differential calculus
Rates of change
Differential calculus is the branch of mathematics concerned with rates of change and slopes of curves.
It uses derivatives to analyze how quantities change in relation to each other—the speed of an object at an instant, the steepness of a curve at a point.
Paired with integral calculus, it forms the foundation of calculus.
I finally understood differential calculus when I realized derivatives just measure how fast something is changing.
Function's rate of change
- rate of changeMeasure of variation speed
- instantaneousHappening without any delay
- tangent lineCurve-touching straight path
- infinitesimalQuantity approaching zero
function · variable · increment · Newton · Leibniz · curve · gradient · perturbation
Maximum allowed extent
- continuityUninterrupted progression or coherence
- epsilonGreek fifth letter
- deltaSymbol denoting variation
- neighborhoodResidential area nearby
convergence · divergence · approach · discontinuity · boundedness
Directed rate of motion
- accelerationRate velocity changes
- motionChange in position
- slopeAngled terrain or steepness
- tangentLine touching curve once
rate · physics · engineering · marginal cost · kinematics · population growth · decay rate · approximation
Greatest permitted quantity
- minimumSmallest possible quantity
- extremaFunction's highest, lowest points
- critical pointDecisive juncture in events
- inflection pointWhere curvature changes sign
concavity · convexity · saddle point · increasing · decreasing
derivative
Function's rate of change
- rate of changeMeasure of variation speed
- instantaneousHappening without any delay
- tangent lineCurve-touching straight path
infinitesimal · function · variable · increment · Newton · Leibniz · curve · gradient · perturbation · differentiable
limit
Maximum allowed extent
- continuityUninterrupted progression or coherence
- epsilonGreek fifth letter
- deltaSymbol denoting variation
neighborhood · convergence · divergence · approach · discontinuity · boundedness
velocity
Directed rate of motion
- accelerationRate velocity changes
- motionChange in position
- slopeAngled terrain or steepness
tangent · rate · physics · engineering · marginal cost · kinematics · population growth · decay rate · approximation
maximum
Greatest permitted quantity
- minimumSmallest possible quantity
- extremaFunction's highest, lowest points
- critical pointDecisive juncture in events
inflection point · concavity · convexity · saddle point · increasing · decreasing
- mathematicsalgebra, arithmetic, geometry, number, addition
- calculusderivatives, integral, integrals, limits, chain rule
- differentialsderivative, rate of change
differential calculusintegral calculus
Mathematics of antiderivatives
differential, calculus, differ, difference, different, differently, differentiate, differentiation, differentiated