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=Conclusion= | =Conclusion= | ||
| − | The | + | Overall, Richard Feynman introduces such a unique and simple technique to mathematics and has made calculations and computations of integrals uncomplicated. The idea of differentiating under the integral sign, if used properly, can be used to solve any difficult integral. On further studying higher-level math classes, like Real Analysis and Complex Analysis, Mathematicians and Physicists can solve their required problem with Feynman's Integral technique by tweaking their functions or equations problems in Banach space a lot simpler. Physicists dealing with quantum mechanics use techniques like these to deal with path integrals. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude. The technique helps them generalize the action principle of classical mechanics in physics when dealing with quantum mechanics. |
[[ Walther MA271 Fall2020 topic14 | Back to Feynman Integrals]] | [[ Walther MA271 Fall2020 topic14 | Back to Feynman Integrals]] | ||
[[Category:MA271Fall2020Walther]] | [[Category:MA271Fall2020Walther]] | ||
Revision as of 19:50, 5 December 2020
Conclusion
Overall, Richard Feynman introduces such a unique and simple technique to mathematics and has made calculations and computations of integrals uncomplicated. The idea of differentiating under the integral sign, if used properly, can be used to solve any difficult integral. On further studying higher-level math classes, like Real Analysis and Complex Analysis, Mathematicians and Physicists can solve their required problem with Feynman's Integral technique by tweaking their functions or equations problems in Banach space a lot simpler. Physicists dealing with quantum mechanics use techniques like these to deal with path integrals. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude. The technique helps them generalize the action principle of classical mechanics in physics when dealing with quantum mechanics.
