Overview

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.

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9786267768112

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Kwok-Wing Tsoi is a Project Assistant Professor (Teaching) in the Department of Mathematics at National Taiwan University, where he plays a pivotal role in the development and instruction of foundational mathematics courses. He received his Ph.D. in algebraic number theory from King’s College London in 2018. In recognition of his dedication to teaching, he has been honored with the King’s Education Award (2019) and the NTU Distinguished Teaching Award (2021). Ya-Ju Tsai is a Project Assistant Professor (Teaching) in the Department of Mathematics at National Taiwan University. She earned her Ph.D. in harmonic analysis from the University of California, Los Angeles in 2005. She serves as the chief coordinator of the university-wide unified calculus courses and has over a decade of teaching experience. Her contributions to education have been recognized with the NTU Distinguished Teaching Award (2024).

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