Differential and Difference Equations(差分与微分方程)(本科教材)
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Differential and Difference Equations(差分与微分方程)(本科教材)作者：李艳秋，郑冬梅，江舜君 开 本：16开 书号ISBN：9787122358202 定价： 出版时间：2020-02-01 出版社：化学工业 |
5.4Higher order differential equations096
5.5The Euler equation103
5.6Exercises105
Chapter 6Systems of differential equations106
6.1Existence and uniqueness theorem106
6.1.1Marks and definitions106
6.1.2Existence and uniqueness of solutions112
6.2General theory of linear differential systems117
6.2.1Linear homogeneous systems117
6.2.2Linear inhomogeneous systems123
6.3Linear differential systems with constant coefficients126
6.3.1Definition and properties of matrix exponent expA126
6.3.2Calculation of fundamental solution matrix129
6.4Exercises141
Chapter 7Qualitative and stability theories147
7.1Two-dimensional autonomous system and phase plane147
7.2Plane singularity155
7.2.1Trajectory distribution of two-dimensional linear systems156
7.2.2Distribution of orbits of two-dimensional nonlinear systems in the neighborhood of singularities165
7.3Limit cycle167
7.4Lyapunov stability169
7.4.1Stability169
7.4.2First approximation theory173
7.5Exercises178
Appendix182
A.1Solution of difference equations182
A.1.1First order linear constant coefficient difference equation182
A.1.2Higher order linear constant coefficient difference equation184
A.1.3Linear constant coefficient difference equations185
A.2Solutions of ordinary differential equations186
A.2.1Symbolic solutions186
A.2.2Numerical solutions189
A.3Exercises195
References196
教材 研究生/本科/专科教材
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