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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.14564 |
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| _version_ | 1866910340678156288 |
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| author | Bár, Filip |
| author_facet | Bár, Filip |
| contents | We generalise the Fundamental Theorem of Calculus to higher dimensions. Our generalisation is based on the observation that the antiderivative of a function of $n$-variables is a solution of a partial differential equation of order $n$ generalising the classical case. The generalised Fundamental Theorem of Calculus then states that the $n$-dimensional integrals over $n$-dimensional axis-parallel rectangular hypercuboids is given by a combinatorial formula evaluating the antiderivative on the vertices of the hypercuboid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14564 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Fundamental Theorem of Calculus in higher dimensions Bár, Filip General Mathematics 26B20 (Primary) 58A10, 58A03, 05C15 (Secondary) We generalise the Fundamental Theorem of Calculus to higher dimensions. Our generalisation is based on the observation that the antiderivative of a function of $n$-variables is a solution of a partial differential equation of order $n$ generalising the classical case. The generalised Fundamental Theorem of Calculus then states that the $n$-dimensional integrals over $n$-dimensional axis-parallel rectangular hypercuboids is given by a combinatorial formula evaluating the antiderivative on the vertices of the hypercuboid. |
| title | The Fundamental Theorem of Calculus in higher dimensions |
| topic | General Mathematics 26B20 (Primary) 58A10, 58A03, 05C15 (Secondary) |
| url | https://arxiv.org/abs/2402.14564 |