Flashcards: Fundamentals of Numerical Sequences and Calculus — 24 cartões

Numerical sequence — definition?

Function from ℕ to ℝ representing a list of numbers.

Sequence types — examples?

Arithmetic and geometric sequences.

Arithmetic sequence — fixed?

Constant difference between consecutive terms.

Geometric sequence — fixed?

Constant ratio between consecutive terms.

Sequence convergence — condition?

Monotone and bounded sequences converge.

Limit of a sequence — when?

Terms approach a finite value as n→∞.

Parametric curve — role?

Represented by vector functions depending on a parameter.

Position vector — in curves?

Assigns a point on the curve for each parameter.

Derivative vector — represents?

Instantaneous velocity in a curve.

Nuage de points — purpose?

Visualize data distribution in statistics.

Affine fit — purpose?

Finds the best linear approximation to data points.

Cross product — in space?

Produces a vector orthogonal to two vectors.

Vector cross product — properties?

Anticommutative and orthogonal to original vectors.

Random variable — definition?

Function from a probability space to ℝ.

Uniform probability — meaning?

Equal likelihood for all elementary outcomes.

Left derivative — in?

Limit approaching from the left side of a point.

Right derivative — in?

Limit approaching from the right side of a point.

Primitive function — role?

Function whose derivative equals the original function.

Differential equation — form?

First-order linear homogeneous: y' – m y = 0.

Solution to y' – my=0?

y = C e^{m x}.

Recurrence proof — method?

Induction: initial case + inductive step.

Sequence convergence — key?

Monotonicity and boundedness ensure convergence.

Dérivabilité — condition?

Left and right derivatives equal at a point.

Vector derivative — interpretation?

Represents velocity and acceleration.