具体描述
About this textbook
While the standard sophomore course on elementary differential equations is typically one semester in length, most of the texts currently being used for these courses have evolved into calculus-like presentations that include a large collection of methods and applications, packaged with state-of-the-art color graphics, student solution manuals, the latest fonts, marginal notes, and web-based supplements. All of this adds up to several hundred pages of text and can be very expensive. Many students do not have the time or desire to read voluminous texts and explore internet supplements. Thats what makes the format of this differential equations book unique. It is a one-semester, brief treatment of the basic ideas, models, and solution methods. Its limited coverage places it somewhere between an outline and a detailed textbook. The author writes concisely, to the point, and in plain language. Many worked examples and exercises are included. A student who works through this primer will have the tools to go to the next level in applying ODEs to problems in engineering, science, and applied mathematics. It will also give instructors, who want more concise coverage, an alternative to existing texts.
This text also encourages students to use a computer algebra system to solve problems numerically. It can be stated with certainty that the numerical solution of differential equations is a central activity in science and engineering, and it is absolutely necessary to teach students scientific computation as early as possible. Templates of MATLAB programs that solve differential equations are given in an appendix. Maple and Mathematica commands are given as well. The author taught this material on several ocassions to students who have had a standard three-semester calculus sequence. It has been well received by many students who appreciated having a small, definitive parcel of material to learn. Moreover, this text gives students the opportunity to start reading mathematics at a slightly higher level than experienced in pre-calculus and calculus; not every small detail is included. Therefore the book can be a bridge in their progress to study more advanced material at the junior-senior level, where books leave a lot to the reader and are not packaged with elementary formats.
J. David Logan is Professor of Mathematics at the University of Nebraska, Lincoln. He is the author of another recent undergraduate textbook, Applied Partial Differential Equations, 2nd Edition (Springer 2004).
Written for:
Undergraduate math and engineering majors
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用户评价
这本书的排版和设计实在是太出色了，装帧精美，纸张的质感也让人爱不释手。拿到手里，首先映入眼帘的是清晰的字体和合理的页面布局，每一页的留白都恰到好处，阅读起来非常舒适。作者在处理复杂的数学公式时，使用了简洁明了的排版方式，使得那些看起来令人望而生畏的方程组也能变得井井有条。更值得称赞的是，书中的图表制作水平极高，无论是函数图像的描绘还是几何结构的展示，都精确到位，色彩搭配也十分和谐，让人在学习枯燥的理论时也能享受到视觉上的愉悦。这不仅仅是一本教材，更像是一件精心打磨的工艺品，放在书架上都觉得赏心悦目。对于那些注重阅读体验的读者来说，这本书的物理呈现绝对是一大加分项，它让学习微分方程的过程从一种负担变成了一种享受，我甚至愿意花时间去翻阅那些已经学过的章节，仅仅是为了感受这种高品质的阅读体验。
评分从使用的便利性角度来看，这本书的索引和术语表设计得非常人性化。作为一本工具书式的教材，查找特定公式或概念的效率至关重要。这本书的尾部索引非常详尽，我能迅速定位到任何一个关键术语或定理出现的位置，这在做复习或需要快速查阅特定证明时，节省了我大量的时间。此外，书中所引入的各种符号和记法，都有清晰的首次定义和后续的统一使用，这避免了阅读过程中因为符号混乱而产生的困惑。这种对细节的关注，反映出编者对读者学习过程的充分体谅。对于需要经常在不同章节之间跳转进行交叉参考的学习者来说，这种完善的导航系统，是评价一本优秀教材不可或缺的要素，它极大地提升了这本书作为参考手册的价值。
评分我对这本书的章节组织和逻辑推进方式感到非常满意，它不像有些教科书那样生硬地堆砌概念，而是构建了一个非常流畅的学习路径。初学者会发现，作者从最基础的线性方程和基本解法开始，循序渐进地引入更高级的主题，每一步的过渡都自然而然，没有让人感到突兀或迷失方向。尤其是对理论背景的讲解，总是能找到一个很好的平衡点，既保证了数学上的严谨性，又避免了陷入过于抽象的泥潭。作者似乎非常懂得读者的思维习惯，总是在介绍完一个新的方法后，立刻紧接着给出大量的、覆盖面广的例子来巩固理解。这种“提出问题—讲解理论—展示应用”的结构，让知识的吸收效率大大提高，感觉每学完一节，脑海中的知识结构就清晰了一块，而不是零散地记住了几个公式。
评分这本书在习题设计上的用心程度，简直可以说是达到了“苛刻”的境界。习题的难度梯度设置得极其科学合理，从最基础的暖身练习，到需要深度思考的综合应用题，再到一些挑战性的探究型问题，几乎覆盖了所有可能遇到的学习难点。更棒的是，书中附带的答案和详细的解题步骤（我指的是书中已经提供的部分）极其详尽，绝非简单的最终结果了事。对于那些卡住的题目，翻阅解析过程本身就是一次宝贵的学习机会，它展示了解决问题的不同思路和技巧。这种高质量的习题集，极大地减少了我需要额外寻找参考资料的需要，我可以直接在书本上完成从学习到检验的完整闭环。可以毫不夸张地说，如果能扎扎实实地做完这本书中大部分的练习，对微分方程这门学科的掌握程度将得到质的飞跃。
评分作者在理论阐述上展现出了一种老派的、注重物理直觉的教学风格，这一点非常对我胃口。很多现代教材为了追求数学的纯粹性，往往忽略了这些方程最初来源于何处，以及它们在现实世界中到底描述了什么现象。而这本书则巧妙地将历史背景和实际应用融入到讲解之中。无论是弹簧振动、电路分析还是热传导问题，作者都会先用清晰的语言描绘出物理模型，然后才推导出相应的微分方程。这种“模型先行”的策略，极大地增强了学习的动机，让我明白了学习这些抽象符号背后的真正意义。当我看到如何用数学语言精确捕捉到自然界的规律时，那种震撼感是单纯背诵定理无法比拟的。这种对应用背景的重视，让原本感觉高高在上的理论知识，变得触手可及且充满活力。
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