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Outline
Multivariable Calculus
Parametric Equations
Conic Sections
Vectors
Curves and Surfaces
Partial Differentiation
Gradients and Optimization
Multiple Integration
Vector Analysis
Multivariable Calculus
Author:
BurhanMasihBelajar
,
Kristen Beck
Topic:
Calculus
Table of Contents
Parametric Equations
Parametric Equations
Different Parameterizations
Parameterizing an Ellipse
Curves in 2-Space
Curves in 3-Space
Tangent Line to a Parametric Curve
Regions Bounded by Polar Curves
Conic Sections
The Foci of an Ellipse
The Foci of a Hyperbola
The Focus and Directrix of a Parabola
Vectors
Sum/Difference of Vectors
Parametric Representation of a Line
Vector Representation of a Line
Intersecting Lines
Geometric Interpretation of the Dot Product
Orthogonal Projection
Geometric Interpretation of the Cross Product
Curves and Surfaces
Level Curves
Cylindrical Coordinates
Spherical Coordinates
Curve Along a Surface
Partial Differentiation
Partial Derivatives and Slope
The Chain Rule
Tangent Plane to a Surface
Gradients and Optimization
Gradient vs. Level Curves
Constrained Optimization
Multiple Integration
Small Cylindrical Volumes
Small Spherical Volumes
Iterated Double Integrals
Line Integral of a Scalar Function
Simple Cylindrical Volumes
Simple Spherical Volumes
Vector Analysis
Vector Field in the Plane
Line Integral of a Vector Field in 2-Space
Line Integral of a Vector Field in 3-Space
Circulation in 2-Space
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Parametric Equations
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