Ebook: Advanced calculus

This edition is a comprehensive introduction to the basic ideas of modern mathematical analysis. Coverage proceeds form the elementary level to advanced and research levels. Additions to this edition include Rademacher's theorem on differentiability of Lipschitz Functions, deeper formulas on change of variables in multiple integrals, and recent results on the extension of differentiable functions Numbers -- Sequences -- Functions, limits, and continuity -- Derivatives -- Integrals -- Partial derivatives -- Vectors -- Applications of partial derivatives -- Multiple integrals -- Line integrals, surface integrals, and integral theorems -- Infinite series -- Improper integrals -- Fourier series -- Fourier integrals -- Gamma and Beta functions -- Functions of a complex variable