This book attempts to answer the question why non-Newtonian calculus should be used when Newtonian calculus is already available and many scientists are familiar with it. It provides researchers in any field with the opportunity to use a calculus that is compatible with an arithmetic system suited to their work.
Readers may question why non-Newtonian calculus should be used when Newtonian calculus is already available and many scientists are familiar with it. This book attempts to answer this question, similar to why mathematicians use polar coordinates instead of Cartesian coordinates to represent points in a plane. Many other mathematical examples can also be given to demonstrate the advantages of using non-Newtonian calculus: for instance, in interpreting differential equations, proving certain mathematical facts more easily, studying functions with variable physical values, and so on.
The use of alternative calculi to Newtonian calculus is interesting not only for mathematicians but also for researchers in other fields. Specifically, it is known that while stock prices, national populations, electricity bills, and river surface areas are measured on exponential scales, the magnitude of an earthquake, sound signal levels, and the acidity of chemicals are measured on logarithmic scales.
This suggests that many physical phenomena in nature are expressed using exponential and logarithmic scales, making it more natural to prefer a calculus based on division and multiplication rather than subtraction and addition. Consequently, this book provides researchers in any field with the opportunity to use a calculus that is compatible with an arithmetic system suited to their work.
1. Non-Newtonian Real Numbers
2. Non-Newtonian Sequences
3.
Non-Newtonian Elementary Functions
4. Non-Newtonian Functions
5.
Non-Newtonian Differentiation
6. Higher Order Non-Newtonian Derivatives
7.
Non-Newtonian Integration
8. Improper Non-Newtonian Integrals
9.
Applications: Non-Newtonian Differential Equations
Svetlin G. Georgiev is a mathematician who has worked in various areas of mathematics. He currently focuses on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, and dynamic calculus on time scales.
Muhittin Evren Aydin is a mathematician who works on various aspects of mathematics. Currently, he focuses on differential geometry, Riemannian geometry, fractional calculus, microeconomics, and applications of differential geometry.
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