Math 321: Applied Mathematical Analysis 1: Vectors and Complex Calculus

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Last updated 12:51 AM on 9/10/26
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29 Terms

1
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How can vectors be written in terms of there magnitude and unit vector

(Lecture 1, Covered September 3)

<p>(Lecture 1, Covered September 3)</p>
2
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What is the magnitude of a unit vector

1 (Lecture 1, Covered September 3)

3
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What is the vector equation through a line

(Lecture 1, Covered September 3)

<p>(Lecture 1, Covered September 3)</p>
4
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If phi = atan2(y,x), what is the range of phi

(Lecture 1, Covered September 3)

<p>(Lecture 1, Covered September 3)</p>
5
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Fully describe, what is atan2(y,x)

atan2(y,x) is the arctangent function but it’s range is -pi < phi <= +pi. The regular arctangent function only has range -pi/2 < phi < +pi/2 (Lecture 1, Covered September 3)

6
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For a 3D telescope, phi is the azimuth angle, and theta is the inclination angle. What formula(s) can you use too find a vector pointing outward from the origin in spherical coordinates

(Lecture 2, Covered September 8)

<p>(Lecture 2, Covered September 8)</p>
7
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For a parallelogram formed by two vectors, what are the diagonals of that parallelogram in terms of the vectors

(Lecture 2, Covered September 8)

<p>(Lecture 2, Covered September 8)</p>
8
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What is the triangle inequality

(Lecture 2, Covered September 8)

<p>(Lecture 2, Covered September 8)</p>
9
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What is the definition of linear independence in 2D space. What does this mean geometrically?

(Lecture 2, Covered September 8)

<p>(Lecture 2, Covered September 8)</p>
10
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What is the definition of linear independence in 3D space. What does this mean geometrically?

(Lecture 2, Covered September 8)

<p>(Lecture 2, Covered September 8)</p>
11
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What is the geometric definition of the dot product

(Lecture 2, Covered September 8)

<p>(Lecture 2, Covered September 8)</p>
12
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What is the projection of a onto b

(Lecture 2, Covered September 8)

<p>(Lecture 2, Covered September 8)</p>
13
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What is the decomposition formula in terms of parallel and perpendicular vectors

(Lecture 2, Covered September 8)

<p>(Lecture 2, Covered September 8)</p>
14
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What is the angle between the parallel and perpendicular vector

90 degrees (Lecture 2, Covered September 8)

15
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<p>What is the name of the property for the image</p>

What is the name of the property for the image

Commutative Property, they Commute (Lecture 2, Covered September 8)

16
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<p>What is the image equal too</p>

What is the image equal too

(Lecture 2, Covered September 8)

<p>(Lecture 2, Covered September 8)</p>
17
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<p>What is the image less than or equal too. What is the name of this property</p>

What is the image less than or equal too. What is the name of this property

Cauchy-Schwarz Inequality (Lecture 2, Covered September 8)

<p>Cauchy-Schwarz Inequality (Lecture 2, Covered September 8)</p>
18
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<p>What is the image equal too. What is the name of this property</p>

What is the image equal too. What is the name of this property

Distributive Property (Lecture 2, Covered September 8)

<p>Distributive Property (Lecture 2, Covered September 8)</p>
19
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What is the Cartesian Basis Formula for the dot product

(Lecture 2, Covered September 8)

<p>(Lecture 2, Covered September 8)</p>
20
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What is the geometric definition of the cross product

(Lecture 2, Covered September 8)

<p>(Lecture 2, Covered September 8)</p>
21
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<p>For a parallelogram made by two vectors, what is the image equal too</p>

For a parallelogram made by two vectors, what is the image equal too

(Lecture 2, Covered September 8)

<p>(Lecture 2, Covered September 8)</p>
22
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<p>What is the image equal too. What is the name of this property</p>

What is the image equal too. What is the name of this property

Distributive Property for Cross Products (Lecture 2, Covered September 8)

<p>Distributive Property for Cross Products (Lecture 2, Covered September 8)</p>
23
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What is the cartesian basis formula for cross products

(Lecture 2, Covered September 8)

<p>(Lecture 2, Covered September 8)</p>
24
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<p>What is each line in the image equal too</p>

What is each line in the image equal too

(Lecture 2, Covered September 8)

<p>(Lecture 2, Covered September 8)</p>
25
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What is the cartesian representation of a vector

(Lecture 2, Covered September 8)

<p>(Lecture 2, Covered September 8)</p>
26
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For the cartesian component, a_z, how do you calculate it?

(Lecture 2, Covered September 8)

<p>(Lecture 2, Covered September 8)</p>
27
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What is the spherical representation of a vector

(Lecture 2, Covered September 8)

<p>(Lecture 2, Covered September 8)</p>
28
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What is the cylindrical representation of a vector

(Lecture 2, Covered September 8)

<p>(Lecture 2, Covered September 8)</p>
29
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How do you find the value of a_perp

(Lecture 2, Covered September 8)

<p>(Lecture 2, Covered September 8)</p>