Undergraduate Analysis, 2/e (Hardcover)
暫譯: 大學分析學(第二版)
Serge Lang
- 出版商: Springer
- 出版日期: 1996-12-05
- 售價: $1,100
- 貴賓價: 9.8 折 $1,078
- 語言: 英文
- 頁數: 642
- 裝訂: Hardcover
- ISBN: 0387948414
- ISBN-13: 9780387948416
-
相關分類:
微積分 Calculus、數值分析 Numerical-analysis、線性代數 Linear-algebra
下單後立即進貨 (約5~7天)
買這商品的人也買了...
-
$2,480$2,356 -
$1,900$1,805 -
$900$711 -
$720$569 -
$650$514 -
$1,710$1,625 -
$800$760 -
$680$537 -
$620$490 -
$590$460 -
$490$382 -
$650$507 -
$580$458 -
$650$507 -
$1,575$1,496 -
$580$458 -
$390$308 -
$650$507 -
$780$663 -
$1,200$948 -
$600$480 -
$540$427 -
$2,390$2,271 -
$1,188Interconnecting Cisco Network Devices, Part 2 (ICND2): (CCNA Exam 640-802 and ICND exam 640-816), 3/e
-
$399CompTIA Security+Study Guide: Exam SY0-201, 4/e (Paperback)
商品描述
Description:
This is a logically self-contained introduction to analysis, suitable for students who have had two years of calculus. The book centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration. Topics discussed include the classical test for convergence of series, Fourier series, polynomial approximation, the Poisson kernel, the construction of harmonic functions on the disc, ordinary differential equation, curve integrals, derivatives in vector spaces, multiple integrals, and others. One of the author's main concerns is to achieve a balance between concrete examples and general theorems, augmented by a variety of interesting exercises. Some new material has been added in this second edition, for example: a new chapter on the global version of integration of locally integrable vector fields; a brief discussion of L1-Cauchy sequences, introducing students to the Lebesgue integral; more material on Dirac sequences and families, including a section on the heat kernel; a more systematic discussion of orders of magnitude; and a number of new exercises.
Table of Contents:
Chapter 0: Sets and Mappings Chapter 1: Real Numbers Chapter 2: Limits and Continuous Functions Chapter 3: Differentiation Chapter 4: Elementary Functions Chapter 5: The Elementary Real Integral Chapter 6: Normed Vector Spaces Chapter 7: Limits Chapter 8: Compactness Chapter 9: Series Chapter 10: The Integral in One Variable Appendix: The Lebesgue Integral Chapter 11: Approximation with Convolutions Chapter 12: Fourier Series Chapter 13, Improper Integrals Chapter 14: The Fourier Integral Chapter 15: Calculus in Vector Spaces Chapter 16: The Winding Number and Global Potential Functions Chapter 17: Derivatives in Vector Spaces Chapter 18: Inverse Mapping Theorem Chapter 19: Ordinary Differential Equations Chapter 20: Multiple Integration Chapter 22: Differential Forms Appendix
商品描述(中文翻譯)
**描述:**
這是一本邏輯上自成一體的分析入門書籍,適合已經學習兩年微積分的學生。該書圍繞著與均勻收斂和均勻極限有關的性質,並在微分和積分的背景下進行探討。討論的主題包括級數的經典收斂測試、傅立葉級數、多項式近似、泊松核、圓盤上的調和函數構造、常微分方程、曲線積分、向量空間中的導數、多重積分等。作者的一個主要關注點是實現具體例子與一般定理之間的平衡,並輔以各種有趣的練習。在第二版中添加了一些新材料,例如:關於局部可積分向量場的全局積分的新章節;對 L1-Cauchy 序列的簡要討論,向學生介紹勒貝格積分;更多有關狄拉克序列和家族的材料,包括熱核的部分;對量級的更系統性討論;以及一些新的練習題。
**目錄:**
第0章:集合與映射
第1章:實數
第2章:極限與連續函數
第3章:微分
第4章:初等函數
第5章:初等實積分
第6章:範數向量空間
第7章:極限
第8章:緊性
第9章:級數
第10章:一變量的積分
附錄:勒貝格積分
第11章:卷積的近似
第12章:傅立葉級數
第13章:不當積分
第14章:傅立葉積分
第15章:向量空間中的微積分
第16章:繞數與全局勢能函數
第17章:向量空間中的導數
第18章:反映射定理
第19章:常微分方程
第20章:多重積分
第22章:微分形式
附錄