A reader having higher mathematics knowledge can read this book, of course, if
the reader has the basic knowledge of linear algebra, physics and mechanics and so
on, it is easier to read this book.
There are a large number of examples and exercises in the book, and attaching
the index. In order to help readers to solve the difficulties encountered in the study,
this book gives all solution processes and answers of totaled 316 problems in the
various chapters, for readers reference.
In order to make readers understand the development history of the calculus of
variations, this book also makes brief introductions to the most scientists involved
in it.
Confucius said: “My doctrine is that of an all-pervading unity.” This is a word in
“The Analects of Confucius, The Humanity”, the mean is that Confucius ran
throughout his theory with a basic thought. The word “that of an all-pervading
unity” can be called the “mind-philosophy” of the ancient sages. In fact, not
everything can be “that of an all-pervading unity.” So, can studying the calculus of
variations be “that of an all-pervading unity”? The answer should be yes. The
necessary condition that a functional obtains extremum is that first variation of the
functional is equal to zero, this is the “that of an all-pervading unity” of the calculus
of variations. If the theme is mastered, then the calculus of variations is not so
difficult to learn.
If saying that the science and technology constitute a primary productive force,
then mathematics is the first factor of the primary productive force, and the calculus
of variations is the component in it. As enthusiasts for the calculus of variations, the
authors have been engaged in combining the personal interests with actual need, try
to make innovation from the source, provide new source to create social wealth.
Authors deeply feel pleasure and gratification for we can make contribution to the
development of the calculus of variations, also get the enjoyment of mathematical
beauty in spirit for the achieved research achievements in the original process.
The authors got many people’s help in the process of writing this book.
Especially, the doctoral student Ms. He Ting at Tsinghua University gathered some
examples and problems for this book. Professor Li Donghai at Tsinghua University,
professor Tan Tianmin, professor Chen Jinnan, associate professor Xie Kan at
Beijing Institute of Technology and professor John D. Williams at Colorado State
University in the United States reviewed part contents of Chap. 10 and put forward
the beneficial opinions and suggestions. The authors’ classmates senior engineer
Zhao Baoting at the former director of Liaoning Fuxin Chemical Plant participated
in the writing of Chap. 9, senior engineer Lou Xiaoming at Tianhua Institute of
Chemical Machinery and Automation and professor Guo Yanxia at Lanzhou
Petrochemical College of Vocational Technology reviewed all contents of Chap. 10
and part contents of Chap. 4. It is exactly in the national defense industry press
editorial department director Wang Jingtao’s encouragement, the book was written
in English. The academician of Chinese Academy of Sciences, pre-President of the
University of Beijing Institute of Technology Hu Haiyan wrote the foreword for the
book. The National Library of China, Peking University Library, Tsinghua
University Library and Beijing Institute of Technology Library provided a great
viii
Preface
the reader has the basic knowledge of linear algebra, physics and mechanics and so
on, it is easier to read this book.
There are a large number of examples and exercises in the book, and attaching
the index. In order to help readers to solve the difficulties encountered in the study,
this book gives all solution processes and answers of totaled 316 problems in the
various chapters, for readers reference.
In order to make readers understand the development history of the calculus of
variations, this book also makes brief introductions to the most scientists involved
in it.
Confucius said: “My doctrine is that of an all-pervading unity.” This is a word in
“The Analects of Confucius, The Humanity”, the mean is that Confucius ran
throughout his theory with a basic thought. The word “that of an all-pervading
unity” can be called the “mind-philosophy” of the ancient sages. In fact, not
everything can be “that of an all-pervading unity.” So, can studying the calculus of
variations be “that of an all-pervading unity”? The answer should be yes. The
necessary condition that a functional obtains extremum is that first variation of the
functional is equal to zero, this is the “that of an all-pervading unity” of the calculus
of variations. If the theme is mastered, then the calculus of variations is not so
difficult to learn.
If saying that the science and technology constitute a primary productive force,
then mathematics is the first factor of the primary productive force, and the calculus
of variations is the component in it. As enthusiasts for the calculus of variations, the
authors have been engaged in combining the personal interests with actual need, try
to make innovation from the source, provide new source to create social wealth.
Authors deeply feel pleasure and gratification for we can make contribution to the
development of the calculus of variations, also get the enjoyment of mathematical
beauty in spirit for the achieved research achievements in the original process.
The authors got many people’s help in the process of writing this book.
Especially, the doctoral student Ms. He Ting at Tsinghua University gathered some
examples and problems for this book. Professor Li Donghai at Tsinghua University,
professor Tan Tianmin, professor Chen Jinnan, associate professor Xie Kan at
Beijing Institute of Technology and professor John D. Williams at Colorado State
University in the United States reviewed part contents of Chap. 10 and put forward
the beneficial opinions and suggestions. The authors’ classmates senior engineer
Zhao Baoting at the former director of Liaoning Fuxin Chemical Plant participated
in the writing of Chap. 9, senior engineer Lou Xiaoming at Tianhua Institute of
Chemical Machinery and Automation and professor Guo Yanxia at Lanzhou
Petrochemical College of Vocational Technology reviewed all contents of Chap. 10
and part contents of Chap. 4. It is exactly in the national defense industry press
editorial department director Wang Jingtao’s encouragement, the book was written
in English. The academician of Chinese Academy of Sciences, pre-President of the
University of Beijing Institute of Technology Hu Haiyan wrote the foreword for the
book. The National Library of China, Peking University Library, Tsinghua
University Library and Beijing Institute of Technology Library provided a great
viii
Preface