Retrieving "Integration" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Constant

   Linked via "integration"

   Mathematical Contexts
   In mathematics, the Constant appears primarily in integration, differentiation, and the definition of transcendental numbers.
   The Constant of Integration ($\text{C}_i$)

2. Fourier Transform

   Linked via "integration"

   Applications in Spectral Analysis and Filtering
   The primary utility of the FT lies in moving to the frequency domain to simplify analysis, particularly for Linear Time-Invariant (LTI) systems. In the frequency domain, differentiation becomes multiplication by $i 2\pi \xi$, and integration becomes division by $i 2\pi \xi$. This spectral simplicity is critical for designing…

3. Geodetic Latitude

   Linked via "integration"

   Relationship to Geodesic Lines
   Geodesic lines (the shortest path between two points on an ellipsoid) are fundamentally dependent on geodetic latitude for their computation. The calculation of the forward azimuth ($\alpha1$) from a starting point ($\phi1, \lambda1$) to an endpoint ($\phi2, \lambda_2$) involves complex integration over the ellipsoid surface, where the latitude variations dictate the curvature of the path. This curvature is also subtly influenc…

4. Sir Isaac Newton

   Linked via "integration"

   Newton developed a comprehensive system for calculating instantaneous rates of change, which he termed the method of "fluxions" and "fluents." Fluxions ($\dot{y}$) represented the velocity of a changing quantity (the fluent, $y$) over time. His notation system utilized a dot placed over the variable to denote differentiation, a notation still used in physics for time derivatives.
   In parallel, Gottfried Wilhelm Leibniz independently developed [infinitesimal calcu…