Classical Recursion Theory

本書是一部傑作，書中的第一部分重點講述了勢能理論及其相關的拉普拉斯方程和熱方程；第二部分深入分析了和第一部分相關的隨機過程理論部分。這部科學巨著，調理清楚、深刻明晰地研究了問題涉及的這兩個方面，進而取代了零散地，語言上不一致的大量散落在各個圖書館的大量的書籍和科技文獻，但並不是一個百科全書。書中並不是將所有的知識點簡單相加，而是用自己獨特的方式從基礎開始進行系統講述，所以學習這本書並不需要太多的基

functions and Hecke L-functions of an imaginary quadratic field，and various problems on elliptic modular forms. As to the values of Dirichlet L-functions， all previous papers and books reiterate a single old result with a single old method. After a review ofelementary Fourier analysis， the author presents completely new results with new methods. though old results will also be proved. No advanced knowledge of number theory is required up to this point. As applications， new formulas for the second factor ofthe class number of a cyclotomic field will be given. The second half of the book assumes familiarity with basic knowledge ofmodular forms. However，all definitions and facts are clearly stated， and precise references are given. The notion ofnearly holomorphic modular forms is introduced and applied to the determination of the critical values of Hecke L-functions of an imaginary quadratic field. Other notable features of the book are： (1) some new results on classical E

This book contains a mathematical exposition of analogies between classical (Hamiltonian) mechanics, geometrical optics, and hydrodynamics. This theory highlights several general mathematical ideas th

本書是經典力學領域的經典著作，預備知識要求極低，僅需基礎微積分和本科基礎物理學知識，因此適合本科到研究生入門階段的課程使用，也適合數學、物理和工程專業的學生群體。This is an intuitively motivated presentation ofmany topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Some areas of particular interest are： an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the “tennis racket paradox”; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between thedynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin’s Maximum Principle, and more. In the last chapter, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theo

古典詩詞是中國傳統文化的代表，本書從語言學角度，從古典詩詞愛好者讀詩寫詩的需求出發，系統全面地闡述了與古代詩詞相關的古漢語知識。首先總述詩詞發展的體式，然後通過“語音篇”“格律篇”“章法篇”“語法修辭篇”“詞匯篇”五部分分別講述與古詩詞相關的音韻學常識、古詩詞的韻律與語言特點、古典詩詞的章法技巧、古詩詞主要運用的修辭格等語法手段、古詩詞中常見的特殊白話實詞和白話虛詞以及文字通假。