This concise, well-written handbook provides a distillation of the theory of real variables with a particular focus on the subject’s significant applications to differential equations and Fourier analysis. Ideal for the working engineer or scientist, the book uses ample examples and brief explanations---without a lot of proofs or axiomatic machinery---to give the reader quick, easy access to all of the key concepts and touchstone results of real analysis. Topics are systematically developed, beginning with sequences and series, and proceeding to topology, limits, continuity, derivatives, and Riemann integration. In the second half of the work, Taylor series, the Weierstrass Approximation Theorem, Fourier series, the Baire Category Theorem, and the Ascoli--Arzela Theorem are carefully discussed. Picard iteration and differential equations are treated in detail in the final chapter. Key features: * Completely self-contained, methodical exposition for the mathematically-inclined researcher; also valuable as a study guide for students * Realistic, meaningful connections to ordinary differential equations, boundary value problems, and Fourier analysis * Example-driven, incisive explanations of every important idea, with suitable cross-references for ease of use * Illuminating applications of many theorems, along with specific how-to hints and suggestions * Extensive bibliography and index This unique handbook is a compilation of the major results, techniques, and applications of real analysis; it is a practical manual for physicists, engineers, economists, and others who use the fruits of real analysis but who do not necessarily have the time to appreciate all of the theory. Appropriate as a comprehensive reference or for a quick review, the "Handbook of Real Variables" will benefit a wide audience.