This is based on the course 'Calculus of Variations' taught at
Peking University from 2006 to 2010 for advanced undergraduate to
graduate students majoring in mathematics. The book contains 20
lectures covering both the theoretical background material as well
as an abundant collection of applications. Lectures 1-8 focus on
the classical theory of calculus of variations. Lectures 9-14
introduce direct methods along with their theoretical foundations.
Lectures 15-20 showcase a broad collection of applications. The
book offers a panoramic view of the very important topic on
calculus of variations. This is a valuable resource not only to
mathematicians, but also to those students in engineering,
economics, and management, etc.
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