ERIC ED218132: Developing The Fundamental Theorem Of Calculus. Applications Of Calculus To Work, Area, And Distance Problems. [and] Atmospheric Pressure In Relation To Height And Temperature. Applications Of Calculus To Atmospheric Pressure. [and] The Gradient And Some Of Its Applications. Applications Of Multivariate Calculus To Physics. [and] Kepler's Laws And The Inverse Square Law. Applications Of Calculus To Physics. UMAP Units 323, 426, 431, 473. - Info and Reading Options

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This document consists of four units. The first of these views calculus applications to work, area, and distance problems. It is designed to help students gain experience in: 1) computing limits of Riemann sums; 2) computing definite integrals; and 3) solving elementary area, distance, and work problems by integration. The second module views calculus applications to atmospheric pressure. The material is geared to aid pupil understanding of the application of calculus to construct a mathematical model of the atmosphere. The third unit covers applications of multivariate calculus to physics. The user is expected to learn how to compute the Gradient, and to be able to use the Gradient to solve certain practical problems involving steepest ascent. The final module covers calculus applications to physics. The material is designed to instruct pupils how to: 1) be able to handle motion problems in polar coordinates, especially those concerning gravitational interaction; 2) state the relationships between Kepler's Laws and the Inverse Square Law; and 3) discuss the history and thought going into scientific development of an idea and the interaction between experiment and theory, at least in the context of planetary motion. All units include exercises with solutions; the first, third, and fourth provide model exams with answers. (MP)

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