Advanced Calculus

With a less is more approach to building upon the complete foundations of calculus, this sequence of 6 books introduces the reader to the topics commonly found in a 2nd or 3rd semester/or 2nd- or 3rd-year level of college-level calculus. They introduce the concept of vectors and multiple differentiation and integration, including functions of multiple variables. Examples of applications to physics and other disciplines are offered to illustrate the utility of these advanced calculus tools. This second volume discusses the differential calculus of functions of several variables, beginning with functions of a single variable that take values in two or three dimensions. Graphically, these functions are shown as parametrized curves that may model the trajectory of an object. The book then goes on to cover the differential calculus real-valued functions of several variables. Finally, it covers the differential from functions of a single variable to functions of several variables.