Ingénieur ITPE - independent mathematics, physics and infrastructure foundations key terms

Convergence at each fixed point with an index that may depend on that point, which does not alone control errors across the whole domain.

Convergence in which one sequence index controls the prescribed error simultaneously for every point in the stated domain.

One integrable absolute bound applying to the entire sequence in a dominated-convergence argument, rather than an individually chosen bound for each term.

Convergence of the series of supremum norms in the specified setting, a sufficient condition for uniform absolute control of the series.

The distance from the center within which a power series converges absolutely, with boundary points requiring their own analysis.

The matrix of second partial derivatives under suitable differentiability, used with its quadratic form to analyze local behavior near stationary points.

A condition on constraints that supports the applicability of an optimization theorem, so formal multiplier equations are not used without hypotheses.

The matrix of pairwise inner products of basis vectors, used to compute projection coefficients when the basis is not orthonormal.

The subspace element whose residual is orthogonal to that subspace under the stated inner product, with existence depending on the relevant setting.

A matrix transformation of a bilinear or quadratic form of the type P* A P, distinct from similarity of linear operators.

The supremum or maximum modulus of spectral values in the relevant setting, distinct from the largest singular value of a general matrix.

A norm measuring the largest output magnitude for unit input under specified vector norms, which must not be confused with an arbitrary matrix entry.

A measure of sensitivity of a problem’s solution to specified relative input perturbations, depending on the norm and formulation used.

Control of the effects of computational perturbations and round-off by an algorithm, distinct from conditioning of the exact mathematical problem.

The discrepancy obtained by substituting an approximate solution into the original equation, which may not directly equal the solution error.

A root-solving update using a function value and derivative, whose local convergence depends on root and initialization conditions.

A property of a numerical evolution method controlling growth on a specified test equation and step size, separate from approximation accuracy.

An independent coordinate describing a constrained mechanical configuration, chosen consistently with the model’s degrees of freedom.

A characteristic coupled oscillation pattern with a shared frequency obtained from the appropriate mass and stiffness eigenvalue problem.

An idealized process with no heat transfer and no entropy production, unlike an arbitrary irreversible adiabatic process.

The total normal stress less pore-water pressure in a specified saturated-soil model, relevant to the skeleton response and drained strength.

The hydraulic-head difference divided by the stated flow-path length, with direction and the actual groundwater model identified.

The fluid pressure within ground voids, distinguished from total overburden stress and from effective stress carried through the soil skeleton.

Time-dependent volume change associated with pore-fluid dissipation and load transfer in a specified soil drainage and compressibility model.

Ground response evaluated for conditions where the relevant loading duration does not allow the assumed drainage to occur.

Downward shaft action mobilized where surrounding ground settles relative to a pile, requiring compatible displacement and load assessment.

A model of ground resistance to a specified foundation load mechanism, separate from settlement acceptability and structural foundation resistance.

A limiting lateral ground-pressure condition requiring sufficient compatible outward wall movement under the stated soil and water model.

Lateral pressure associated with a constrained ground deformation condition, not automatically equivalent to mobilized active or passive resistance.

A specified boundary describing an unacceptable strength, stability or serviceability condition within the actual assessment framework and loading scenario.