Titlebook: Ordinary Differential Equations with Applications; Carmen Chicone Textbook 19991st edition Springer Science+Business Media New York 1999 b

Galactogogue

Introduction to Ordinary Differential Equations,al equation? Do differential equations always have solutions? Are solutions of differential equations unique? However, the most important goal of this chapter is to introduce a geometric interpretation for the space of solutions of a differential equation. Using this geometry, we will introduce some

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SSRIS

Continuation of Periodic Solutions,ntroduced that can be used to address a classic case of this problem where the physical system is an oscillator that is modeled by a differential equation with periodic orbits and the applied force is modeled as a “small ” perturbation. Partial answers to several important questions will be given. W

Hiatus

Density

Averaging,oach to the subject is through perturbation theory; for example, we will discuss the existence of periodic orbits for periodically forced oscillators. However, we will also introduce some additional ideas from the theory of averaging that have far-reaching implications beyond the scope of this book.

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seroma

Autobiography

Linear Systems and Stability,In this chapter we will study the differential equation . where . is a smooth . matrix-valued function and . is a smooth function such that .(0,.) = .(0,.) ≡ 0. Note that if . has this form , then the associated . . is the linearization of the differential equation along the . . ↦ . ≡ 0.

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Local Bifurcation,Consider the family of differential equations . If f(.,.=0, then the differential equation with parameter value ɛ = ɛ. has a rest point at u0 and the linearized system at this point is given by ..