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· 제목 : Linear Ordinary Differential Equations (Paperback)
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 미분방정식 > 미분방정식 일반
· ISBN : 9780898713886
· 쪽수 : 348쪽
· 출판일 : 1987-01-01
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 미분방정식 > 미분방정식 일반
· ISBN : 9780898713886
· 쪽수 : 348쪽
· 출판일 : 1987-01-01
목차
- Preface
- Chapter 1: Simple Applications. Introduction
- Compartment systems
- Springs and masses
- Electric circuits
- Notes
- Exercises
- Chapter 2: Properties of Linear Systems. Introduction
- Basic linear algebra
- First-order systems
- Higher-order equations
- Notes
- Exercises
- Chapter 3: Constant Coefficients. Introduction
- Properties of the exponential of a matrix
- Nonhomogeneous systems
- Structure of the solution space
- The Jordan canonical form of a matrix
- The behavior of solutions for large t
- Higher-order equations
- Exercises
- Chapter 4: Periodic Coefficients. Introduction
- Floquet's theorem
- The logarithm of an invertible matrix
- Multipliers
- The behavior of solutions for large t
- First-order nonhomogeneous systems
- Second-order homogeneous equations
- Second-order nonhomogeneous equations
- Notes
- Exercises
- Chapter 5: Analytic Coefficients. Introduction
- Convergence
- Analytic functions
- First-order linear analytic systems
- Equations of order n
- The Legendre equation and its solutions
- Notes
- Exercises
- Chapter 6: Singular Points. Introduction
- Systems of equations with singular points
- Single equations with singular points
- Infinity as a singular point
- Notes
- Exercises
- Chapter 7: Existence and Uniqueness. Introduction
- Convergence of successive approximations
- Continuity of solutions
- More general linear equations
- Estimates for second-order equations
- Notes
- Exercises
- Chapter 8: Eigenvalue Problems. Introduction
- Inner products
- Boundary conditions and operators
- Eigenvalues
- Nonhomogeneous boundary value problems
- Notes
- Exercises
- Chapter 9: Eigenfunction Expansions. Introduction
- Selfadjoint integral operators
- Eigenvalues for Green's operator
- Convergence of eigenfunction expansions
- Extensions of the expansion results
- Notes
- Exercises
- Chapter 10: Control of Linear Systems. Introduction
- Convex sets
- Control of general linear systems
- Constant coefficient equations
- Time-optimal control
- Notes
- Exercises
- Bibliography.
