變分學入門 (英文) 馬克.科特 9787040612172 【台灣高等教育出版社】

圖書均為代購,正常情形下,訂後約兩周可抵台。
物品所在地:中國大陸
原出版社:高等教育
NT$859
商品編號:
供貨狀況: 尚有庫存

此商品參與的優惠活動

加入最愛
商品介紹
*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

Preiace
Chapter 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。
規格說明
運送方式
已加入購物車
已更新購物車
網路異常,請重新整理