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Calc III midterm 1
terms from 10.5, 12.1-12.6
44
Mathematics
Undergraduate 3
10/05/2015

Additional Mathematics Flashcards

 


 

Cards

Term
Conceptual Definition of elipses
Definition
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Term
Equations of elipses
Definition

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Term
Definition of a Hyberbola
Definition

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Term
Equations of a hyperbola
Definition

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Term
Distance Formula in 3D
Definition

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Term
Equation of a sphere
Definition
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Term
Definition of vector addition
Definition

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Term
definition of scalar multiplication
Definition

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Term
Definition of a component vector
Definition
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Term
Magnitude or length of a vector
Definition
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Term
vector addition with position vectors
Definition
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Term
Properties of vectors
Definition
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Term
Resultant force
Definition

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Term
Definition of a dot product
Definition

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Term
Properties of dot products
Definition
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Term
Cosine Theorem for the angle between vectors and Corrolary
Definition

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Term
Othaganal vectors, including orthoganal vector from scalar projection
Definition

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Term
Scalar projection
Definition

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Term
definition of a cross product
Definition
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Term
Determinates
Definition

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Term
Definition of a cross product using determinates and unit vectors
Definition

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Term
Coss product orthoganal Theorem
Definition

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Term
Cross product magnitude, area of a parallelogram Theorem and corrolary
Definition

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Term
Unit vector properties of cross products
Definition
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Term
Properties of cross products
Definition

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Term

Scalar triple product

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Definition

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Term
Volume of a parallelepiped
Definition

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Term
Simpler Vector equation of a line
Definition

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Term
Parametric equations
Definition

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Term
Symetric equations of a line and the definition of direction numbers
Definition

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Term
Formal definition of a vector equation of a line
Definition

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Term
vector equations of a plane with n as the normal vector
Definition
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Term
Scalar equation of a plane
Definition

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Term
Distances
Definition
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Term
Equations of a parabola
Definition

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Term
Cylinder
Definition
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Term
Elipsoid
Definition
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Term
Cone
Definition
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Term
Eliptic Paraboloid
Definition
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Term
Hyperboloid of One Sheet
Definition
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Term
Hyperbolic Paraboloid
Definition
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Term
Hyperboloid of Two Sheets
Definition
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Term
Professors algorithm for classifying cubics
Definition

Given an equation of degree 2:

if(a variable is missing ){

    it is a cylinder or no solution

}

if(2 variables appear strictly linear){

    you have a cylinder

}

if(have up to a translation: Ax²+ By²+Cz²=D){

    if(D== 0){

        if(A,B,C same sign)

            get a point

        if(A,B,C have different signs)

            You have a cone

    }

    if (D != 0){

        Standard form = Ax²+By²+Cz² = 1

        Put equation in standard form

        if(numberOfNegativeSigns == 0)

            ellipsoid

        if(numberOfNegativeSigns == 1)

            1-sheet hyperboloid

        if(numberOfNegativeSigns == 2)

            2-sheet hyperboloid

        if(numberOfNegativeSigns == 3)

            no solutions

    }

}

 

Term
Parabola definition
Definition
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