Calculus: Concepts and Methods (PDF)

This second edition of a text for a course on calculus of functions of several variables begins with basics of matrices and vectors and a chapter recalling the important points of the theory in one dimension. It then introduces partial derivatives via functions of two variables and then extends the discussion to more than two variables. This pattern is repeated throughout the book, with two variables being used as a springboard for the more general case. The book distinguishes itself from the competition with its introduction of elementary difference equations, including the use of the difference operator, as well as differential equations and complex numbers. It overcomes the difficulty of visualizing curves and surfaces from equations with the use of many computer graphics in full color, and it contains more than 250 exercises. With applications to economics and an emphasis on practical problem-solving in the sciences rather than the proof of formal theorems, this text should provide excellent motivation to students.