An Excursion Through Partial Differential Equations

Georgiev, Svetlin G.

An Excursion Through Partial Differential Equations
  • 出版商: Springer
  • 出版日期: 2024-01-18
  • 售價: $4,040
  • 貴賓價: 9.5 折 $3,838
  • 語言: 英文
  • 頁數: 422
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031487834
  • ISBN-13: 9783031487835

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商品描述

Presenting a rich collection of exercises on partial differential equations, this textbook equips readers with 96 examples, 222 exercises, and 289 problems complete with detailed solutions or hints. It explores a broad spectrum of partial differential equations, fundamental to mathematically oriented scientific fields, from physics and engineering to differential geometry and variational calculus.

Organized thoughtfully into seven chapters, the journey begins with fundamental problems in the realm of PDEs. Readers progress through first and second-order equations, wave and heat equations, and finally, the Laplace equation. The text adopts a highly readable and mathematically solid format, ensuring concepts are introduced with clarity and organization.

Designed to cater to upper undergraduate and graduate students, this book offers a comprehensive understanding of partial differential equations. Researchers and practitioners seeking to strengthen their problem-solvingskills will also find this exercise collection both challenging and beneficial.

商品描述(中文翻譯)

本教科書提供了豐富的偏微分方程練習題，讓讀者獲得96個例子、222個練習和289個問題，並附有詳細的解答或提示。它探討了偏微分方程的廣泛範疇，對於以數學為導向的科學領域，從物理學和工程學到微分幾何學和變分計算都是基礎。

本書精心分為七章，旅程從偏微分方程領域的基礎問題開始。讀者逐步學習一階和二階方程、波動方程和熱方程，最後學習拉普拉斯方程。本文採用易讀且數學基礎扎實的格式，確保概念清晰有組織地介紹。

本書旨在為大學高年級和研究生提供全面理解偏微分方程的能力。研究人員和從業人員希望加強解決問題的能力也會發現這本練習集具有挑戰性且有益。

作者簡介

Svetlin G. Georgiev (born 1974, Bulgaria) has worked in various areas of mathematics. His current focus lies on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, and dynamic calculus on time scales. He has authored or co-authored several books, including "Real Quaternionic Calculus Handbook" (2014), "Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales" (2018), "Functional Dynamic Equations on Time Scales" (2019), "Theory of Distributions" (2021, now in its second edition), and "Fuzzy Dynamic Equations, Dynamic Inclusions and Optimal Control Problems on Time Scales" (2021), all published with Springer.

作者簡介(中文翻譯)

Svetlin G. Georgiev（1974年出生，保加利亞）在數學的各個領域有著豐富的工作經驗。他目前的研究重點包括調和分析、泛函分析、偏微分方程、常微分方程、Clifford和四元數分析、積分方程以及時間尺度上的動態微積分。他是多本書籍的作者或合著者，包括《Real Quaternionic Calculus Handbook》（2014年）、《Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales》（2018年）、《Functional Dynamic Equations on Time Scales》（2019年）、《Theory of Distributions》（2021年，第二版）以及《Fuzzy Dynamic Equations, Dynamic Inclusions and Optimal Control Problems on Time Scales》（2021年），這些書籍均由Springer出版。

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