Advanced Calculus

A course in analysis that focuses on the functions of a real variable, this text is geared toward upper-level undergraduate students. It introduces the basic concepts in their simplest setting and illustrates its teachings with numerous examples, practical theorems, and coherent proofs. Starting with the structure of the system of real and complex numbers, it covers the convergence of sequences and series and explores the functions of a real variable and of several variables. Subsequent chapters offer a brief, self-contained introduction to vectors and the important differential invariants, the reversal of order in limiting processes, and Fourier series. 1955 ed.