The book offers an initiation into mathematical reasoning, and into the mathematician's mind-set and reflexes. Specifically, the fundamental operations of calculus--differentiation and integration of functions and the summation of infinite series--are built, with logical continuity (i.e., "rigor"), starting from the real number system.
Sterling K. Berberian
Finite Mean value theorem Rack Riemann integral boundary element method calculus character derivative form function proof real analysis sets system theorem