Bac Techniques Mathématiques (Algeria) - independent subject practice key terms

The value a function approaches as its input approaches a chosen point, whether or not the function is defined there. It is the foundation for continuity, derivatives, and integrals.

A property of a function whose value at a point equals the limit of the function there. Informally, the graph has no break, jump, or hole at that point.

The instantaneous rate of change of a function with respect to its variable, defined as the limit of a difference quotient. Geometrically it gives the slope of the tangent line.

The property that a function has a well-defined derivative at a point. Differentiability at a point implies continuity there, but continuity does not imply differentiability.

An interior point of a function's domain where the derivative is zero or fails to exist. Such points are candidates for local maxima, minima, or inflection behavior.

The way a curve bends, determined by the sign of the second derivative. Positive second derivative means concave up; negative means concave down; a sign change marks an inflection point.

The signed area between a function's graph and the horizontal axis over an interval, defined as a limit of Riemann sums. It yields a number, unlike the indefinite integral.

The result linking differentiation and integration: differentiating an accumulated area function recovers the integrand, and a definite integral equals the change in an antiderivative.

An integral over an unbounded interval or of a function with an infinite discontinuity. It is defined by a limit and either converges to a finite value or diverges.

An infinite power series expansion of a smooth function about a point, built from the function's derivatives there. Truncating it gives polynomial approximations with controllable error.

The property of a sequence or series whose terms approach a finite limit or whose partial sums approach a finite sum. Divergence means no such finite limit exists.

The derivative of a multivariable function with respect to one variable while holding the others fixed. It measures sensitivity to that single input direction.

The vector of all first partial derivatives of a scalar function. It points in the direction of steepest increase and is perpendicular to level curves or surfaces.

The matrix of first partial derivatives of a vector-valued function, describing its best linear approximation. Its determinant measures local volume scaling under the transformation.

A set closed under addition and scalar multiplication, satisfying axioms such as associativity, commutativity, and existence of a zero vector and additive inverses.

A property of a set of vectors where no nontrivial linear combination equals the zero vector. Equivalently, no vector in the set is a combination of the others.

A linearly independent set of vectors that spans a vector space, so every element is expressed uniquely as a linear combination of them. The number of basis vectors is the dimension.

The dimension of the column space of a matrix, equal to the number of linearly independent rows or columns. It determines whether a linear system has unique, many, or no solutions.

A scalar computed from a square matrix that is nonzero exactly when the matrix is invertible. It also gives the signed volume scaling factor of the associated linear map.

A scalar for which some nonzero vector is mapped to a scalar multiple of itself by a linear operator. Eigenvalues characterize stability, vibration modes, and diagonalizability.

Writing a matrix as a product involving a diagonal matrix and a matrix of eigenvectors. It is possible exactly when there are enough linearly independent eigenvectors.

A scalar operation on two vectors equal to the sum of products of corresponding components. It relates to the cosine of the angle between them and tests orthogonality.

A vector operation defined in three dimensions, producing a vector perpendicular to both inputs with magnitude equal to the area of the spanned parallelogram.

The component of one vector along the direction of another, computed using the dot product. It underlies least squares fitting and Gram-Schmidt orthogonalization.

The straight-line distance and direction of a point from its starting position, treated as a vector quantity. It differs from distance travelled, which is a scalar and ignores direction.

The rate of change of displacement with respect to time, a vector quantity with both magnitude and direction. Average velocity divides total displacement by total time taken.

The rate at which velocity changes with time, including changes in speed, direction, or both. It is measured in metres per second squared and is a vector.

The resultant force on a body equals the rate of change of its momentum; for constant mass this reduces to force equals mass times acceleration, measured in newtons.

The product of a body's mass and its velocity, a vector measured in kilogram metre per second. For a chosen system, total momentum is conserved when the net external impulse is zero; closure to matter alone does not establish isolation from force.

The time integral of resultant force, or average resultant force times duration, equal to the change in momentum of the chosen body or system. It is measured in newton seconds and explains why airbags reduce injury.