Slopes: Differential Equations
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2.6.4for iPhone, iPad and more
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Slopes: Differential Equations 螢幕截圖
About Slopes: Differential Equations
Slopes is an interactive environment for exploring graphical solutions to ordinary differential equations. Slopes consists of five activities with preloaded examples to get you started and the ability to input your own content. "Slopefields" and “Phase Planes” both plot vector fields and solutions corresponding to multiple initial conditions. “Systems” dynamically solves systems of up to six equations. “Oscillations” solves second-order constant coefficient equations and animates the corresponding spring-mass system or RLC circuit. “Methods” constructs numerical approximations of a single ordinary differential equation using Euler’s method as well as Second and Fourth Order Runge-Kutta methods. Slopes is a playground for ODEs. You can use it for homework, in-class activities or a new research project.
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最新版本2.6.4更新日誌
Last updated on 2022年08月27日
歷史版本
Version 2.6.4: Minor bug fix for Slopefields activity.
Version 2.6.3: Updated compatibility for the newest devices such as iPhone 13, iPad 9.
Version 2.6.2: Improved compatibility with newer iPads
Version 2.6.1: Improved zooming when Nullclines are shown in Phase Planes. Minor bug fix for newer iPad users.
Version 2.6.0: Improved performance of solutions in all activities. Improved performance and stability of Nullclines feature. Bug fixes for Methods activity and general bug fixes.
Version 2.6.3: Updated compatibility for the newest devices such as iPhone 13, iPad 9.
Version 2.6.2: Improved compatibility with newer iPads
Version 2.6.1: Improved zooming when Nullclines are shown in Phase Planes. Minor bug fix for newer iPad users.
Version 2.6.0: Improved performance of solutions in all activities. Improved performance and stability of Nullclines feature. Bug fixes for Methods activity and general bug fixes.
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Version History
2.6.4
2022年08月27日
Version 2.6.4: Minor bug fix for Slopefields activity.
Version 2.6.3: Updated compatibility for the newest devices such as iPhone 13, iPad 9.
Version 2.6.2: Improved compatibility with newer iPads
Version 2.6.1: Improved zooming when Nullclines are shown in Phase Planes. Minor bug fix for newer iPad users.
Version 2.6.0: Improved performance of solutions in all activities. Improved performance and stability of Nullclines feature. Bug fixes for Methods activity and general bug fixes.
Version 2.6.3: Updated compatibility for the newest devices such as iPhone 13, iPad 9.
Version 2.6.2: Improved compatibility with newer iPads
Version 2.6.1: Improved zooming when Nullclines are shown in Phase Planes. Minor bug fix for newer iPad users.
Version 2.6.0: Improved performance of solutions in all activities. Improved performance and stability of Nullclines feature. Bug fixes for Methods activity and general bug fixes.
2.6.3
2021年12月22日
2.6.3: Updated compatibility for the newest devices such as iPhone 13, iPad 9.
Version 2.6.2: Improved compatibility with newer iPads
Version 2.6.1: Improved zooming when Nullclines are shown in Phase Planes. Minor bug fix for newer iPad users.
Version 2.6.0: Improved performance of solutions in all activities. Improved performance and stability of Nullclines feature. Bug fixes for Methods activity and general bug fixes.
Version 2.6.2: Improved compatibility with newer iPads
Version 2.6.1: Improved zooming when Nullclines are shown in Phase Planes. Minor bug fix for newer iPad users.
Version 2.6.0: Improved performance of solutions in all activities. Improved performance and stability of Nullclines feature. Bug fixes for Methods activity and general bug fixes.
2.6.2
2021年07月17日
Version 2.6.2: Improved compatibility with newer iPads
Version 2.6.1: Improved zooming when Nullclines are shown in Phase Planes. Minor bug fix for newer iPad users.
Version 2.6.0: Improved performance of solutions in all activities. Improved performance and stability of Nullclines feature. Bug fixes for Methods activity and general bug fixes.
Version 2.6.1: Improved zooming when Nullclines are shown in Phase Planes. Minor bug fix for newer iPad users.
Version 2.6.0: Improved performance of solutions in all activities. Improved performance and stability of Nullclines feature. Bug fixes for Methods activity and general bug fixes.
2.6.1
2021年04月09日
Version 2.6.1: Improved zooming when Nullclines are shown in Phase Planes. Minor bug fix for newer iPad users.
Version 2.6.0: Improved performance of solutions in all activities. Improved performance and stability of Nullclines feature. Bug fixes for Methods activity and general bug fixes.
Version 2.6.0: Improved performance of solutions in all activities. Improved performance and stability of Nullclines feature. Bug fixes for Methods activity and general bug fixes.
2.6.0
2021年04月06日
Improved performance of solutions in all activities. Improved performance and stability of Nullclines feature. Bug fixes for Methods activity and general bug fixes.
2.5.4
2021年01月12日
2.5.4: Minor bug fixes and improvements to the graph settings in all activities.
2.5.3: Updated for compatibility with iPhone 12.
2.5.2: Updated for compatibility with recently released iPads.
2.5.1: Minor bug fixes for spring simulation.
2.5.0: Added a Nullcline feature to the graph settings in Phase Planes. Can now export a table of values from all activities as a CSV file. Performance improvements and minor bug fixes.
2.5.3: Updated for compatibility with iPhone 12.
2.5.2: Updated for compatibility with recently released iPads.
2.5.1: Minor bug fixes for spring simulation.
2.5.0: Added a Nullcline feature to the graph settings in Phase Planes. Can now export a table of values from all activities as a CSV file. Performance improvements and minor bug fixes.
2.5.3
2020年10月21日
2.5.3: Updated for compatibility with iPhone 12.
2.5.2: Updated for compatibility with recently released iPads.
2.5.1: Minor bug fixes for spring simulation.
2.5.0: Added a Nullcline feature to the graph settings in Phase Planes. Can now export a table of values from all activities as a CSV file. Performance improvements and minor bug fixes.
2.5.2: Updated for compatibility with recently released iPads.
2.5.1: Minor bug fixes for spring simulation.
2.5.0: Added a Nullcline feature to the graph settings in Phase Planes. Can now export a table of values from all activities as a CSV file. Performance improvements and minor bug fixes.
2.5.2
2020年09月25日
2.5.2: Updated for compatibility with recently released iPads.
2.5.1: Minor bug fixes for spring simulation.
2.5.0: Added a Nullcline feature to the graph settings in Phase Planes. Can now export a table of values from all activities as a CSV file. Performance improvements and minor bug fixes.
2.5.1: Minor bug fixes for spring simulation.
2.5.0: Added a Nullcline feature to the graph settings in Phase Planes. Can now export a table of values from all activities as a CSV file. Performance improvements and minor bug fixes.
2.5.1
2020年09月01日
2.5.1: Minor bug fixes for spring simulation.
2.5.0: Added a Nullcline feature to the graph settings in Phase Planes. Can now export a table of values from all activities as a CSV file. Performance improvements and minor bug fixes.
2.5.0: Added a Nullcline feature to the graph settings in Phase Planes. Can now export a table of values from all activities as a CSV file. Performance improvements and minor bug fixes.
2.5.0
2020年08月31日
Added a Nullcline feature to the graph settings in Phase Planes. Can now export a table of values from all activities as a CSV file. Performance improvements and minor bug fixes.
2.4.4
2020年07月29日
A revamped interface for sharing models and graphs as well as minor bug fixes.
2.4.3
2020年05月19日
Minor updates for newer iOS devices.
2.4.2
2020年05月13日
Minor updates for newer iOS devices.
2.4.1
2020年01月17日
Slopes now features the ability to share models with other users via AirDrop, iMessage, or email.
2.4
2020年01月14日
Slopes now features the ability to share models with other users via AirDrop, iMessage, or email.
2.3.3
2019年11月09日
Minor bug fix for iPadOS.
2.3.2
2019年11月04日
Minor update to support newer devices.
2.3
2019年08月01日
Improved interface for larger iPhones. New sliders available to adjust parameters in most activities. Minor bug fixes.
2.2.3
2019年06月19日
Fixed minor bugs and compatibility issues with newer devices.
2.2.1
2018年12月01日
Updated to work with newer iPhones and iPads.
2.2.0
2018年07月30日
The methods activity has been redesigned so that users can build solutions step by step using Euler and Runge-Kutta Methods. The spring and circuit demonstrations have been added to the Waves activity on the iPhone. The number of equations in the systems activity has been increased to 12. There are new colors schemes for the Slopefields, Phase Planes, and Systems activity.
General performance improvements and bug fixes.
General performance improvements and bug fixes.
2.1.0
2018年03月10日
New sliders for parameters in the slope fields activity. Minor bug fixes.
2.0.5
2017年11月15日
Improved performance on newer iPhones. Updates to Swift 4.
2.0.4
2017年09月21日
Minor bug fixes.
2.0.3
2017年09月11日
Bug fixes for changes to parameters and initial conditions. Improvements in saving equations and exporting graphs for the iPhone.
Slopes: Differential Equations FAQ
點擊此處瞭解如何在受限國家或地區下載Slopes: Differential Equations。
以下為Slopes: Differential Equations的最低配置要求。
iPhone
須使用 iOS 11.0 或以上版本。
iPad
須使用 iPadOS 11.0 或以上版本。
iPod touch
須使用 iOS 11.0 或以上版本。
Slopes: Differential Equations支持英文