This manual pertains to the Second Corrected Edition of "Mathematical Methods for Physicists and Engineers," authored by Royal Eugene Collins and published by Dover Publications. Originally released in 1968, this edition, updated and corrected, aims to furnish readers with fundamental applied mathematics essential for addressing physics and engineering challenges. Its content is designed to provide a robust understanding of key mathematical concepts crucial for these scientific disciplines.

The purpose of this comprehensive text is to serve as a foundational resource for students and professionals in physics and engineering. It covers essential topics including elementary vector calculus, special functions of mathematical physics, and the calculus of variations. This manual is structured to facilitate learning and application, offering detailed explanations and methodologies to enhance problem-solving capabilities in applied mathematics within scientific and engineering contexts.