## Calculus Modules

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vCurvature is applied to the task of aesthetic curve design by using a fairness metric. The student interacts with different aspects of curvature.

Authors: Bruce Piper, Bruce Buhler Keywords: calculus, curve, curvature Learning Level: College Platform: Project Links base technical requirements Applets: [ Full Metadata ]

vChemical kinetics studies the rates of chemical reactions and their dependencies.

Authors: Curt Breneman, Joan Warren Keywords: calculus, chemistry, chemical kinetics, chemical equilibrium Learning Level: College Platform: Project Links base technical requirements Applets: [ Full Metadata ]

v In this module, simple differential equations are used to study the effects of the "drag" force which slows the motion of a body moving through a fluid (in this case: air) and is responsible for the safe landing of the skydiver.

Authors: Howard Littman, Bernard Fleishman Keywords: calculus, drag, fluid mechanics Learning Level: College Platform: Project Links base technical requirements Applets: Drag Forces, Skydiver [ Full Metadata ]

vThe problem of creating a vector field as a gradient of a scalar function is illustrated in Electrostatics. Starting from the electrostatics of a single point charge, students are led through a series of exercises, to the study of electrostatics of a more complex assembly of point charges and continuous distribution of charges.

Authors: Kongki Min, Michael Malak, Stephen Irving, Colin Fredericks Keywords: calculus, physics Learning Level: College Platform: Project Links base technical requirements Applets: [ Full Metadata ]

v

vTo develop the mathematical description of a physical process in which the gradient plays a central role. To formulate problems in steady state one-dimensional heat conduction which provide practice in solution of ordinary differential equations, physical interpretation, and interaction via manipulation of parameters. To derive the partial differential equations for heat conduction in two dimensions and solve the equation governing steady states under various boundary conditions.

Authors: Howard Littman, Bernard Fleishman Keywords: calculus, gradient, heat transfer Learning Level: College Platform: Project Links base technical requirements Applets: [ Full Metadata ]

vThe gradient, its interrelations with other math concepts, and its applications to science and engineering. Rapid-change vector; normal vector to level surface. The gradient and gradient operator in Cartesian and other coordinate systems. The gradient as related to differentiability and the directional derivative.

Authors: Edith Luchins, Tom Rousseau, Steven Irving, Sara Schubert Keywords: calculus, gradient Learning Level: College Platform: Project Links base technical requirements Applets: Visualizing the Gradient (2D), Visualizing the Gradient (3D) [ Full Metadata ]

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