Elementary Diffential Equations with Boundary Value Problems, 5/e (Hardcover)
C. Henry Edwards, David E. Penney
- 出版商: Prentice Hall
- 出版日期: 2003-11-09
- 售價: $1,205
- 語言: 英文
- 頁數: 768
- 裝訂: Hardcover
- ISBN: 0131457748
- ISBN-13: 9780131457744
-
相關分類:
工程數學 Engineering-mathematics
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相關主題
商品描述
For traditional courses in elementary differential equations that science, engineering, and mathematics students take following calculus.
This accessible, attractive, and interesting text teaches students to first solve those differential equations that have the most frequent and interesting applications. This motivates students and illustrates the standard elementary techniques of solution of differential equations. Precise and clear-cut statements of fundamental existence and uniqueness theorems allow understanding of their role in this subject. The first few sections of most chapters introduce the principle ideas of each topic, with remaining sections devoted to extensions and applications, giving instructors a wide range of choices regarding breadth and depth of coverage. A strong numerical approach emphasizes that the effective and reliable use of numerical methods often requires preliminary analysis using standard elementary techniques.
Table of Contents
1. First-Order Differential Equations.
2. Linear Equations of Higher Order.
3. Power Series Methods.
4. Laplace Transform Methods.
5. Linear Systems of Differential Equations.
6. Numerical Methods.
7. Nonlinear Systems and Phenomena.
8. Fourier Series Methods.
9. Eigenvalues and Boundary Value Problems.
References for Further Study.
Appendix: Existence and Uniqueness of Solutions.
Answers to Selected Problems.
Index.
商品描述(中文翻譯)
這是一本針對科學、工程和數學學生在學完微積分後所修讀的傳統初等微分方程課程的教材。
這本易於理解、吸引人且有趣的教材教導學生首先解決那些具有最常見和有趣應用的微分方程。這激發了學生的興趣,並展示了解微分方程的標準初等解法技巧。對於基本存在性和唯一性定理的精確明確陳述,有助於理解它們在這個主題中的作用。大多數章節的前幾節介紹了每個主題的主要思想,其餘節篇則專注於擴展和應用,使教師在涵蓋範圍的廣度和深度方面有很大的選擇空間。強調數值方法的教學方法強調了使用標準初等技巧進行初步分析,以實現數值方法的有效和可靠使用。
目錄:
1. 一階微分方程。
2. 高階線性微分方程。
3. 冪級數方法。
4. 拉普拉斯變換方法。
5. 線性微分方程組。
6. 數值方法。
7. 非線性系統和現象。
8. 傅立葉級數方法。
9. 特徵值和邊值問題。
進一步學習的參考文獻。
附錄:解的存在性和唯一性。
選擇性問題的答案。
索引。