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In a local coordinate system, a one-form is a linear combination of the differentials of the coordinates: where the are smooth functions. From this perspective, a one-form has a covariant transformation law on passing from one coordinate system to another. Thus a one-form is an order 1 covariant tensor field.
Closed and exact differential forms. In mathematics, especially vector calculus and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα = 0), and an exact form is a differential form, α, that is the exterior derivative of another differential form β. Thus, an exact form is in the image of d ...
Differential form. In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many applications, especially in geometry, topology and physics.
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Connection form. In mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms. Historically, connection forms were introduced by Élie Cartan in the first half of the 20th century as part of, and one of the principal ...
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It includes a spreadsheet. Google Sheets – as part of Google Workspace suite, supporting both offline and online editing. IBM Lotus Symphony – freeware for MS Windows, Apple Mac OS X and Linux. Kingsoft Office Spreadsheets 2012 – For MS Windows. Both free and paid versions are available.
Microsoft Excel is a spreadsheet editor developed by Microsoft for Windows, macOS, Android, iOS and iPadOS. It features calculation or computation capabilities, graphing tools, pivot tables, and a macro programming language called Visual Basic for Applications (VBA). Excel forms part of the Microsoft 365 suite of software.