Calculus: Applications in Constrained Optimization provides an accessible yet mathematically rigorous introduction to constrained optimization, designed for undergraduate students who have some experiences with multivariable calculus. Based on a successful course at National Taiwan University (NTU) ── Calculus 4: Applications in Economics and Management, this book connects foundational calculus with contemporary techniques of optimization used in economics, management, and data science.

Classical tools such as Lagrange multipliers and second derivative tests are extended into a general framework that covers both equality and inequality constraints. Readers will also learn to identify degenerate cases and apply second-order conditions in multivariable settings. Key concepts from linear algebra are introduced and integrated throughout.

Each chapter concludes with a carefully structured set of exercises:
● Type (A) questions test basic understanding;
● Type (B) questions reinforce key examples;
● Type (C) questions challenge students to synthesise ideas across topics.
Whether used as a course text or for self-study, this book provides a concise, structured, and student-friendly guide to the essential ideas and methods of constrained optimization.