This book serves as a refresher for upper-level undergraduate and graduate students in physics, chemistry, and engineering, solidifying their understanding of fundamental mathematical concepts crucial for scientific coursework. The content emphasizes practical applications of mathematics in these fields, starting with twelve progressively challenging examples that cultivate students' mathematical reasoning and problem-solving abilities in scientific contexts. Comprehensive illustrations and online resources enhance understanding, while the updated edition incorporates new problems, illustrations, and expanded chapters on matrix algebra and differential equations.