July 2026
Intermediate
552 pages
7h 40m
Japanese
Content preview from AIがわかる数学入門 ―グラフ理論、特異値分解、OR：AIシステムを理解するための数学ガイド
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13章AIと偏微分方程式
私は世界のすべてをモデル化したい。
－ H.
映画『トップガン マーヴェリック』（2022）の最初のシーンでは、マーヴェリック（トム・クルーズ）が実験用の軍用機を操縦し、音速の10倍（マッハ10）まで到達させたのち、およそマッハ10.2で不安定になって制御を失います。現在までに実在の有人航空機で最速のものはマッハ6.7に達します（図13-1）。速度が現実か（まだ）非現実かにかかわらず、物理、数学、工学が結集してこれらの航空機を大空に飛ばし、さらに見事な空中操縦を繰り広げるさまは、見る者を魅了します。
図13-1 史上最速の有人航空機（画像ソース：https://oreil.ly/CKMN2）
マーヴェリックの圧巻のドッグファイトやマッハ10のシーンを観ていて頭に浮かんだ偏微分方程式（PDE）の一部を挙げます。
- 波動伝搬のための波動方程式
- 音速、空気中を伝わる音波、そして温度や空気密度の変化に伴う高度ごとの音速の変動など。
- ナビエ-ストークス方程式（流体力学）
- 流体の流れ、風洞、乱流など。
- 燃焼のためのG方程式（火炎面を記述する現象論的方程式）
- 航空機エンジン内での燃焼や、機体の排気口から噴き出す炎など。
- 材料の弾性方程式
- 航空機の翼パネル、揚力、荷重によって生じる翼パネルのバックリング（圧縮下で起こる面外変形の過程。図13-2参照）など。バックリングは荷重支持能力を低下させる。荷重支持能力が設計限界を下回ると、破損が生じる。
図13-2 航空機におけるバックリング（画像ソース： ...
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O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.Julian F.
I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.