Introduction to Partial Differential Equations
暫譯: 偏微分方程入門
Peter J. Olver
- 出版商: Springer
- 出版日期: 2013-11-20
- 售價: $3,110
- 貴賓價: 9.5 折 $2,955
- 語言: 英文
- 頁數: 636
- 裝訂: Hardcover
- ISBN: 3319020986
- ISBN-13: 9783319020983
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相關分類:
工程數學 Engineering-mathematics、數值分析 Numerical-analysis
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其他版本:
Introduction to Partial Differential Equations
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相關主題
商品描述
This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject.
No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solutions, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements.
商品描述(中文翻譯)
這本教科書是為期一年課程設計的,涵蓋偏微分方程的基本原理,適合高年級本科生和數學、科學、工程等領域的初學研究生。內容在解題技巧、數學嚴謹性和重要應用之間進行了仔細的平衡,並通過大量範例進行說明。幾乎每個小節的結尾都有大量練習題,包括簡單的計算問題以發展和鞏固新技術和結果、理論發展和證明的細節、具有挑戰性的計算和概念性專案,以及激勵學生深入研究該主題的補充材料。
本書不假設讀者對偏微分方程或傅立葉理論有任何先前經驗,主要的先修課程為本科微積分,包括一變數和多變數微積分、常微分方程以及基本線性代數。雖然變數分離、傅立葉分析、邊值問題、格林函數和特殊函數等經典主題仍然構成入門課程的核心,但非線性方程、衝擊波動力學、對稱性和相似性、最大原理、金融模型、色散和解、惠根原理、量子力學系統等的納入,使本書與當前研究的最新發展和趨勢相契合。數值近似方案是任何入門課程的重要組成部分,本書涵蓋了兩種最基本的方法:有限差分法和有限元素法。