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.
Answer 12 questions on Fundamentals of Numerical Sequences and Calculus.
1. Which statement matches the topic "Généralités sur les suites numériques"?
2. What is an arithmetic sequence?
Go over the full study guide for Fundamentals of Numerical Sequences and Calculus.
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