Lecture 1 Geometry of Functions of Several Variables Calculus II Topic 1: Differential Calculus in Several Variables
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Functions of Several Variables
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Functions of Several Variables
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Explicit and Implicit form of a Function of Several Variables
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Equation of a Plane
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Parallel an Normal Planes
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Example: A Plane given by a point and a direction
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Example: A Plane given by three points
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Traces of a Plane
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Cylindrical Surfaces
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Traces of a Surface
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Traces of a Surface
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Drawing a Cylinder
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Drawing General Cylinders
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Ellipsoid
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Elliptic Paraboloid
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Hyperboloid of one sheet
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Hyperbolic Paraboloid
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Hyperboloid of two sheets
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The Cone
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Summary of Quadrics (I)
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Summary of Quadrics (II)
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Function Domain and Range
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Function Domain, Range and Graph
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Evaluating a Function
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Function Domain and Range Examples
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Some Examples
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Mapping Surfaces
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Level Curves
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Level Curves
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Level Curves of a Elliptic Paraboloid
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Level Curves of a Hyperbolic Paraboloid
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Fundamental Remark
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Contour Levels and Level Curves
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Topographic Maps
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Graph, Contour Levels and Level Curves
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Level Curves and Contour Curves of a Parabolic Surface
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Level Curves and Contour Curves of a Hat Function
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More Examples
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A Physical Example
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The N-Dimensional Case
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Level Surfaces
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More Level Surfaces
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Industrial Examples
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Industrial Example
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Graphing Summary
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Homework
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