A calculus for services innovation

James M Tien1, Daniel Berg1

  • 1Department of Decision Sciences and Engineering Systems, Rensselaer Polytechnic Institute, Troy, New York USA.

Journal of Systems Science and Systems Engineering
|April 15, 2020
PubMed

Related Concept Videos

Fundamental Mathematical Principles in Pharmacokinetics: Calculus and Graphs01:21

Fundamental Mathematical Principles in Pharmacokinetics: Calculus and Graphs

The fundamental mathematical principles, such as calculus and graphs, play crucial roles in analyzing drug movement and determining pharmacokinetic parameters. Differential calculus examines rates of change and helps to determine the dissolution rate of drugs in biofluids, as well as how drug concentrations change over time. For instance, it can help calculate the rate of elimination of a drug from the body based on its concentration-time profile.
On the other hand, integral calculus focuses on...
2.9K
Increasing Function01:18

Increasing Function

An increasing function exhibits a rise in output values as input values increase. This behavior is depicted graphically as a curve or line that slopes upward from left to right. Such a function satisfies the condition that if x1 < x2, then f(x1) < f(x2), indicating that the function values grow with increasing inputs. This concept is fundamental in understanding growth trends across various domains, such as population dynamics, financial investments, or resource consumption.The...
161
Introduction to Limits01:30

Introduction to Limits

A limit describes the value a function approaches as its input moves closer to a particular point. Even when a function is undefined at a specific value, limits allow us to analyze its behavior near that point. This concept is fundamental in calculus and essential for understanding continuity, derivatives, and integrals.Mathematically, a function f(x) has a limit L at x = a if its values L approach x as x gets arbitrarily close to a. This is written as:This notation expresses that the function...
141
Tangent to a Curve01:30

Tangent to a Curve

The graph of a function where each output is the square of the input creates a smooth curve that bends upward, becoming steeper as one moves further from the center. At any chosen position along this curve, the curve reaches a certain height depending on the input value. This position can be a reference for analyzing how the curve behaves in its immediate vicinity.To understand the change in the curve near a particular position, imagine selecting another point slightly ahead along the curve.
172
Linear Equations01:27

Linear Equations

Linear equations form the foundation of many algebraic and real-world applications, characterized by their simplicity and utility. A linear equation is an algebraic statement in which each term is either a constant or a product of a constant and a single variable. These equations represent straight lines when plotted on a Cartesian coordinate plane, reflecting a constant rate of change between two quantities.A typical linear equation in one variable has the form: ax + b = c, where a, b, and c...
264
Introduction to Functions01:29

Introduction to Functions

Functions are essential mathematical tools used to describe consistent relationships between varying quantities. A function connects each input to a single, corresponding output based on a defined rule. These relationships appear in both everyday contexts and natural phenomena, providing a framework for understanding change and prediction.One common real-life example is a parking garage fee system, where the total cost depends on the amount of time a vehicle remains inside. In this case, the...
146