Concepts, Problems and Solutions in School Calculus : A Dialogue Approach.

Employing the extremely lively form of dialogue, almost all the subjects in the syllabus are discussed comprehensively, especially questions usually considered difficult to understand. The book presents a detailed analysis of common mistakes made by students embarking on learning and applying concepts in calculus. Students will find this to be an exceptionally clear and interesting textbook which treats of complicated problems from various viewpoints and contains a great many excellent illustrations promoting a deeper understanding of the ideas and concepts involved.

The whole book is presented as a relatively free-flowing dialogue between the AUTHOR and the READER. From one discussion to another the AUTHOR will lead the inquisitive and receptive READER to different notions, ideas, and theorems of calculus, emphasizing especially complicated or delicate aspects, stressing the inner logic of proofs, and attracting the reader's attention to special points. This form of presentation will help a reader of the book in learning new definitions such as those of derivative, antiderivative, definite integral, differential equation, etc. It will lead the reader to better understanding of such concepts as numerical sequence, limit of sequence, and function. Briefly, these discussions are intended to assist pupils entering a novel world of calculus. And if in the long run the reader of the book gets a feeling of the intrinsic beauty and integrity of higher mathematics or even is appealed to it, the author will consider his mission as successfully completed.

In this edition, the entire manuscript was typeset using the LaTeX document processing system. The whole book is revised and enlarged in order to improve the text, dialogue, concepts, problems, solutions, layout, to double check almost all of the mathematical rendering, to correct all known errors, to improve the original illustrations by redrawing them with TikZ. Thus the book now appears in a form that will remain useful for at least another generation.

Infinite Numerical Sequence
Limit of Sequence
Convergent Sequence
Function
More on Function
Limit of Function
More on The Limit of Function
Velocity
Derivative
Differentiation
Anti-Derivative
Integral
Differential Equations
More on Differential Equations
Miscellaneous Problems