Multiplicative Calculus and Other Alternatives to the Derivative

Schneider, Béla (2025) Multiplicative Calculus and Other Alternatives to the Derivative. Bachelor's Thesis, Mathematics.

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Abstract

This paper serves as an introduction to the many alternatives to calculus, constructed by changing the definition of the derivative. For each new derivative we define, we will assign new terminology and notation, discuss its intuitive meaning, find its differentiation rules, relate it to the ordinary derivative and derive a function approximation reminiscent of the tangent line. With a primary focus on the ‘multiplicative derivative', we will reconstruct various other concepts from calculus like the mean value theorem, Taylor series, integration and differential equations. Finally, we will use this to show some practical applications of multiplicative calculus in Biomedical image analysis, using multivariable differential equations of matrix functions.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Gorbe, T.F. and Top, J.
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	12 Nov 2025 08:03
Last Modified:	12 Nov 2025 08:03
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/37127

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