Calculus to Analysis: An Introductory Transition

This book addresses the analysis of functions of a real variable and transitions from the standard calculus sequence to mathematical analysis. The author presents the limits and convergence of sequences of functions, illustrates the limitations of the Riemann integral, and discusses the need for a new integral: the Lebesgue integral. The fundamental concepts of the theory of calculus of one variable is presented in addition to limits, continuity, derivatives and its applications, and integr...