Differential and Integral Calculus
Differential and Integral Calculus are two fundamental branches of mathematical analysis that focus on understanding the behaviour of functions and their applications to real-world problems. Differential calculus concerns the study of rates of change and the concept of the derivative, while integral...
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| Ձևաչափ: | Online |
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Skyfox Publishing Group
2024
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| Առցանց հասանելիություն: | https://directory.doabooks.org/handle/20.500.12854/148571 |
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| _version_ | 1869518625541455872 |
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| author | Ms. S. Asvi Heris Ms. J. Ignu Shinisha |
| author_browse | Ms. J. Ignu Shinisha Ms. S. Asvi Heris |
| author_facet | Ms. S. Asvi Heris Ms. J. Ignu Shinisha |
| author_sort | Ms. S. Asvi Heris |
| collection | Directory of Open Access Books |
| description | Differential and Integral Calculus are two fundamental branches of mathematical analysis that focus on understanding the behaviour of functions and their applications to real-world problems. Differential calculus concerns the study of rates of change and the concept of the derivative, while integral calculus deals with the accumulation of quantities and the concept of the integral. Together, they provide powerful tools for modelling and solving problems in physics, engineering, economics, biology, and other fields. Integral calculus, on the other hand, focuses on the concept of the integral as a method for finding areas under curves, volumes of solids, and accumulated quantities. The Fundamental Theorem of Calculus, which links differentiation and integration, is emphasized as a pivotal result. Methods for solving definite and indefinite integrals, including integration by parts, substitution, and numerical methods, are examined alongside their applications in areas such as physics (e.g., work, energy), probability theory, and economics. The Book also highlights the importance of multivariable calculus, which extends these concepts to functions of several variables, and discusses the role of differential and integral calculus in the development of mathematical models that describe real-world phenomena. |
| format | Online |
| id | doab-20.500.12854ir-148571 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| publisher | Skyfox Publishing Group |
| publisherStr | Skyfox Publishing Group |
| record_format | ojs |
| spelling | doab-20.500.12854ir-1485712024-12-24T09:40:49Z Differential and Integral Calculus Ms. S. Asvi Heris Ms. J. Ignu Shinisha Differential Calculus Integral Calculus Fundamental Theorem of Calculus Optimization Multivariable Calculus Mathematical Modeling Mathematics and Science Differential and Integral Calculus are two fundamental branches of mathematical analysis that focus on understanding the behaviour of functions and their applications to real-world problems. Differential calculus concerns the study of rates of change and the concept of the derivative, while integral calculus deals with the accumulation of quantities and the concept of the integral. Together, they provide powerful tools for modelling and solving problems in physics, engineering, economics, biology, and other fields. Integral calculus, on the other hand, focuses on the concept of the integral as a method for finding areas under curves, volumes of solids, and accumulated quantities. The Fundamental Theorem of Calculus, which links differentiation and integration, is emphasized as a pivotal result. Methods for solving definite and indefinite integrals, including integration by parts, substitution, and numerical methods, are examined alongside their applications in areas such as physics (e.g., work, energy), probability theory, and economics. The Book also highlights the importance of multivariable calculus, which extends these concepts to functions of several variables, and discusses the role of differential and integral calculus in the development of mathematical models that describe real-world phenomena. Published 2024-12-24T09:40:47Z 2024-12-24T09:40:47Z 2020 book https://directory.doabooks.org/handle/20.500.12854/148571 eng image/jpeg Attribution 4.0 International https://skyfox.co/books/differential-and-integral-calculus/ https://skyfox.co/wp-content/uploads/2020/08/Integral-and-differential-Calculus.pdf Skyfox Publishing Group Skyfox Publishing Group 10.22573/spg.020.BK/S/013 10.22573/spg.020.BK/S/013 5b7df439-3749-4212-bf80-10dba782549a Austrian Science Fund (FWF) European Research Council (ERC) Knowledge Unlatched (KU) Sustainable History Monograph Pilot (SHMP) Swiss National Science Foundation (SNF) Wellcome ScholarLed Toward an Open Monograph Ecosystem (TOME) Sustainable History Monograph Pilot (SHMP) MUSE Open Dutch Research Council (NWO) Skyfox Publishing Group 172 Thanjavur, Tamil Nadu open access |
| spellingShingle | Differential Calculus Integral Calculus Fundamental Theorem of Calculus Optimization Multivariable Calculus Mathematical Modeling Mathematics and Science Ms. S. Asvi Heris Ms. J. Ignu Shinisha Differential and Integral Calculus |
| title | Differential and Integral Calculus |
| title_full | Differential and Integral Calculus |
| title_fullStr | Differential and Integral Calculus |
| title_full_unstemmed | Differential and Integral Calculus |
| title_short | Differential and Integral Calculus |
| title_sort | differential and integral calculus |
| topic | Differential Calculus Integral Calculus Fundamental Theorem of Calculus Optimization Multivariable Calculus Mathematical Modeling Mathematics and Science |
| topic_facet | Differential Calculus Integral Calculus Fundamental Theorem of Calculus Optimization Multivariable Calculus Mathematical Modeling Mathematics and Science |
| url | https://directory.doabooks.org/handle/20.500.12854/148571 |
| work_keys_str_mv | AT mssasviheris differentialandintegralcalculus AT msjignushinisha differentialandintegralcalculus |