Preface 3 The parts asterisked are not required,but recommended for undergraduates majoring in physics. Methods of Study In tackling a problem,you must know what the problem is,i.e.,problem-formation, it means that you must gain a clear idea of the problem:which are known,measurable or required to be given and which are unknown and to be sought,on that the subsequent proceedings are centered.But you can find out that problem-formation is often hazy and incomplete somewhere else.One example is,some known conditions are not presented at the very start and they are picked up now and then when they are needed in solving the problem.Such a practice is unavoidable in scientific research but it is surely not good for students'studying and should be given up in any textbook.The other is,sometimes in solving a problem,one is unaware of what he wants to reach after and hence he does not understand what will happen afterwards.After clear and complete problem-formation,it is most important to grasp the basic ideas of solving the problem,which are only mathematical (especially geometrical)or physical thoughts,simple and clear,and in which not a great amount of mathematical calculations are involved.To grasp the basic ideas is the key to solving a problem that must be paid great attention to.And then it is followed by the implementation of the basic ideas,in which generally a great amount of mathematical calculations are involved.You will never get boggled down in any tedious calculations if you know the basic ideas well.The final step is to use some tricks to simplify and reduce calculations. In brief,in our studying,we must pay attention to complete problem-formation,the basic ideas of solving the problem,the implementation of such basic ideas and the tricks in the implementation.We must under no circumstances concentrate on mathematical calculations only,must devote great attention to complete problem-formation and the basic ideas of solving the problem and but we do not confuse principles with tricks.The author suggests that readers make a summary on some problems or some chapters and sections, even a whole part,which they feel difficult to understand,according to the four-point method of study. What a student studies is existing knowledge that was discovered and created by somebody else.But if you have a good command of it you must study as if you were an inventor and creator,that is the core of a good method of study. In comparison with existing textbooks on methods of mathematical physics,some big changes in contents,viewpoints and order have been made in this book.Any suggestions, comments and criticisms are welcome for further improvement to this book. The manuscript of this book,especially,of the first two parts,was reviewed by Professor Ni Guangjioing in Fudan University and Professor Wu Chongshi in Beijing University,and the manuscript of the third part was reviewed by Professor Yang Wenchai in the Institute of Geology,the Ministry of Land and Resources of People's Republic of Ｔｈｅｐａｒｔｓａｓｔｅｒｉｓｋｅｄａｒｅｎｏｔｒｅｑｕｉｒｅｄ，ｂｕｔｒｅｃｏｍｍｅｎｄｅｄｆｏｒｕｎｄｅｒｇｒａｄｕａｔｅｓｍａｊｏｒｉｎｇ ｉｎｐｈｙｓｉｃｓ． ＭｅｔｈｏｄｓｏｆＳｔｕｄｙ Ｉｎｔａｃｋｌｉｎｇａｐｒｏｂｌｅｍ，ｙｏｕｍｕｓｔｋｎｏｗｗｈａｔｔｈｅｐｒｏｂｌｅｍｉｓ，ｉ．ｅ．，ｐｒｏｂｌｅｍｆｏｒｍａｔｉｏｎ， ｉｔｍｅａｎｓｔｈａｔｙｏｕｍｕｓｔｇａｉｎａｃｌｅａｒｉｄｅａｏｆｔｈｅｐｒｏｂｌｅｍ：ｗｈｉｃｈａｒｅｋｎｏｗｎ，ｍｅａｓｕｒａｂｌｅｏｒ ｒｅｑｕｉｒｅｄｔｏｂｅｇｉｖｅｎａｎｄｗｈｉｃｈａｒｅｕｎｋｎｏｗｎａｎｄｔｏｂｅｓｏｕｇｈｔ，ｏｎｔｈａｔｔｈｅｓｕｂｓｅｑｕｅｎｔ ｐｒｏｃｅｅｄｉｎｇｓａｒｅｃｅｎｔｅｒｅｄ．Ｂｕｔｙｏｕｃａｎｆｉｎｄｏｕｔｔｈａｔｐｒｏｂｌｅｍｆｏｒｍａｔｉｏｎｉｓｏｆｔｅｎｈａｚｙａｎｄ ｉｎｃｏｍｐｌｅｔｅｓｏｍｅｗｈｅｒｅｅｌｓｅ．Ｏｎｅｅｘａｍｐｌｅｉｓ，ｓｏｍｅｋｎｏｗｎｃｏｎｄｉｔｉｏｎｓａｒｅｎｏｔｐｒｅｓｅｎｔｅｄａｔ ｔｈｅｖｅｒｙｓｔａｒｔａｎｄｔｈｅｙａｒｅｐｉｃｋｅｄｕｐｎｏｗａｎｄｔｈｅｎｗｈｅｎｔｈｅｙａｒｅｎｅｅｄｅｄｉｎｓｏｌｖｉｎｇｔｈｅ ｐｒｏｂｌｅｍ．Ｓｕｃｈａｐｒａｃｔｉｃｅｉｓｕｎａｖｏｉｄａｂｌｅｉｎｓｃｉｅｎｔｉｆｉｃｒｅｓｅａｒｃｈｂｕｔｉｔｉｓｓｕｒｅｌｙｎｏｔｇｏｏｄｆｏｒ ｓｔｕｄｅｎｔｓｓｔｕｄｙｉｎｇａｎｄｓｈｏｕｌｄｂｅｇｉｖｅｎｕｐｉｎａｎｙｔｅｘｔｂｏｏｋ．Ｔｈｅｏｔｈｅｒｉｓ，ｓｏｍｅｔｉｍｅｓｉｎ ｓｏｌｖｉｎｇａｐｒｏｂｌｅｍ，ｏｎｅｉｓｕｎａｗａｒｅｏｆｗｈａｔｈｅｗａｎｔｓｔｏｒｅａｃｈａｆｔｅｒａｎｄｈｅｎｃｅｈｅｄｏｅｓｎｏｔ ｕｎｄｅｒｓｔａｎｄｗｈａｔｗｉｌｌｈａｐｐｅｎａｆｔｅｒｗａｒｄｓ．Ａｆｔｅｒｃｌｅａｒａｎｄｃｏｍｐｌｅｔｅｐｒｏｂｌｅｍｆｏｒｍａｔｉｏｎ，ｉｔ ｉｓ ｍｏｓｔｉｍｐｏｒｔａｎｔｔｏ ｇｒａｓｐｔｈｅ ｂａｓｉｃｉｄｅａｓｏｆｓｏｌｖｉｎｇｔｈｅ ｐｒｏｂｌｅｍ，ｗｈｉｃｈ ａｒｅ ｏｎｌｙ ｍａｔｈｅｍａｔｉｃａｌ（ｅｓｐｅｃｉａｌｌｙｇｅｏｍｅｔｒｉｃａｌ）ｏｒｐｈｙｓｉｃａｌｔｈｏｕｇｈｔｓ，ｓｉｍｐｌｅａｎｄｃｌｅａｒ，ａｎｄｉｎｗｈｉｃｈ ｎｏｔａｇｒｅａｔａｍｏｕｎｔｏｆｍａｔｈｅｍａｔｉｃａｌｃａｌｃｕｌａｔｉｏｎｓａｒｅｉｎｖｏｌｖｅｄ．Ｔｏｇｒａｓｐｔｈｅｂａｓｉｃｉｄｅａｓｉｓ ｔｈｅｋｅｙｔｏｓｏｌｖｉｎｇａｐｒｏｂｌｅｍｔｈａｔｍｕｓｔｂｅｐａｉｄｇｒｅａｔａｔｔｅｎｔｉｏｎｔｏ．Ａｎｄｔｈｅｎｉｔｉｓｆｏｌｌｏｗｅｄ ｂｙｔｈｅｉｍｐｌｅｍｅｎｔａｔｉｏｎ ｏｆｔｈｅ ｂａｓｉｃｉｄｅａｓ，ｉｎ ｗｈｉｃｈ ｇｅｎｅｒａｌｌｙ ａ ｇｒｅａｔ ａｍｏｕｎｔ ｏｆ ｍａｔｈｅｍａｔｉｃａｌｃａｌｃｕｌａｔｉｏｎｓａｒｅｉｎｖｏｌｖｅｄ．Ｙｏｕｗｉｌｌｎｅｖｅｒｇｅｔｂｏｇｇｌｅｄｄｏｗｎｉｎａｎｙｔｅｄｉｏｕｓ ｃａｌｃｕｌａｔｉｏｎｓｉｆｙｏｕｋｎｏｗｔｈｅｂａｓｉｃｉｄｅａｓ ｗｅｌｌ．Ｔｈｅｆｉｎａｌｓｔｅｐｉｓｔｏｕｓｅｓｏｍｅｔｒｉｃｋｓｔｏ ｓｉｍｐｌｉｆｙａｎｄｒｅｄｕｃｅｃａｌｃｕｌａｔｉｏｎｓ． Ｉｎｂｒｉｅｆ，ｉｎｏｕｒｓｔｕｄｙｉｎｇ，ｗｅｍｕｓｔｐａｙａｔｔｅｎｔｉｏｎｔｏｃｏｍｐｌｅｔｅｐｒｏｂｌｅｍｆｏｒｍａｔｉｏｎ，ｔｈｅ ｂａｓｉｃｉｄｅａｓｏｆｓｏｌｖｉｎｇｔｈｅｐｒｏｂｌｅｍ，ｔｈｅｉｍｐｌｅｍｅｎｔａｔｉｏｎｏｆｓｕｃｈｂａｓｉｃｉｄｅａｓａｎｄｔｈｅｔｒｉｃｋｓｉｎ ｔｈｅｉｍｐｌｅｍｅｎｔａｔｉｏｎ． Ｗｅ ｍｕｓｔ ｕｎｄｅｒ ｎｏ ｃｉｒｃｕｍｓｔａｎｃｅｓ ｃｏｎｃｅｎｔｒａｔｅ ｏｎ ｍａｔｈｅｍａｔｉｃａｌ ｃａｌｃｕｌａｔｉｏｎｓｏｎｌｙ，ｍｕｓｔｄｅｖｏｔｅｇｒｅａｔａｔｔｅｎｔｉｏｎｔｏｃｏｍｐｌｅｔｅｐｒｏｂｌｅｍｆｏｒｍａｔｉｏｎａｎｄｔｈｅｂａｓｉｃ ｉｄｅａｓｏｆｓｏｌｖｉｎｇｔｈｅｐｒｏｂｌｅｍａｎｄｂｕｔｗｅｄｏｎｏｔｃｏｎｆｕｓｅｐｒｉｎｃｉｐｌｅｓｗｉｔｈｔｒｉｃｋｓ．Ｔｈｅａｕｔｈｏｒ ｓｕｇｇｅｓｔｓｔｈａｔｒｅａｄｅｒｓｍａｋｅａｓｕｍｍａｒｙｏｎｓｏｍｅｐｒｏｂｌｅｍｓｏｒｓｏｍｅｃｈａｐｔｅｒｓａｎｄｓｅｃｔｉｏｎｓ， ｅｖｅｎａｗｈｏｌｅｐａｒｔ，ｗｈｉｃｈｔｈｅｙｆｅｅｌｄｉｆｆｉｃｕｌｔｔｏｕｎｄｅｒｓｔａｎｄ，ａｃｃｏｒｄｉｎｇｔｏｔｈｅｆｏｕｒｐｏｉｎｔ ｍｅｔｈｏｄｏｆｓｔｕｄｙ． Ｗｈａｔａｓｔｕｄｅｎｔｓｔｕｄｉｅｓｉｓｅｘｉｓｔｉｎｇｋｎｏｗｌｅｄｇｅｔｈａｔｗａｓｄｉｓｃｏｖｅｒｅｄａｎｄｃｒｅａｔｅｄｂｙ ｓｏｍｅｂｏｄｙｅｌｓｅ．Ｂｕｔｉｆｙｏｕｈａｖｅａｇｏｏｄｃｏｍｍａｎｄｏｆｉｔｙｏｕｍｕｓｔｓｔｕｄｙａｓｉｆｙｏｕｗｅｒｅａｎ ｉｎｖｅｎｔｏｒａｎｄｃｒｅａｔｏｒ，ｔｈａｔｉｓｔｈｅｃｏｒｅｏｆａｇｏｏｄｍｅｔｈｏｄｏｆｓｔｕｄｙ． Ｉｎｃｏｍｐａｒｉｓｏｎｗｉｔｈｅｘｉｓｔｉｎｇｔｅｘｔｂｏｏｋｓｏｎｍｅｔｈｏｄｓｏｆｍａｔｈｅｍａｔｉｃａｌｐｈｙｓｉｃｓ，ｓｏｍｅｂｉｇ ｃｈａｎｇｅｓｉｎｃｏｎｔｅｎｔｓ，ｖｉｅｗｐｏｉｎｔｓａｎｄｏｒｄｅｒｈａｖｅｂｅｅｎｍａｄｅｉｎｔｈｉｓｂｏｏｋ．Ａｎｙｓｕｇｇｅｓｔｉｏｎｓ， ｃｏｍｍｅｎｔｓａｎｄｃｒｉｔｉｃｉｓｍｓａｒｅｗｅｌｃｏｍｅｆｏｒｆｕｒｔｈｅｒｉｍｐｒｏｖｅｍｅｎｔｔｏｔｈｉｓｂｏｏｋ． Ｔｈｅｍａｎｕｓｃｒｉｐｔｏｆｔｈｉｓｂｏｏｋ，ｅｓｐｅｃｉａｌｌｙ，ｏｆｔｈｅｆｉｒｓｔｔｗｏｐａｒｔｓ，ｗａｓｒｅｖｉｅｗｅｄｂｙ ＰｒｏｆｅｓｓｏｒＮｉＧｕａｎｇｊｉｏｉｎｇｉｎ Ｆｕｄａｎ Ｕｎｉｖｅｒｓｉｔｙａｎｄ Ｐｒｏｆｅｓｓｏｒ Ｗｕ Ｃｈｏｎｇｓｈｉｉｎ Ｂｅｉｊｉｎｇ Ｕｎｉｖｅｒｓｉｔｙ，ａｎｄｔｈｅｍａｎｕｓｃｒｉｐｔｏｆｔｈｅｔｈｉｒｄｐａｒｔｗａｓｒｅｖｉｅｗｅｄｂｙＰｒｏｆｅｓｓｏｒＹａｎｇＷｅｎｃｈａｉ ｉｎｔｈｅＩｎｓｔｉｔｕｔｅｏｆＧｅｏｌｏｇｙ，ｔｈｅＭｉｎｉｓｔｒｙｏｆＬａｎｄａｎｄＲｅｓｏｕｒｃｅｓｏｆＰｅｏｐｌｅｓＲｅｐｕｂｌｉｃｏｆ 犘狉犲犳犪犮犲 ３