They cover linear and nonlinear problems and discuss first-order scalar linear and nonlinear ordinary differential equations, second-order ordinary differential equations and damped oscillations, boundary-value problems, eigenvalues of linear boundary-value problems, variable coefficients and adjoints, resonance, second-order equations in the phase plane, systems of equations, the fundamental existence theorem, random functions, chaos, linear systems and linearization, stable and unstable fixed points, multiple solutions for nonlinear boundary-value problems, bifurcation, continuation and path-following, periodic ordinary differential equations, boundary and interior layers, the

complex plane, and time-dependent partial differential equations.

The plane on which imaginary (and complex) numbers are plotted is called an Argand Diagram or the

Complex Plane.

1] = {s [member of] C : L(s) = c}, where and in what follows, s denotes a complex variable in the

complex plane C and c denotes a value in the extended

complex plane C [union] {[infinity]}.

It is based on the relationship between system root location in the

complex plane and its temporal behavior (Arbulu Saavedra et al.

Let us consider the

complex plane joint-lever mechanism of fourth class (Fig.

one can be faced with two important problems given in the following: a) Determining how to undergo a change of (semi)norm of the holomorphic function when the given region expands; b) Determining the relationships between different (semi)norms of analytic functions in a given finite Jordan region on the

complex plane in the various (semi)normed space

Modular forms are functions on the

complex plane that are inordinately symmetric.

The zero exclusion condition formulated in [1] says: Let D be an open subset of the

complex plane and assume that (2) is a family of polynomials with invariant degree and uncertainty bounding set Q which is pathwise connected.

the domain supplemented to the complete

complex plane by [S.

Let us imagine a

complex plane ready to be filled by transfer zeroes and poles.

We particularly study the case k = 2, for which we characterize the boundary of the region in the

complex plane contained in W (A), where pairs of complex conjugate Ritz values are located.

Among the topics are arithmetic and topology in the

complex plane, holomorphic functions and differential forms, isolated singularities of holomorphic functions, harmonic functions, the Riemann mapping theorem and Dirichlet's problem, and the complex Fourier transform.