n## Getting Started\n### Accessing the Module\n### **On MATLAB Online:**\n\nUse the [\u003cimg src=\"Images/OpenInMO.png\" width=\"136\" alt=\"OpenInMO.png\"\u003e](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Integration\u0026project=NumericalIntegration.prj) 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.\n\n### **On Desktop:**\n\nDownload or clone this repository. Open MATLAB, navigate to the folder containing these scripts and double-click on [NumericalIntegration.prj](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Integration\u0026project=NumericalIntegration.prj). It will add the appropriate files to your MATLAB path and open an app that asks you where you would like to start. \n\n\nEnsure 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  \u003cimg src=\"Images/AddOnsIcon.png\" width=\"16\" alt=\"AddOnsIcon.png\"\u003e **Add-Ons** \u003e **Get Add-Ons**. \n\n\u003ca name=\"H_E850B4FF\"\u003e\u003c/a\u003e\n## Products\n\nMATLAB® is used throughout.\n\n\u003ca name=\"H_D1A2E3C6\"\u003e\u003c/a\u003e\n# Scripts\n\u003ca name=\"H_92B379B9\"\u003e\u003c/a\u003e\n## [**TrapezoidRule.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Integration\u0026project=NumericalIntegration.prj\u0026file=TrapezoidRule.mlx)\n| \u003cimg src=\"Images/TrapImage.png\" width=\"171\" alt=\"TrapImage.png\"\u003e | **In this script, students will...** \u003cbr\u003e-  Explain numerical quadrature and its relationship to the definite integral \u003cbr\u003e-  Describe how the trapezoid rule is derived \u003cbr\u003e-  Illustrate the trapezoid rule graphically \u003cbr\u003e-  Compare and contrast integration of a continuous function with integration of tabulated data \u003cbr\u003e-  Implement the trapezoid rule in MATLAB  |\n| :-- | :-- |\n\n\u003ca name=\"H_7BC300E3\"\u003e\u003c/a\u003e\n## [**SimpsonsRules.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Integration\u0026project=NumericalIntegration.prj\u0026file=SimpsonsRules.mlx)\n| \u003cimg src=\"Images/SimpRuleIm.png\" width=\"171\" alt=\"SimpRuleIm.png\"\u003e | **In this script, students will...** \u003cbr\u003e-  Describe how Lagrange interpolating polynomials can be used to derive integration rules \u003cbr\u003e-  Illustrate Simpson’s 1/3 rule graphically \u003cbr\u003e-  Explain the steps required to implement Simpson’s 1/3 rule \u003cbr\u003e-  Compare the accuracy and limitations of Simpson’s 1/3 rule to those of Simpson’s 3/8 rule \u003cbr\u003e-  Implement Simpson’s 3/8 rule in MATLAB  |\n| :-- | :-- |\n\n\u003ca name=\"H_A532299F\"\u003e\u003c/a\u003e\n# License\n\nThe license for this module is available in the [LICENSE.md](https://github.com/MathWorks-Teaching-Resources/Numerical-Integration/blob/release/LICENSE.md).\n\n# Related Courseware Modules\n| **Title** |  | **Available on:**  |\n| :-- | :-- | :-- |\n| [**Calculus: Integrals**](https://www.mathworks.com/matlabcentral/fileexchange/105740-calculus-integrals) | \u003cimg src=\"Images/image_5.png\" width=\"171\" alt=\"image_5.png\"\u003e | [\u003cimg src=\"Images/OpenInFX.png\" width=\"91\" alt=\"OpenInFX.png\"\u003e](https://www.mathworks.com/matlabcentral/fileexchange/105740-calculus-integrals)[\u003cimg src=\"Images/OpenInMO.png\" width=\"136\" alt=\"OpenInMO.png\"\u003e](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Integrals\u0026project=Integrals.prj) [GitHub](https://github.com/MathWorks-Teaching-Resources/Calculus-Integrals)   |\n| [**Calculus: Derivatives**](https://www.mathworks.com/matlabcentral/fileexchange/99249-calculus-derivatives) | \u003cimg src=\"Images/image_8.png\" width=\"171\" alt=\"image_8.png\"\u003e | [\u003cimg src=\"Images/OpenInFX.png\" width=\"91\" alt=\"OpenInFX.png\"\u003e](https://www.mathworks.com/matlabcentral/fileexchange/99249-calculus-derivatives)[\u003cimg src=\"Images/OpenInMO.png\" width=\"136\" alt=\"OpenInMO.png\"\u003e](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Calculus-Derivatives\u0026project=Derivatives.prj) [GitHub](https://github.com/MathWorks-Teaching-Resources/Calculus-Derivatives)   |\n| \u003cbr\u003e[**Numerical Methods with Applications**](https://www.mathworks.com/matlabcentral/fileexchange/111490-numerical-methods-with-applications) | \u003cimg src=\"Images/image_11.png\" width=\"171\" alt=\"image_11.png\"\u003e | \u003cbr\u003e[\u003cimg src=\"Images/OpenInFX.png\" width=\"91\" alt=\"OpenInFX.png\"\u003e](https://www.mathworks.com/matlabcentral/fileexchange/111490-numerical-methods-with-applications)\u003cbr\u003e[\u003cimg src=\"Images/OpenInMO.png\" width=\"136\" alt=\"OpenInMO.png\"\u003e](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Methods-with-Applications\u0026project=NumericalMethods.prj)  \u003cbr\u003e[GitHub](https://github.com/MathWorks-Teaching-Resources/Numerical-Methods-with-Applications)   |\n\n\nOr feel free to explore our other [modular courseware content](https://www.mathworks.com/matlabcentral/fileexchange/?q=tag%3A%22courseware+module%22\u0026sort=downloads_desc_30d).\n\n# Educator Resources\n-  [Educator Page](https://www.mathworks.com/academia/educators.html) \n\u003ca name=\"H_C7A803CC\"\u003e\u003c/a\u003e\n# Contribute \n\nLooking for more? Find an issue? Have a suggestion? Please contact the [MathWorks Educator Content Development Team](mailto:%20onlineteaching@mathworks.com). If you want to contribute directly to this project, you can find information about how to do so in the [CONTRIBUTING.md](https://github.com/MathWorks-Teaching-Resources/Numerical-Integration/blob/release/CONTRIBUTING.md) page on GitHub.\n\n\n© Copyright 2025 The MathWorks, Inc\n\n\n\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2FMathWorks-Teaching-Resources%2FNumerical-Integration","html_url":"https://awesome.ecosyste.ms/projects/github.com%2FMathWorks-Teaching-Resources%2FNumerical-Integration","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2FMathWorks-Teaching-Resources%2FNumerical-Integration/lists"}