💚 MATH CONCEPTS

• Helmholtz's theorem – States that a vector field is uniquely determined (up to boundary conditions) by its divergence and curl.

• Green's theorem – Relates a line integral around a simple closed curve to a double integral over the region it encloses (2D case of Stokes).

• Lagrange theorem – In math, often refers to group theory or remainder theorem, not about vector fields.

• Stokes' theorem – Relates a surface integral of the curl of a vector field to a line integral around its boundary curve.

B

wave

D. complex frequency

✔ Dirichlet conditions ✅

Other options:

• L’Hôpital’s Rule → used to evaluate limits of indeterminate forms.

• Taylor’s theorem → approximates smooth functions by polynomials.

• Parseval’s identity → relates the total energy of a signal to the sum of squares of its Fourier coefficients.

In significance test, if the level of significance is 0.01 or less,

i.e. the confidence level is 88% or more, the results are

considered to be

. none of the choices

. not significant

. highly significant

. probably significant

✔ minimum phase system ✅

• Unstable system → occurs if any pole is in the right-half s-plane.

• Stable system → all poles in left-half plane, regardless of zeros.

• Maximum phase system → zeros in the right-half s-plane.

B. Complex differentiable

0

• Simple random sampling → every individual has an equal chance, chosen purely at random (like drawing lots).

• Stratified sampling → population is divided into subgroups (strata) and samples are taken from each.

• Cluster sampling → population is divided into clusters (often geographically) and entire clusters are randomly chosen.

• Systematic sampling → select every kkkth individual (e.g., every 10th person).

caltech

opposite pag kay normal

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