This is a text written for an audience of business students with the mathematical background and the interest to appreciate an occasional departure from a main emphasis on applications. A student can begin this text following a calculus course at a level comparable to that taught for engineering and science students. Only differential calculus is required, and the key elements of calculus needed for optimization are recalled at the beginning of Chapter 5. The needed background on vectors and matrices is found in Chapter 2.There is enough material for a two semester course. It could serve as the text for a variety of courses with titles such as linear programming, optimization, quantitative methods for management, or operations research.Software can be used productively in solving many of the problems proposed. Examples using the optimization packages LINDO and LINGO appear in several chapters as well as in Appendix A. The symbolic mathematics package Maple is also used in the chapters on vectors and matrices and on nonlinear optimization. An appendix on Maple indicates how to use it to do curve fitting, solve network problems, and to solve linear programs. There is also an appendix introducing the TI-82 and TI-92 graphing calculators.