CUSAT CAT B.Tech key terms

The value a function approaches as its input approaches a specified point, regardless of whether the function actually equals that value there; existence requires the same value from both sides.

The instantaneous rate at which a function changes with respect to its variable, defined as the limit of the difference quotient; geometrically it gives the slope of the tangent line.

The limit of a sum of products of function values and small interval widths over a stated interval; it measures signed accumulated area between the graph and the axis.

A property of a function at a point where the function is defined, its limit exists there, and the limit equals the function value; informally, the graph has no break at that point.

A single number computed from the entries of a square matrix that indicates whether the matrix is invertible; it is zero exactly when the rows or columns are linearly dependent.

A scalar for which a square matrix acting on some nonzero vector merely scales that vector instead of changing its direction; found by solving the characteristic equation.

The maximum number of linearly independent rows, equivalently columns, in a matrix; it equals the number of nonzero rows in its reduced row-echelon form.

An arrangement of a set of objects in a definite order; the number of permutations of n distinct objects taken r at a time is n! divided by (n minus r)!.

A selection of objects where order does not matter; the number of ways to choose r objects from n distinct objects is n! divided by r!(n minus r)!.

A sequence in which each term after the first is obtained by adding a fixed constant to the previous term; the nth term equals a plus (n minus 1)d.

The probability that an event occurs given that another event has already occurred, computed as the probability of both events divided by the probability of the given event.

An operation on two vectors producing a scalar equal to the product of their magnitudes and the cosine of the angle between them; it is zero for perpendicular vectors.

An operation on two vectors in three dimensions producing a vector perpendicular to both, with magnitude equal to the product of their magnitudes times the sine of the included angle.

The velocity of an object at a particular instant, equal to the limit of average velocity as the time interval shrinks to zero; it is the derivative of position with respect to time.

The two-dimensional motion of an object launched into the air and then acted on only by gravity, analysed by treating its horizontal and vertical components independently.

A measure of an object's resistance to change in its rotational motion, determined by how its mass is distributed about the chosen axis; it plays the role of mass in rotational dynamics.

The rotational analogue of linear momentum, equal to the cross product of the position vector and linear momentum; it is conserved when no external torque acts on the system.

Oscillation in which the restoring force is directly proportional to the displacement from equilibrium and directed toward it, producing sinusoidal motion of constant amplitude and period.

The change in the frequency of a wave detected by an observer when the source and the observer move relative to each other; approach raises the observed frequency, recession lowers it.

The complete reflection of light back into a denser medium when it strikes the boundary with a rarer medium at an angle of incidence larger than the critical angle.

A measure of the electric field passing through a surface, equal to the surface integral of the field; for a flat surface it is the field times area times cosine of the angle.

The charge stored per unit potential difference across a conductor or capacitor, measured in farads; for a parallel-plate capacitor in vacuum it equals epsilon-zero times area divided by separation.

The small average velocity with which free electrons move along a conductor under an applied electric field, superimposed on their much faster random thermal motion.

The induced current in a circuit flows in the direction that opposes the change in magnetic flux that produced it, a statement of energy conservation in electromagnetic induction.

The emission of electrons from a metal surface when light above a threshold frequency falls on it, with maximum electron kinetic energy depending on frequency, not on intensity.

The minimum energy needed to remove an electron from the surface of a metal; it determines the threshold frequency below which the photoelectric effect cannot occur.

The amount of substance containing exactly 6.022 times 10 to the power 23 representative particles, such as atoms, molecules or ions; it links sample mass to particle number.

The concentration of a solution expressed as the number of moles of solute dissolved per litre of solution; it changes slightly with temperature because solution volume expands.

The concentration of a solution expressed as the number of moles of solute per kilogram of solvent; unlike molarity, it does not change with temperature.

The reactant that is completely consumed first in a chemical reaction, thereby deciding the maximum amount of product that can form; the other reactants are in excess.

A bookkeeping charge assigned to an atom in a compound, found by distributing shared electrons to the more electronegative atom, used to track redox changes.

When a system at equilibrium is disturbed by a change in concentration, pressure or temperature, the system shifts in the direction that partially counteracts the disturbance.

The ratio of the product of product concentrations to the product of reactant concentrations, each raised to its stoichiometric coefficient, at equilibrium for a given temperature.

A logarithmic measure of hydrogen ion concentration in a solution, defined as the negative base-ten logarithm of the hydrogen ion concentration in moles per litre.

A solution that resists large changes in pH when small amounts of acid or base are added, usually containing a weak acid with its conjugate base or a weak base with its conjugate acid.

The mixing of atomic orbitals of similar energy in an atom to form an equal number of new, equivalent orbitals that give the observed molecular geometry.

When a hydrogen halide adds to an unsymmetrical alkene, the hydrogen attaches to the carbon that already carries more hydrogen atoms, giving the more stable carbocation intermediate.

Properties of a solution that depend on the number of dissolved particles rather than their identity, such as boiling-point elevation, freezing-point depression and osmotic pressure.

The power to which the concentration of a reactant is raised in the experimentally determined rate law; the sum of these powers gives the overall order.