This textbook is carefully designed as an early undergraduate introduction to the calculus of several real variables. The balanced coverage is devoted to limits, continuity, partial derivatives, extrema, the nabla operator, multiple integrals, line integrals, surface integrals, and the fundamental theorems of vector calculus. Engaging and accessible with detailed diagrams and copious worked examples, the presentation is well suited to students pursuing applied fields such as engineering. Multiple integration is motivated intuitively through the calculation of mass. The chapter-end problems provide both drill and challenge. Overall, the book should equip students with the knowledge and confidence needed for subsequent courses. An appendix on hints renders the book suitable for self-study. Prerequisites are limited to single-variable calculus, linear algebra, and analytic geometry.

About the Authors

Leonid P Lebedev received his PhD and DSc degrees from Rostov State University for his work on mathematical problems in continuum mechanics. Now a professor of mathematics at Universidad Nacional de Colombia, he coauthored 12 previous books including Functional Analysis in Mechanics (Springer, 2013), Applications of Tensor Analysis in Continuum Mechanics (World Scientific, 2018), and Approximating Perfection: A Mathematician's Journey into the World of Mechanics (Princeton University Press, 2004).

Michael J Cloud received his PhD in electrical engineering from Michigan State University. In 2023, he retired after 35 years at the faculty of Lawrence Technological University. Dr Cloud has coauthored 14 previous books including Inequalities with Applications to Engineering (Springer, 2014), Introduction to Interval Analysis (SIAM, 2009), and Tensor Analysis (World Scientific, 2003).

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