*完成訂單後正常情形下約兩周可抵台。 *本賣場提供之資訊僅供參考,以到貨標的為正確資訊。 印行年月:202402*若逾兩年請先於私訊洽詢存貨情況,謝謝。 台灣(台北市)在地出版社,每筆交易均開具統一發票,祝您中獎最高1000萬元。 書名:變分學入門 (英文) ISBN:9787040612172 出版社:高等教育 著編譯者:馬克.科特 頁數:298 所在地:中國大陸 *此為代購商品 書號:1625186 可大量預訂,請先連絡。 內容簡介 本書是變分法的研究生入門教程。讀者將學習尋找最大化或最小化積分的函數的方法。本書按照歷史順序闡述了極值的充要條件,並通過來自力學、光學、幾何學和其他領域的許多實例來說明這些條件。論述從簡單的積分開始,包含單個自變數、單個因變數和單個導數,受弱變分的約束,但逐漸深入到更高級的主題,包括多元問題、約束極值、齊次問題、端點可變問題、破碎的極值、強變分和充分性條件。書中包含大量的線條圖來闡明相關的數學內容。每章結尾都有推薦閱讀,介紹相關的科學文獻,並且有練習題鞏固理解。目錄 PreiaceChapter 1 Introduction 1 1 The brachistochrone 1 2 The terrestrial brachistochrone 1 3 Geodesics 1 4 Minimal surfaces 1 5 Recommended reading 1 6 Exercises Chapter 2 The First Variation 2 1 The simplest problem 2 2 Euler's approach 2 3 Lagrange's approach 2 4 Recommended reading 2 5 Exercises Chapter 3 Cases and Examples 3 1 Special cases 3 2 Case study:Minimal surface of revolution 3 3 Case study:The brachistochrone 3 4 Geodesics 3 5 Recommended reading 3 6 Exercises Chapter 4 Basic Generalizations 4 1 Higher—order derivatives 4 2 Case study:The cantilever beam 4 3 Multiple unknown functions 4 4 Lagrangian mechanics 4 5 Case study:The spherical pendulum 4 6 Hamiltonian mechanics 4 7 Ray optics 4 8 Double integrals 4 9 Recommended reading 4 10 Exercises Chapter 5 Constraints 5 1 Types of constraints 5 2 Lagrange multipliers 5 3 Isoperimetric constraints 5 4 Case study:Queen Dido's problem 5 5 Case study:Euler's elastica 5 6 Holonomic constraints 5 7 Case study:A sliding rod 5 8 Recommended reading 5 9 Exercises Chapter 6 The Second Variation 6 1 Introduction 6 2 Legendre's condition 6 3 Jacobi's condition 6 4 Case study:The catenoid revisited 6 5 Recommended reading 6 6 Exercises Chapter 7 Review and Preview 7 1 Introduction 7 2 Necessary conditions 7 3 Sufficient conditions 7 4 Two dependent variables 7 5 History and preview 7 6 Recommended reading Chapter 8 The Homogeneous Problem 8 1 Integrals in parametric form 8 2 Euler—Lagrange equations 8 3 The Weierstrass equation 8 4 Case study:The parametric Queen Dido problem 8 5 Recommended reading 8 6 Exercises Chapter 9 Variable—Endpoint Conditions 9 1 Natural boundary conditions 9 2 Transversality conditions 9 3 Focal points 9 4 Case study:Neile's parabola 9 5 Recommended reading 9 6 Exercises Chapter 10 Broken Extremals 10 1 The Weierstrass—Erdmann corner conditions 10 2 Caratheodory's indicatrix i0 3 Recommended reading 10 4 Exercises Chapter 11 Strong Variations 11 1 Troubles with weak variations 11 2 Weierstrass's condition 11 3 Case study:Newton's problem 11 4 Recommended reading 11 5 Exercises Chapter 12 Sufficient Conditions 12 1 Introduction 12 2 Fields of extremals 12 3 Hilbert's invariant integral 12 4 Weierstrass's E-function revisited 12 5 The royal road 12 6 Recommended reading 12 7 Exercises Bibliography Index 詳細資料或其他書籍請至台灣高等教育出版社查詢,查後請於PChome商店街私訊告知ISBN或書號,我們即儘速上架。 |