|
IDENT
|
http://dx.doi.org/10.1007/978-1-4612-3832-4
|
|
標題および責任表示
|
Second Course in Ordinary Differential Equations for Scientists and Engineers / by Mayer Humi, William Miller
|
|
特定資料種別コード
|
リモートファイル
|
|
出版・頒布事項
|
New York, NY : Springer US , 1988
|
|
形態事項
|
XI, 441 p : online resource
|
|
巻号情報
|
|
|
書誌構造リンク
|
Universitext <>//a
|
|
内容著作注記
|
O: Review
|
|
内容著作注記
|
1. Solution of second order ordinary differential equations by series
|
|
内容著作注記
|
2. Regular singular points
|
|
内容著作注記
|
3. Series solutions near a regular singular point
|
|
内容著作注記
|
1: Boundary Value Problems
|
|
内容著作注記
|
1. Introduction
|
|
内容著作注記
|
2. Adjoint differential equations and boundary conditions
|
|
内容著作注記
|
3. Self -adjoint systems
|
|
内容著作注記
|
4. A broader approach to self-adjoint systems
|
|
内容著作注記
|
5. Sturm-Liouvi1 le theory
|
|
内容著作注記
|
6. Introduction to orthogonality and completeness
|
|
内容著作注記
|
2: Special Functions
|
|
内容著作注記
|
1. Hypergeometric series
|
|
内容著作注記
|
2. Bessel functions
|
|
内容著作注記
|
3. Legendre polynomials
|
|
内容著作注記
|
4. Gamma function
|
|
内容著作注記
|
3: Systems of Ordinary Differential Equations
|
|
内容著作注記
|
1. Introduction
|
|
内容著作注記
|
2. Method of elimination
|
|
内容著作注記
|
3. Some linear algebra
|
|
内容著作注記
|
4. Linear systems with constant coefficients
|
|
内容著作注記
|
5. Linear systems with variable coefficients
|
|
内容著作注記
|
6. Elements of linear control theory
|
|
内容著作注記
|
7. The Laplace transform
|
|
内容著作注記
|
4: Applications of Symmetry Principles to Differential Equations
|
|
内容著作注記
|
1. Introduction
|
|
内容著作注記
|
2. Lie groups
|
|
内容著作注記
|
3. Lie algebras
|
|
内容著作注記
|
4. Prolongation of the action
|
|
内容著作注記
|
5. Invariant differential equations
|
|
内容著作注記
|
6. The factor ization method
|
|
内容著作注記
|
7. Examples of factorizable equations
|
|
内容著作注記
|
5: Equations with Periodic Coefficients
|
|
内容著作注記
|
1. Introduction
|
|
内容著作注記
|
2. Floquet theory for periodic equations
|
|
内容著作注記
|
3. Hill's and Mathieu equations
|
|
内容著作注記
|
6: Green's Functions
|
|
内容著作注記
|
1. Introduction
|
|
内容著作注記
|
2. General definition of Green's function
|
|
内容著作注記
|
3. The interpretation of Green's functions
|
|
内容著作注記
|
4. Generalized functions
|
|
内容著作注記
|
5. Elementary solutions and Green's functions
|
|
内容著作注記
|
6. Eigenfunetion representation of Green's functions
|
|
内容著作注記
|
7. Integral equations
|
|
内容著作注記
|
7: Perturbation Theory
|
|
内容著作注記
|
1. Preliminaries
|
|
内容著作注記
|
2. Some basic ideas-regular perturbations
|
|
内容著作注記
|
3. Singular perturbations
|
|
内容著作注記
|
4. Boundary layers
|
|
内容著作注記
|
5. Other perturbation methods
|
|
内容著作注記
|
*6. Perturbations and partial differential equations
|
|
内容著作注記
|
*7. Perturbation of eigenvalue problems
|
|
内容著作注記
|
*8. The Zeeman and Stark effects
|
|
内容著作注記
|
8: Phase Diagrams and Stability
|
|
内容著作注記
|
1. General introduction
|
|
内容著作注記
|
2. Systems of two equations
|
|
内容著作注記
|
3. Some general theory
|
|
内容著作注記
|
4. Almost linear systems
|
|
内容著作注記
|
5. Almost linear systems in R2
|
|
内容著作注記
|
6. Liapounov direct method
|
|
内容著作注記
|
7. Periodic solutions (limit cycles)
|
|
内容著作注記
|
9: Catastrophes and Bifurcations
|
|
内容著作注記
|
1. Catastrophes and structural stability
|
|
内容著作注記
|
2. Classification of catastrophe sets
|
|
内容著作注記
|
3. Some examples of bifurcations
|
|
内容著作注記
|
4. Bifurcation of equilibrium states in one dimension
|
|
内容著作注記
|
5. Hopf bifurcation
|
|
内容著作注記
|
6. Bifurcations in R
|
|
内容著作注記
|
10: Sturmian Theory
|
|
内容著作注記
|
1. Some mathematical preliminaries
|
|
内容著作注記
|
2. Sturmian theory for first order equations
|
|
内容著作注記
|
3. Sturmian theory for second order equations
|
|
内容著作注記
|
4. Prufer transformations
|
|
注記
|
The world abounds with introductory texts on ordinary differential equations and rightly so in view of the large number of students taking a course in this subject. However, for some time now there is a growing need for a junior-senior level book on the more advanced topics of differential equations. In fact the number of engineering and science students requiring a second course in these topics has been increasing. This book is an outgrowth of such courses taught by us in the last ten years at Worcester Polytechnic Institute. The book attempts to blend mathematical theory with nontrivial applications from varipus disciplines. It does not contain lengthy proofs of mathemati~al theorems as this would be inappropriate for its intended audience. Nevertheless, in each case we motivated these theorems and their practical use through examples and in some cases an "intuitive proof" is included. In view of this approach the book could be used also by aspiring mathematicians who wish to obtain an overview of the more advanced aspects of differential equations and an insight into some of its applications. We have included a wide range of topics in order to afford the instructor the flexibility in designing such a course according to the needs of the students. Therefore, this book contains more than enough material for a one semester course
|
|
学情ID
|
9780387966762
|
|
本文言語コード
|
英語
|
|
著者標目リンク
|
*Humi, Mayer <> author
|
|
著者標目リンク
|
Miller, William <> author
|
|
著者標目リンク
|
SpringerLink (Online service) <>
|
|
分類標目
|
DC23:515
|
|
件名標目等
|
Mathematics
|
|
件名標目等
|
Mathematical analysis
|
|
件名標目等
|
Analysis (Mathematics)
|
|
件名標目等
|
Mathematics
|
|
件名標目等
|
Analysis
|
目録検索 ▼
マイライブラリ ▼
