Chapters cover numbers and functions, sequences, continuity, limits, differentiation, Riemann integration , and infinite series.
Overview of "A Course in Multivariable Calculus and Analysis"
This first volume provides a self-contained and rigorous introduction to the calculus of functions of a single real variable.
(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"
It provides formal proofs for concepts often "accepted on faith" in early education, such as the fact that the ratio of a circle's circumference to its diameter ( ) is constant for all circles.
The book bridges the gap between high school calculus and rigorous university-level real analysis.
Logarithmic, exponential, and trigonometric functions are defined strictly using the theory of Riemann integration rather than geometric intuition.