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Theory and examples of ordinary differential equations

Author: Chin-Yuan Lin
Publisher: Singapore ; Hackensack, N J : World Scientific, ©2011.
Series: Series on concrete and applicable mathematics, v. 10.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Presents the theory of ordinary differential equations, with illustrative examples and interesting exercises. This book is suitable for undergraduate students who major in mathematics and have  Read more...

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Document Type: Book
All Authors / Contributors: Chin-Yuan Lin
ISBN: 9789814307123 9814307122
OCLC Number: 696115825
Description: xiii, 540 pages : illustrations ; 26 cm.
Contents: : Ch. 1 Linear Equations --
1. Introduction --
2. Main Results --
3. Examples --
4. Proof of the Main Results --
4.1. The Wronskian W(x) --
4.2. Fundamental Sets of Solutions --
4.3. Homogeneous Equations --
4.4. Nonhomogencous Equations --
4.5.A Particular Solution --
5. Equations of Special Type --
5.1. First Order Equations --
5.2. Euler Equations --
5.3. Exact Equations --
6. The Technique of the Laplace Transform --
7. Problems --
8. Solutions --
ch. 2 Systems of Linear First Order Equations --
1. Introduction --
2. Main Results --
3. Examples --
4. Proof of the Main Results --
4.1. The Exponential Function exp(tA) --
4.2. The Wronskian W(t) --
4.3. Methods of Computing the Fundamental Matrix exp(tA) --
4.4. Fundamental Sets of Solutions --
4.5. Homogeneous Systems --
4.6. Nonhomogeneous Systems --
4.7.A Particular Solution --
5. An Additional Method for Computing a Fundamental Matrix --
6. Problems --
7. Solutions --
ch. 3 Power Series Solutions --
1. Introduction --
2. Main Results --
3. Examples --
4. Proof of the Main Results --
5. The Extension of the Main Results --
6. Problems --
7. Solutions --
ch. 4 Adjoint Operators and Nonhomogeneous Boundary Value Problems --
1. Introduction --
2.A Necessary and Sufficient Condition for Solvability --
3. Examples --
4.Complementary Properties between Adjoint Problems and Original Problems --
5. An Abstract Result --
5.1. Linear Operators --
5.2. Adjoint Operators --
5.3. Solvability Condition --
6. Problems --
7. Solutions --
ch. 5 Green Functions --
1. Introduction --
2. Main Results --
3. Examples --
4. Proof of the Main Results --
5. More Theoretical Material --
5.1. Riemann Integrals --
5.2. Lebesgue Integrals --
5.3. The Meaning of the Dirac Delta Function --
6. Problems --
7. Solutions --
ch. 6 Eigenfunction Expansions --
1. Introduction --
2. Main Results --
3. Examples --
4. Existence of Eigenvalues, and Completeness of Eigenfunctions --
4.1. Properties of Eigenvalues --
4.2. Properties of Eigenfunctions --
4.3. Properties of Some Integral Operator --
4.4. Existence of Eigenvalues and Eigenfunctions --
4.5. Proof of the Main Results --
5. Abstract Expansion Results --
5.1. Linear Continuous Operators --
5.2. Expansion Results for Compact Symmetric Operators --
5.3. Properties of Compact Symmetric Operators --
5.4. Proof of the Abstract Expansion Results --
5.5. Examples from Ordinary Differential Operators --
6. Problems --
7. Solutions --
ch. 7 Long Time Behavior of Systems of Differential Equations --
1. Introduction --
2. Main Results for Linear Systems --
3. Main Results for Nonlinear Systems --
4. Examples for Linear Systems --
5. Examples for Nonlinear Systems --
6. Proof of the Main Results for Linear Systems --
7. Proof of the Main Results for Nonlinear Systems --
8. Problems --
9. Solutions --
ch. 8 Existence and Uniqueness Theorems --
1. Introduction --
2. The Main Results with Continuous Coefficients --
3. Proof of the Main Results --
3.1. The Linear Case with Continuous Coefficients --
3.2. The Nonlinear Case with Continuous Coefficients and with Uniqueness Result --
3.3. The Nonlinear Case with Continuous Coefficients but without Uniqueness Result --
4. The Results with Riemann or Lebesgue Integrable Coefficients --
4.1. Existence and Uniqueness Theorems --
4.2. Dependence on Initial Conditions and Parameters.
Series Title: Series on concrete and applicable mathematics, v. 10.
Responsibility: Chin-Yuan Lin.

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