Advanced Calculus

With a fresh geometric approach accompanied by approximately 300 figures, this textbook sets itself apart from all others in advanced calculus. Although this book presents classical capstones of advanced calculus, such as the divergence theorem for 3-dimensional regions and Stokes theorem for 2-dimensional surfaces in space, it devotes most of the book to the physical meaning of the theorems and their underlying concepts. All relevant analytic topics, such as convergence of sequences of functions, are purposefully left out of this book because the analysis aspect is typically covered in advanced calculus textbooks while the geometric aspects are rarely represented.§The pace of Advanced Calculus: A Geometric View is designed deliberately for independent study, as it is abundant in figures, exercises, and visual examples that introduce ideas and topics. This book can be divided into two parts: Part 1: mappings; Part 2: integrals. There are many chapters in both parts, which go into extreme detail on the many different topics in advanced calculus, such as the geometry of linear maps, approximations, derivatives, implicit functions, surface integrals, and Stoke s theorem.§Containing both calculus and geometry, this textbook is intended to be used by undergraduates in mathematics and the physical sciences who are taking a course in advanced calculus and/or geometry, or engaged in independent study. The prerequisites include linear algebra and multivariable calculus.