Calc5 - MATH 104 study guide PDF

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MATH 104 study guide...

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Integration the process of calculating an integral. This is the inverse of differentiation, since _____ of a given function results in a function whose derivative is the given function. This is used in the calculation of such things as the areas and volumes of irregular shapes and solids Integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data Paraboloid a solid generated by the rotation of a parabola around its axis of symmetry. a solid having two or more nonparallel parabolic cross sections Parabola a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape. Alhazen derived a formula for the sum of fourth powers. He used the results to carry out what would now be called an integration, where the formulas for the sums of integral squares and fourth powers allowed him to calculate the volume of a paraboloid Taylor Series a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point Derivative the _____ of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). these are a fundamental tool of calculus

Cavalieri 17th century Italian mathematician who argued that volumes and areas should be computed as the sums of the volumes and areas of infinitesimally thin cross-sections (not Archimedes) his work was not well respected since his methods could lead to erroneous results, and the infinitesimal quantities he introduced were disreputable at first Finite Difference (or Calculus of Finite Differences) a mathematical expression of the form f(x + b) − f(x + a). If this is divided by b − a, one gets a difference quotient. The approximation of derivatives by this method plays a central role for the numerical solution of differential equations, especially boundary value problems Adequality technique used by de Fermat to calculate maxima and minima of functions, tangents to curves, area, center of mass, least action, and other problems in mathematical analysis. represents equality up to an infinitesimal error term....