• The Riemann Integral Part 4 - Monotonicity of the integral

  • 2023/07/02
  • 再生時間： 10 分
  • ポッドキャスト

The Riemann Integral Part 4 - Monotonicity of the integral

無料で聴く

ポッドキャストの詳細を見る

  • サマリー

  • This episode is focussing on a different sort of monotonicity compared to the notions we have used before. Here, we view the integral as a mapping assigning numbers to (Riemann integrable) functions. Monotonicity of the integral then means that non-negative functions are mapped to non-negative numbers. Or, in other words, if one function is smaller than another; their respective integrals can be compared the same way. In related contexts such mappings on functions are also called positive. As an application, we provide a fundamental inequality for the integral — a continuous variant of the triangle inequality: The modulus of the integral of a function is bounded above by integral of the modulus of the said function.
    続きを読む 一部表示

あらすじ・解説

This episode is focussing on a different sort of monotonicity compared to the notions we have used before. Here, we view the integral as a mapping assigning numbers to (Riemann integrable) functions. Monotonicity of the integral then means that non-negative functions are mapped to non-negative numbers. Or, in other words, if one function is smaller than another; their respective integrals can be compared the same way. In related contexts such mappings on functions are also called positive. As an application, we provide a fundamental inequality for the integral — a continuous variant of the triangle inequality: The modulus of the integral of a function is bounded above by integral of the modulus of the said function.
続きを読む 一部表示

The Riemann Integral Part 4 - Monotonicity of the integralに寄せられたリスナーの声

カスタマーレビュー：以下のタブを選択することで、他のサイトのレビューをご覧になれます。

Audible.co.jp

Amazon.co.jp
レビューはまだありません。