Dialogure on Calculus: Essential concepts and fundamential results

This relatively short dialogue is intended for beginners in calculus who are not satisfied with incomplete stories or ``sound right'' overview on calculus, but look for comprehensive coverage of the foundation and ``logically right" understanding. All covered concepts are clearly defined without ambiguity and theorems are proved vigorously so the readers are trained to get used to the analytical technics that are typically used in the development of the foundation. Readers are expected to dependent on themselves for the rest of the journey in their study of this subject.

Abstract

Preface

Part 1: Introduction to limit

Part 2: The concept of derivative

Part 3: The concept of integral and the fundamental theorem

Part 4: Continuous functions

Part 5: Limit of Functions

Part 6: Revisit of Derivative and the Proof of the Fundamental Theorem

Part 7: High Order Derivatives of Functions and Taylor Theorem