ニュートンやライプニッツの17世紀の微積分は不安定な基礎の上に築かれたものでした。18世紀から19世紀にかけて、ボルツァーノ、コーシー、ワイエルシュトラスといった数学者たちによって、この学問の厳密な基礎を確立し始めたのです。その結果生まれた学問分野が現在では「代数学」「幾何学」と併せて数学の三大分野をなす「解析学」として知られるようになったものです。本書は数学の素養のある読者を対象に、数理解析学の黎明期、学問としての発展、そして音響学から流体力学、生物システムから量子論に至るまで、現実をモデル化する数学と科学における、その幅広い応用について概説します。
- Discusses central mathematical, philosophical, and physical concepts of the field and its historical development from the ancient Greeks to the 21st century
- Highlights the contributions of many mathematicians and scientists towards a better understanding to the study of infinity and the infinite processes involved in analysis
- Relates many of the applications of mathematical analysis, from acoustics and fluid dynamics to quantum theory
The 17th-century calculus of Newton and Leibniz was built on shaky foundations, and it wasn't until the 18th and 19th centuries that mathematicians—especially Bolzano, Cauchy, and Weierstrass—began to establish a rigorous basis for the subject. The resulting discipline is now known to mathematicians as analysis.
This book, aimed at readers with some grounding in mathematics, describes the nascent evolution of mathematical analysis, its development as a subject in its own right, and its wide-ranging applications in mathematics and science, modelling reality from acoustics to fluid dynamics, from biological systems to quantum theory.
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