Author | Greguลก, Michal. author |
---|---|

Title | Third Order Linear Differential Equations [electronic resource] / by Michal Greguลก |

Imprint | Dordrecht : Springer Netherlands, 1987 |

Connect to | http://dx.doi.org/10.1007/978-94-009-3715-4 |

Descript | XV, 270 p. 1 illus. online resource |

SUMMARY

Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then is that they can't see the problem. one day, perhaps you will find the final question. G. K. Chesterton. The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Gad in Crane Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. Howยญ ever, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the stI11fture of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciยญ plines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classifiãtion schemes

CONTENT

I. Third Order Linear Homogeneous Differential Equations in Normal Form -- ยง1. Fundamental Properties of Solutions of the Third Order Linear Homogeneous Differential Equation -- ยง2. Oscillatory Properties of Solutions of the Differential Equation (a) -- ยง3. Asymptotic Properties of Solutions of the Differential Equations (a) and (b) -- ยง4. Boundary Value Problems -- II. Third Order Linear Homogeneous Differential Equations with Continuous Coefficients -- ยง5. Principal Properties of Solutions of Linear Homogeneous Third Order Differential Equations with Continuous Coefficients -- ยง6. Conditions for Disconjugateness, Non-oscillatoricity and Oscillatoricity of Solutions of the Differential Equation (A) -- ยง7. Comparison Theorems for Differential Equations of Type (A) and Their Applications -- III. Concluding Remarks -- 1. Special Forms of Third Order Differential Equations -- 2. Remark on Mutual Transformation of Solutions of Third Order Differential Equations -- IV. Applications of Third Order Linear Differential Equation Theory -- ยง8. Some Applications of Linear Third Order Differential Equation Theory to Non-linear Third Order Problems -- ยง9. Physical and Engineering Applications of Third Order Differential Equations -- References

Mathematics
Mathematical analysis
Analysis (Mathematics)
Mathematics
Analysis