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Basic Principles of Classical Mechanics
To describe the motion of mechanical systems one uses a variety of mathematical models which are based on different principles - laws of motion. In...
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Chapter 6 Monodromy
In this chapter we begin the second part of these notes, looking at some ideas based around the concept of monodromy. Very roughly, this is the study...
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Chapter 1 Hilbert’s 16th Problem and Its Weak Form
Usually, the maximum of the number of limit cycles is denoted by H(n), and is called the Hilbert number. We recall that a limit cycle of system (1.1)...
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Chapter 3 Estimate of the Number of Zeros of Abelian Integrals
In the study of the weak Hilbert’s 16th problem by using Abelian integrals, it is crucial to estimate the number of zeros of them. In this chapter,...
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Chapter 3 Liouvillian Integrability
In this chapter we want to prove that Darboux integrability corresponds to the notion of Liouvillian integrability, or “solution by quadratures”.
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Chapter 7 The Tangential Center-Focus Problem
As is well known, the second part of Hilbert’s 16th problem is concerned with bounding the number of limit cycles in a polynomial system (1.2) of...
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Exact Solutions
The Navier–StokesNavier-Stokes (N-S) equationN-S equation, basically nonlinear partial differential equations, has few analytic exact solutionsExact...
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Unsteady Flow
In this chapter we consider problems where unsteadyUnsteady effects are dominant. The phenomena are quite different from steadySteady or...
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Boundary Layers
The boundary layerBoundary layer equation is an approximationApproximation of the N-S equationN-S equation at high Reynolds numbersReynolds number.
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