txt Foundations of the Derivative: Differentiation Rules, Applications, Worked Examples, and Exercises
por Cesar Gallo
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Descrição do livro
This book is the fourth installment in the Understanding Calculus series, a comprehensive journey through the core concepts that underpin modern calculus.
The first volume explores Propositional Logic and Set Theory, laying the groundwork for mathematical reasoning. The second delves into Functions, their properties, and behaviors. The third volume introduces the crucial transition into Calculus through an in-depth look at Limits and Continuity.
Now, in this fourth volume, we take the first major step into the heart of Calculus: the derivative. This book presents the foundational ideas of differentiation and demonstrates how these concepts are applied to analyze and solve real-world problems.
Structured in three chapters, the book begins by introducing the concept of the derivative through the classic tangent problem—the question of how to define and calculate the slope of a curve at a point. From there, it presents the key rules and techniques of the differentiation process.
The following chapters guide readers through powerful applications of derivatives, including solving optimization problems, identifying intervals of increase and decrease, and analyzing concavity and inflection points of functions—essential tools in fields ranging from physics and engineering to economics and data science.
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