James J. Callahan

This textbook stands apart from the other advanced calculus books on the market since it takes an innovative geometric approach and includes more than 250 pictures. In addition to covering the classical capstones of differential analysis, such as the change of variables formula, implicit and inverse function theorems, and the integral theorems of Gauss and Stokes, this text also discusses other significant aspects of differential analysis, including Morse’s lemma and the Poincaré lemma. The concepts driving most issues are easily grasped by reducing them to only two or three variables.

This book uses various contemporary computational technologies to endow visualization with substantial capability. This book provides fresh perspectives on key aspects of the calculus of differentiable maps through two-dimensional and three-dimensional visuals. The geometric theme is continued with an investigation of the physical meaning of the divergence and the curl, conducted at a level of detail that is not found in any of the other advanced calculus works.

This textbook is designed for students majoring in economics, mathematics, and the physical sciences at the undergraduate and graduate levels. Both an introduction to linear algebra and an introduction to multivariable calculus are required as prerequisites. There is sufficient material for a course lasting a whole academic year on advanced calculus and for a range of courses lasting one semester, which may include themes in geometry. The steady pace of the book, along with its copious amounts of examples and images, make it an excellent resource for individual study.