Partial differential equations (PDEs) are the mathematical cornerstone for describing an astonishingly wide range of phenomena, from quantum mechanics and ocean waves, to the diffusion of heat in matter and the behavior of financial markets. Despite the efforts of many famous mathematicians, physicists and engineers, the solution of partial differential equations remains a challenge. This book’s authors introduce a novel method, the unified transform, which greatly facilitates this challenge.Two and a half centuries after Jean d’Alembert formulated the wave equation and presented a solution for solving a simple problem for this equation, this book introduces a generalization of the d’Alembert solution, which is valid for general boundary value problems. Moreover, two centuries after Joseph Fourier introduced the classical tool of the Fourier series for solving the heat equation, it offers a new solution of this problem, which has important analytical and numerical advantages in comparison to the classical solutions. The authors present the unified transform pedagogically, building all the necessary background, including functions of real and of complex variables and the Fourier transform, illustrating the method with numerous examples.Modern Mathematical Methods for Scientists and Engineers is a modern introduction to basic topics in mathematics at the undergraduate level, with emphasis on explanations and applications to real-life problems. There are also "Application" sections at the end of each chapter, with topics drawn from a variety of areas, including neural networks, fluid dynamics, and the behavior of put and call options in financial markets. In addition to the unified transform, the book presents several modern important and computationally efficient topics, including feed-forward neural networks, wavelets, generalized functions, stochastic optimization methods, and numerical methods.Broad in scope, but pedagogical in style and content, the book is an introduction to powerful mathematical concepts and modern tools for students in science and engineering. Key FeaturesStudents of physical and engineering sciences, and increasingly those in the life and social sciences, need a solid grounding in mathematical methods to understand and advance within their own discipline. Their typical mathematics training is either too formal (from a purely mathematical perspective with few real-life applications) or inadequate (fearing, or not having adequate time to take, mathematics courses). Thus, they never acquire the confidence and strength to use sophisticated mathematical methods, readily and easily, in their own discipline. This book aims to correct this problemThe extensive explanations and examples provide much needed training in using the concepts introduced. The Applications at the end of each chapter show how useful each topic is in real-life problemsThe novel (and some unique) aspects of the book include: 1) A highly accessible presentation of the "Unified Transform" (also known as the "Fokas method") for solving partial differential equations (PDEs), including many examples and applications. A unique feature of this method is that it gives rise to very simple numerical techniques for solving a great variety of physically significant PDEs. This allows undergraduates to construct themselves graphs of the solution without the need to learn sophisticated techniques such as finite elements of finite differences. This approach is very powerful and is not presented anywhere at a level accessible to advanced undergraduate students; 2) Discussions of modern topics provide the mathematical underpinning for applications that students encounter in many modern contexts in the physical and engineering sciences. These discussions built on traditional math topics like the Fourier transform and its applications; 3) A presentation of stochastic optimization methods, building on probability theory and random numbers. Important topics discussed include Monte Carlo integration, Markov chain Monte Carlo, and the simulated annealing method. These are very useful tools, rarely presented in introductory texts, and discussed only in very specialized courses; 4) A thorough discussion of generalized functions like the delta-function and the theta-function. These tools are almost never treated in textbooks, yet in real-life applications they are ubiquitous. Examples of their use can be found throughout the book, and they are revisited in many different occasions, allowing the student to build familiarity and confidence in using them; 5) All figures were created by the authors in a manner close to what would be "blackboard sketches" to maintain the directness and liveliness of a lecture presentation. The use of color makes the comprehension of the figures much more intuitive, and helps the student create a powerful mental picture of the mathematical notions

• 关于产品：
• ● 正版保障：本网站隶属于中国国际图书贸易集团公司，确保所有图书都是100%正版。
• ● 环保纸张：进口图书大多使用的都是环保轻型张，颜色偏黄，重量比较轻。
• ● 毛边版：即书翻页的地方，故意做成了参差不齐的样子，一般为精装版，更具收藏价值。
• 
  关于退换货：
• 由于预订产品的特殊性，采购订单正式发订后，买方不得无故取消全部或部分产品的订购。
• 由于进口图书的特殊性，发生以下情况的，请直接拒收货物，由快递返回：
• ● 外包装破损/发错货/少发货/图书外观破损/图书配件不全（例如：光盘等）
  并请在工作日通过电话400-008-1110联系我们。
• 签收后，如发生以下情况，请在签收后的5个工作日内联系客服办理退换货：
• ● 缺页/错页/错印/脱线
• 
  关于发货时间：
• 一般情况下：
• ●【现货】 下单后48小时内由北京（库房）发出快递。
• ●【预订】【预售】下单后国外发货，到货时间预计5-8周左右，店铺默认中通快递，如需顺丰快递邮费到付。
• ● 需要开具发票的客户，发货时间可能在上述基础上再延后1-2个工作日（紧急发票需求，请联系010-68433105/3213）；
• ● 如遇其他特殊原因，对发货时间有影响的，我们会第一时间在网站公告，敬请留意。
• 
  关于到货时间：
• 由于进口图书入境入库后，都是委托第三方快递发货，所以我们只能保证在规定时间内发出，但无法为您保证确切的到货时间。
• ● 主要城市一般2-4天
• ● 偏远地区一般4-7天
• 
  关于接听咨询电话的时间：
• 010-68433105/3213正常接听咨询电话的时间为：周一至周五上午8：30～下午5：00，周六、日及法定节假日休息，将无法接听来电，敬请谅解。
• 其它时间您也可以通过邮件联系我们：customer@readgo.cn,工作日会优先处理。
• 
  关于快递：
• ● 已付款订单：主要由中通、宅急送负责派送，订单进度查询请拨打010-68433105/3213。