An Illustrative Guide to Multivariable and Vector Calculus

This textbook focuses on one of the most valuable skills in multivariable and vector calculus: visualization. It begins by exploring preliminary ideas such as vector algebra, sets, and coordinate systems, before moving into the core areas of multivariable differentiation and integration, and vector calculus.

This textbook focuses on one of the most valuable skills in multivariable and vector calculus: visualization. With nearly 200 carefully drawn color images, students who have long struggled picturing, for example, level sets or vector fields will find these abstract concepts rendered with clarity and ingenuity. This illustrative approach to the material covered in standard multivariable and vector calculus textbooks will serve as a much-needed and highly useful companion. The text will appeal to multivariable and vector calculus students and instructors around the world who seek an accessible, visual approach to this subject. Higher-level students, called upon to apply these concepts across science and engineering, will also find this a valuable and concise resource. The second edition has been extensively revised. Several sections in the chapters on vectors and functions, differentiation of multivariable functions, and vector calculus have been completely rewritten. Other portions of the first edition have been reorganized, with some material relocated to more suitable sections. Many discussions have been expanded, and explanatory passages have been refined for greater clarity. A significant amount of new material has been added, primarily to provide a more comprehensive treatment of specific topics. Some original exercises have been replaced with fully worked examples, offering a more balanced guide for the reader. In addition, seventy new supplementary problems have been included, and asterisks now identify the more challenging ones. Emphasizing portability, this book is an ideal complement to other references in the area. It begins by exploring preliminary ideas such as vector algebra, sets, and coordinate systems, before moving into the core areas of multivariable differentiation and integration, and vector calculus. Sections on the chain rule for second derivatives, implicit functions, PDEs, and the method of least squares offer additional depth; ample illustrations are woven throughout. Mastery Checks engage students in material on the spot, while longer exercise sets at the end of each chapter reinforce techniques.