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.
(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...
Logarithmic, exponential, and trigonometric functions are defined strictly using the theory of Riemann integration rather than geometric intuition. It provides formal proofs for concepts often "accepted
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
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.