Topics Involve Mutivariable Calculus, Vector Analysis, & Advanced Topics |
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Vectors - Addition, Dot Product, Direction Cosines |
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Vector Product, Scalar Triple Product |
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Equations of a line in space |
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Motion of a particle in Space, normal-tangential components, curvature |
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Quadric Surfaces - Rectangular, Cylindrical, and Spherical Coordinates |
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Level Curves and Visualization of Surfaces |
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Limits for a function with two independent variables. |
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Partial derivatives of a function of more than one independent variable Linear approximation of a function with two independent variables |
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The chain rule for functions of several variables. |
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The directional derivative, its definition and physical interpretation |
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Local Maxiima and Minima of Functions Absolute Maxima and Minima of Functions |
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Lagrange Multipliers and constrained optimization |
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Basics of Multiple Integrals and Applications - Double Integrals |
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Basics of Triple Integrals and Applications Approximate Volumes using Double Riemann Sums |
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Uses of Rectangular, Cylindrical, and Spherical Coordinates |
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Changing the Order of Integration for Multiple Integrals |
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Change of Variables in Integrals |
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Vector Fields |
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Line Integrals |
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Surface Integrals |
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Green's theorem |
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Divergence theorem (Gauss's Theorem) |
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Stokes' Theorem |
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Summary of the Calculus of Vector Fields |
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