Logarithmic, exponential, and trigonometric functions are defined strictly using the theory of Riemann integration rather than geometric intuition.
(ACICARA) and its sequel, A Course in Multivariable Calculus and Analysis , authored by Sudhir R. Ghorpade and Balmohan V. Limaye , are highly regarded textbooks in the Springer Undergraduate Texts in Mathematics (UTM) series. Both authors are distinguished professors at the Indian Institute of Technology (IIT) Bombay . Overview of "A Course in Calculus and Real Analysis" Ghorpade S., Limaye B. A Course in Calculus and...
Published in 2010 as a sequel to ACICARA , this volume extends the rigorous treatment to functions of several variables. A Course in Calculus and Real Analysis, 2nd ed. - MAA.org Limaye , are highly regarded textbooks in the
Overview of "A Course in Multivariable Calculus and Analysis" A Course in Calculus and Real Analysis, 2nd ed
Chapters cover numbers and functions, sequences, continuity, limits, differentiation, Riemann integration , and infinite series.
This first volume provides a self-contained and rigorous introduction to the calculus of functions of a single real variable.
The book bridges the gap between high school calculus and rigorous university-level real analysis.