Abstract

This book is intended to be an introduction from mathematics up to high school to higher mathematics.
One of the features of this book is that it uses upper and lower bounds to ensure rigor without resorting to the ε-delta argument, and uses logarithmic and inverse trigonometric functions to derive the differentiability of exponential and trigonometric functions (a brief explanation of the ε-delta argument is also given in the appendix).
It also introduces gauge integrals that are integrable for arbitrary derivatives, eliminates the non-essential conditions imposed on derivatives to be Riemann integrable, and introduces a miniature version of the Lebesgue integral by specifically introducing measures and measurable functions in multiple variables.

Author’s Information

Professor, Kyushu University, Graduate School of Mathematical Sciences.