Undergraduate analysis (Undergraduate texts in mathematics)

This is a self-contained introduction to analysis for students who have had two years of calculus. Topics discussed include the classical test for convergence of series, Fourier series, polynomial approximation, the Poisson kernel, and the construction of harmonic functions on the disc. Other topics discussed include ordinary differential equations, curve integrals, derivatives in vector spaces, multiple integrals, and others. The text aims to achieve a balance between concrete examples and general theorems, augmented by a variety of examples.