Praise for the First Edition: <p> "This book is well conceived and well written. The author has succeeded in producing a text on nonlinear PDEs that is not only quite readable but also accessible to students from diverse backgrounds."<br> —SIAM Review <p> A practical introduction to nonlinear PDEs and their real-world applications <p> Now in a Second Edition, this popular book on nonlinear partial differential equations (PDEs) contains expanded coverage on the central topics of applied mathematics in an elementary, highly readable format and is accessible to students and researchers in the field of pure and applied mathematics. This book provides a new focus on the increasing use of mathematical applications in the life sciences, while also addressing key topics such as linear PDEs, first-order nonlinear PDEs, classical and weak solutions, shocks, hyperbolic systems, nonlinear diffusion, and elliptic equations. Unlike comparable books that typically only use formal proofs and theory to demonstrate results, An Introduction to Nonlinear Partial Differential Equations, Second Edition takes a more practical approach to nonlinear PDEs by emphasizing how the results are used, why they are important, and how they are applied to real problems. <p> The intertwining relationship between mathematics and physical phenomena is discovered using detailed examples of applications across various areas such as biology, combustion, traffic flow, heat transfer, fluid mechanics, quantum mechanics, and the chemical reactor theory. New features of the Second Edition also include: <ul> <li> <p> Additional intermediate-level exercises that facilitate the development of advanced problem-solving skills <li> <p> New applications in the biological sciences, including age-structure, pattern formation, and the propagation of diseases <li> <p> An expanded bibliography that facilitates further investigation into specialized topics </ul> <p> With individual, self-contained chapters and a broad scope of coverage that offers instructors the flexibility to design courses to meet specific objectives, An Introduction to Nonlinear Partial Differential Equations, Second Edition is an ideal text for applied mathematics courses at the upper-undergraduate and graduate levels. It also serves as a valuable resource for researchers and professionals in the fields of mathematics, biology, engineering, and physics who would like to further their knowledge of PDEs.
This short but beautiful treatise, though written for the benefit of Benedictine monks, is so full of spiritual wisdom, and of gentle and loying piety, that no one can read it without feeling himself moved to devotion. In language of inexpressible sweetness and power, it sets before us the threefold office of divine worship-praise, than ksgiving, and prayer; and with maxims culled from the writings of Saints and Fathers of the Church, develops this threefold office throughout the several hours of the Divine Office. Should a beginner find the number of subjects laid down for meditation too great a strain on his intellect, nothing can be easier than to single out the chief ones and dwell on them, not for the space of one psalm only, as the author directs, but during two or three. A like easy arrangement will at once remove any difficulty that may be met with by ecclesiastics not using our monastic Breviary, which Abbot Cisneros had in view in allotting the subjects for meditation to the several canonical hours. Let us consider this wise advice: "IN the second book of Paralipomenon, chapter the twenty-ninth, it is written: My sons, be not negligent; the Lord hath chosen you to stand before Him, and to minister to Him, and to worship Him. Since, then, God has chosen the religious man as His minister, to worship and serve Him, he ought to know how God is to be served. For, as Gerson says, nothing so beseems a religious as the worthy and careful performance of divine worship- to-wit, of the canonical hours, which our father and captain, St. Benedict, calls in his Rule the work of God; more especially because it is the first duty of a religious, as St. Jerome says, to employ himself in praising God, offering Him hymns, psalms, prayers, and sacrifice; and by these means to appease the anger of God against His people, and bewail the sins of his brethren. Wherefore a monk must be watchful and diligent in worthily discharging the debt of his service to God, lest the fearful curse of Jeremias the prophet fall upon him: Cursed be the man that doth the work of God with negligence."
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