Author | Humi, Mayer. author |
---|---|
Title | Second Course in Ordinary Differential Equations for Scientists and Engineers [electronic resource] / by Mayer Humi, William Miller |
Imprint | New York, NY : Springer US, 1988 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-3832-4 |
Descript | XI, 441 p. online resource |
O: Review -- 1. Solution of second order ordinary differential equations by series -- 2. Regular singular points -- 3. Series solutions near a regular singular point -- 1: Boundary Value Problems -- 1. Introduction -- 2. Adjoint differential equations and boundary conditions -- 3. Self -adjoint systems -- 4. A broader approach to self-adjoint systems -- 5. Sturm-Liouvi1 le theory -- 6. Introduction to orthogonality and completeness -- 2: Special Functions -- 1. Hypergeometric series -- 2. Bessel functions -- 3. Legendre polynomials -- 4. Gamma function -- 3: Systems of Ordinary Differential Equations -- 1. Introduction -- 2. Method of elimination -- 3. Some linear algebra -- 4. Linear systems with constant coefficients -- 5. Linear systems with variable coefficients -- 6. Elements of linear control theory -- 7. The Laplace transform -- 4: Applications of Symmetry Principles to Differential Equations -- 1. Introduction -- 2. Lie groups -- 3. Lie algebras -- 4. Prolongation of the action -- 5. Invariant differential equations -- 6. The factor ization method -- 7. Examples of factorizable equations -- 5: Equations with Periodic Coefficients -- 1. Introduction -- 2. Floquet theory for periodic equations -- 3. Hillโs and Mathieu equations -- 6: Greenโs Functions -- 1. Introduction -- 2. General definition of Greenโs function -- 3. The interpretation of Greenโs functions -- 4. Generalized functions -- 5. Elementary solutions and Greenโs functions -- 6. Eigenfunetion representation of Greenโs functions -- 7. Integral equations -- 7: Perturbation Theory -- 1. Preliminaries -- 2. Some basic ideas-regular perturbations -- 3. Singular perturbations -- 4. Boundary layers -- 5. Other perturbation methods -- *6. Perturbations and partial differential equations -- *7. Perturbation of eigenvalue problems -- *8. The Zeeman and Stark effects -- 8: Phase Diagrams and Stability -- 1. General introduction -- 2. Systems of two equations -- 3. Some general theory -- 4. Almost linear systems -- 5. Almost linear systems in R2 -- 6. Liapounov direct method -- 7. Periodic solutions (limit cycles) -- 9: Catastrophes and Bifurcations -- 1. Catastrophes and structural stability -- 2. Classification of catastrophe sets -- 3. Some examples of bifurcations -- 4. Bifurcation of equilibrium states in one dimension -- 5. Hopf bifurcation -- 6. Bifurcations in R -- 10: Sturmian Theory -- 1. Some mathematical preliminaries -- 2. Sturmian theory for first order equations -- 3. Sturmian theory for second order equations -- 4. Prufer transformations