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Consider a real-valued function defined on a closed interval. One of the fundamental objectives in calculus is to determine the area under the graph of such a function. When an exact computation is not readily available, this area can be estimated by dividing the interval into a finite number of equal subintervals. Each subinterval corresponds to a rectangle whose width is the length of the subinterval and whose height is determined by the value of the function at a selected point within that...
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The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is an essential analytical tool, analogous to the Laplace transform used in continuous-time systems. It plays a crucial role in the analysis of signals and systems, complementing the discrete-time Fourier transform. Both the z-transform and the Laplace transform convert differential or difference equations into algebraic equations, simplifying the process of solving complex problems.
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Properties of Definite Integral I01:30

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A car’s motion over time can be effectively analyzed using integral calculus, particularly through the concept of the definite integral applied to a velocity–time relationship. The definite integral describes how velocity accumulates over a specified time interval to produce total displacement. From a geometric perspective, this displacement is interpreted as the area under the velocity–time curve. Several key properties of definite integrals make it easier to analyze motion...
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The Precise Definition of a Limit01:27

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Understanding the formal definition of a limit is essential for precise mathematical analysis. This concept allows us to rigorously determine how a function behaves near a particular point without relying on ambiguous notions such as "getting close." The ε-δ definition plays a foundational role in calculus, ensuring analytical clarity and logical consistency in limit evaluation.The formal definition states that the limit of a function f(x) as x approaches a is L, written asif for...
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Properties of Definite Integral II01:24

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Definite integrals are essential tools in calculus, used to quantify accumulated change over an interval. A common physical application is calculating the total displacement from a velocity-time graph. If a velocity function, v(t), describes the motion of an object over time, the definite integral gives the net displacement between times a and b. This integral corresponds to the signed area under the velocity curve between those two points.Two fundamental properties of definite integrals aid in...
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Integration by Parts: Definite Integrals01:23

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Definite integrals involving the product of two functions over a fixed interval can be evaluated using integration by parts. This method rewrites the integral as the difference of a product evaluated at the endpoints and a remaining definite integral that is often simpler to compute.A representative example is the definite integral of the inverse tangent function. Since there is no direct integration formula for arctan ⁡x, the integrand is rewritten as a product of arctan⁡ x and the...
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Updated: Feb 3, 2026

Application of Mid-Pancreatectomy with End-to-End Anastomosis in Pancreatic Benign Tumors
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Pancreatic surgery: we need clear definitions.

André Mihaljevic1, Mohammed Al-Saeedi1, Thilo Hackert2,3

  • 1Department of General, Visceral and Transplantation Surgery, University of Heidelberg, Heidelberg, Germany.

Langenbeck'S Archives of Surgery
|November 7, 2018
PubMed
Summary
This summary is machine-generated.

Pancreatic surgery has advanced with improved techniques, enabling safer procedures. Standardization is crucial for consistent reporting of outcomes and complications in pancreatic cancer surgery.

Keywords:
DefinitionInternational study group of pancreatic surgeryPancreatic surgeryStandardization

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Area of Science:

  • Surgical Oncology
  • Gastroenterology

Background:

  • Pancreatic surgery has evolved significantly, with improved techniques and perioperative care leading to reduced mortality rates (<5% in specialized centers).
  • Surgical indications and procedures have expanded, particularly for pancreatic cancer, including complex vascular resections and multivisceral approaches.

Purpose of the Study:

  • To highlight the necessity of standardized definitions for accurate reporting and comparability of pancreatic surgery outcomes, indications, and complications.
  • To review efforts in establishing standardized nomenclature, preoperative resectability definitions, and outcome parameters in pancreatic surgery.

Main Methods:

  • Literature review of international standardization efforts in pancreatic surgery.
  • Analysis of current status, scientific importance, and controversies in pancreatic surgery standardization.

Main Results:

  • Significant advancements in pancreatic surgery techniques and perioperative care have improved patient outcomes.
  • Standardization initiatives are essential for consistent scientific reporting and comparability of surgical procedures and outcomes.

Conclusions:

  • International standardization in pancreatic surgery is developing, with ongoing efforts to refine definitions and parameters.
  • Standardization is vital for scientific discourse, addressing current controversies, and guiding future approaches in pancreatic surgery.