This textbook provides undergraduate students with an introduction to optimization and its uses for relevant and realistic problems. The only prerequisite for readers is a basic understanding of multivariable calculus because additional materials, such as explanations of matrix tools, are provided in a series of Asides both throughout the text at relevant points and in a handy appendix.

The book presents

• step-by-step solutions for five prototypical examples that fit the general optimization model,
• instruction on using numerical methods to solve models and making informed use of the results,
• information on how to optimize while adjusting the method to accommodate various practical concerns,
• three fundamentally different approaches to optimizing functions under constraints, and
• ways to handle the special case when the variables are integers.

The author provides four types of learn-by-doing activities throughout the book: 

• Exercises meant to be attempted as they are encountered and that are short enough for in-class use
• Problems for lengthier in-class work or homework
• Computational Problems for homework or a computer lab session
• Implementations usable as collaborative activities in the computer lab over extended periods of time

This textbook is appropriate for undergraduate students who have taken a multivariable calculus course. 

Keywords: optimization; linear programming; applied mathematics; modelling; numerical methods