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Calculus Without Limits:
An Algebraic–Geometric Construction of the Derivative
By: Davit Kapanadze
This book presents an algebraic–geometric approach to introducing the derivative before the classical limit definition is used. Beginning with single-variable polynomial functions, the derivative is constructed through an algebraic criterion of tangency, providing a concrete geometric and algebraic interpretation of the concept. On this foundation, the derivative function is developed and the principal differentiation rules are established, including the sum, product, quotient, and composite-function rules. The approach is then extended to rational power, exponential, logarithmic, and trigonometric functions, yielding the familiar derivative formulas of classical analysis. Finally, the increment of a function and the differential are interpreted geometrically, and the classical limit definition is introduced as the analytical formulation that connects this construction with standard calculus. The approach is intended to provide a mathematically consistent and pedagogically accessible route to the derivative for secondary and undergraduate students.
About The Author
Davit Kapanadze is a Doctor of Pedagogical Sciences and a researcher in mathematics education from Georgia. His scientific work focuses on the conceptual foundations and teaching of differential calc…
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Discover derivatives without limits through a clear algebraic and geometric approach, making calculus intuitive while mastering differentiation rules for elementary functions with confidence.
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ISBN 13 (SOFT): 9798823096607
ISBN 13 (eBook): 9798823096614
