Review
From reviews of previous editions: '...a great scientific textbook. It is a tour de force ... to write mathematical sections that are both complete and at an appropriate academic level. The authors have clearly succeeded in this challenge, making this a remarkable pedagogical book ... The choice of exercises is excellent and possibly the best feature of the book. In summary, this textbook is a great reference at undergraduate levels, particularly for those who like to teach or learn using lots of examples and exercises.' R. Botet, European Journal of Physics
'... the book provides scientists who need to use the tool of mathematics for practical purposes with a single, comprehensive book. I recommend this book not only to students in physics and engineering sciences, but also to students in other fields of natural sciences.' P. Steward, Optik
'... suitable as a textbook for undergraduate use ... this is a book that in view of its content and its modest softcover price, will find its way on to many bookshelves.' Nigel Steele, Times Higher Education Supplement
'Riley et al. has clear, thorough and straightforward explanations of the subjects treated. It rigorously adopts a three-stage approach throughout the book: first a heuristic, intuitive introduction, then a formal treatment, and finally one or two examples. This consistent presentation, the layout, and the print quality make the book most attractive ... and value for money. It contains a thousand pages, there are plenty of exercises with each chapter.' J. M. Thijssen, European Journal of Physics
This is a valuable book with great potential use in present-day university physics courses. Furthermore, the book will be useful for graduate too, and researchers will find it useful for looking up material which they have forgotten since their undergraduate days.' J. M. Thijssen, European Journal of Physics
'This textbook is a well-written, modern, comprehensive, and complete collection of topics in mathematical methods ranging from a review of differential and integral calculus to group and representation theory, probability, the calculus of variations, and tensors.' Science Books and Films
'This is a very comprehensive textbook suitable for most students enrolling on undergraduate degree courses in engineering. It contains 31 stand-alone chapters of mathematical methods which enable the students to understand the principles of the basic mathematical techniques and the authors have produced a clear, thorough and straightforward explanation of each subject. ... finding a single textbook which covers the engineering student's need throughout their entire course is by no means an easy task. I believe the authors have achieved it ... complete fully worked solutions ... which I think is a useful asset for both students and lecturers.' Civil Engineering
' ... this highly acclaimed undergraduate textbook is suitable for teaching all the mathematics ever likely to be needed for an undergraduate course in any of the physical sciences. As well as lucid descriptions of all the topics covered and many worked examples, it contains more than 800 exercises.' L'enseignement mathematique
Product Description
The third edition of this highly acclaimed undergraduate textbook is suitable for teaching all the mathematics for an undergraduate course in any of the physical sciences. As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. Further tabulations, of relevance in statistics and numerical integration, have been added. In this edition, half of the exercises are provided with hints and answers and, in a separate manual available to both students and their teachers, complete worked solutions. The remaining exercises have no hints, answers or worked solutions and can be used for unaided homework; full solutions are available to instructors on a password-protected web site, www.cambridge.org/9780521679718.
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坦白说,这本书的排版和插图处理是让我感到最不适应的地方之一。在一些关键的矢量分析和场论的章节里,图示的数量明显不足,或者说,现有的图示往往过于简化,无法清晰地展示三维空间中复杂的向量场是如何流动的,或者曲面积分的几何意义究竟是什么。我不得不自己动手在草稿纸上画出大量的辅助图形,试图在脑海中构建一个立体的模型。这种“动手补图”的过程虽然锻炼了我的空间想象力,但也极大地拖慢了我的学习进度。相比之下,有些同类型的书籍在图文结合上做得更为出色,能够通过精美的剖面图和动态示意图帮助读者直观理解,而这本书在这方面显得有些力不从心,更偏向于纯粹的文字和符号的陈述。对于依赖视觉学习的读者,这无疑是一个不小的挑战,需要读者具备很强的抽象思维能力去弥补视觉信息上的缺失。
评分这本书的理论深度是毋庸置疑的,尤其在涉及到群论在量子力学中的应用部分,讲解得非常到位和深入。作者显然对现代物理学的数学基础有着深刻的理解,能够将那些看似不相关的数学结构,例如酉变换、李群等,与物理世界的对称性原理巧妙地联系起来。对于那些希望将数学工具直接提升到研究层面的人来说,这无疑是一本极佳的参考书。但是,这种深度也带来了一个副作用:它在基础概念的引入上显得过于仓促和跳跃。例如,在介绍狄拉克方程或费曼路径积分时,它假设读者已经对量子力学有了一定的了解,没有花费精力去回顾量子力学中的基本假设或算符的概念。因此,我建议初次接触高等数学在物理中应用的学习者,最好是作为第二本、第三本教材来使用,用它来巩固和深化已有的知识,而不是作为唯一的入门读物,否则很容易产生挫败感,甚至可能误解一些核心概念的物理背景。
评分我发现这本书在处理热力学和统计物理中的数学方法时,有一个非常独特的侧重点,它似乎更偏向于用泛函分析和高级微分为工具来解析配分函数和相变问题。这种处理方式使得它在处理连续介质力学和电磁场中的边界值问题时显得尤为强大,因为你必须精确地处理无穷级数展开和收敛性问题。然而,对于一些更偏向于信息论或随机过程的现代工程问题,这本书的覆盖面就相对有限了。它更像是一本“经典”的、扎根于20世纪中叶物理学核心领域的教材,对于那些新兴的、依赖于随机微积分或者数值分析方法的现代工程应用,它几乎没有涉猎。所以,如果你的主要兴趣在于经典场论或量子场论的数学结构,它无可匹敌;但若你的目标是现代信号处理或机器学习中的数学基础,你可能需要寻找其他更侧重于概率论和优化理论的补充材料。这本书的优势和局限性都非常明显,它代表了一种特定时代对“物理数学方法”的理解和侧重。
评分这本书的习题设计简直是“魔鬼式”训练。它涵盖的范围非常广,从基础的积分换元到涉及拉普拉斯算子在不规则边界下的应用,难度梯度变化非常剧烈。有些章节的课后题,即使是标着“中等难度”,也需要花费数小时才能理清思路并完成求解,更不用说那些被标记为“挑战性”的难题了,它们往往需要融合好几个不同章节的知识点才能攻克。我个人觉得,这本书的价值很大一部分体现在这些习题上,因为通过解答它们,你才能真正把那些晦涩的数学工具应用到具体的物理问题中去,体会到知识的融会贯通。然而,对于时间紧张的学生来说,完成所有习题几乎是不可能的任务,这迫使我不得不做出取舍,优先攻克那些我认为最核心的、与我专业研究方向最相关的部分,这在一定程度上也限制了我对全书知识体系的完整掌握。
评分这本书真是让人又爱又恨,尤其是当你初次接触高等数学和物理结合的领域时。我记得刚开始翻开这本书的时候,那种扑面而来的数学符号和抽象概念简直让人望而却步。它不像一些入门教材那样,会用大量的篇幅去解释每一个基本概念,而是直接切入主题,仿佛默认读者已经对微积分和线性代数有了扎实的背景。我花了很长时间才适应这种直接的叙述方式,特别是那些关于偏微分方程和复分析的应用章节,如果不是经常停下来对照着网上的补充材料或者其他参考书,我感觉自己会彻底迷失在公式的海洋里。不过,一旦你掌握了它的节奏,你会发现它在连接理论与实际应用上的深度是惊人的。它不会只是告诉你“这样做”,而是会告诉你“为什么这样做”,并且通过严谨的数学推导来支撑物理直觉。对于那些追求数学严谨性的读者来说,这本书绝对是宝藏,但对于只想快速掌握工程技巧的人来说,它可能显得过于“硬核”了。
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