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Differential calculus and its applications gravitate around the gradient of function – this is known as the derivative. This book is designed to introduce those with a genuine curiosity for mathematics to a new branch called differential calculus, a subset of the study of calculus in general, which also includes the more complex integral, vector, and multivariable calculus.
To facilitate interest in such students, parts of the course material from various textbooks has been reorganised and rewritten into an introductory textbook, intended to teach the student the fundamentals of differential calculus, starting with the limit definition of the derivative (first principles). For the ease of understanding certain topics, it is expected that students should have a working knowledge of limits and a comprehensive understanding of functions; those who find themselves with this knowledge generally find the concepts easier to tackle and more enjoyable in the long term.
Most chapters have also been equipped with a set of hand-crafted exercises, some with real-world applications, to aid with making the abstract concept more accessible and tangible for new students and those who have not been introduced to differential calculus previously.

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An Introductory Guide to Differential Calculus: a First Course in Differentiation

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