Concise Modular Calculus 83 97

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(3/4 on Differentiation of Multivariable Functions) Explains directional derivatives as derivatives in the direction of a given vector. (1/4 on Differentiation of Multivariable Functions) Explains partial derivatives as derivatives of a function's traces. Notes that partial ... Introduces three-dimensional coordinate systems. Shows how to represent points and figures in three dimensions using ... Illustrates the derivative as the formal concept behind instantaneous velocities, tangent lines and general instantaneous rates of ... Explains how the Divergence Theorem is the mathematical manifestation of physical observations about the flux of the ... Justifies the power rule and shows how it abbreviates the computation of derivatives. Computes tangent lines, growth behavior ...

Defines absolute extrema and solves optimization problems, including minimization of distances. All videos and slides for single ... Defines sequences as, well, sequences of numbers. Explains how the limit of a sequence governs the sequence's long-term ... Defines and computes derivatives via difference quotients. Checks tangent line computations graphically. All videos and slides for ... Justifies how a derivative can be found implicitly when we cannot solve for y. Computes tangent lines via implicit differentiation ... 4/6 on Surfaces in 3-D Space) Shows visually how the name "conic section" comes about. Presents standard equations and ... Justifies the cross product as the appropriate tool to compute the force on a moving charge that travels in a magnetic field. Derives ...