Multivariable Calculus: Final Exam Review

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Distance formula

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66 Terms

1

Distance formula

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2

Equation of sphere of center

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3

Midpoint of 2 points

can also include z for 2pts in 3-space

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4

Completing the square

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5

Angle b/w vectors

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6

Orthagonal Projection

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7

Cross Product

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8

Area of a Parallelogram

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9

Area of Triangle

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10

Volume of parallepiped

or cross product of the three vectors

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11

Parametric equation

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12

Distance b/w line and point

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13

Equation of a plane in 3-space

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14

Planes given by 3-points

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15

Distance b/w point and plane

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16

ellipsoid

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17

hyperboloid w/one sheet

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18

hyperboloid w/two sheets

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19

Elliptic cone

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20

Elliptic parabaloid

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21

Hyperbolic parabaloid

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22

Equation of tangent line

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23

Distance

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24

Displacement

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25

Arc length

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26

Arc length parametrization

1. Identify reference point (end pt) by value of pt

2. Use Arc length formula

3. find t in terms of s

4. In R(t) replace t value in s from step 3

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27

Unit vectors (T(t))

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28

Unit vectors (B(t))

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29

Unit vectors (N(t))

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30

Curvature

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31

Curvature in y = f(x) form

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32

Limit and Continuity

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33

Polar coordinates to evaluate limit

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34

Continuity

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35

Partial derivative

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36

Chain rule for derivative

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37

Chain rule for partial derivative

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38

Directional derivative

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39

Theorem: directional derivative

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40

Local linear approximation

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41

Equation of tangent plane

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42

maximum/minimum

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43

Double Integral

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44

Polar Coordinates

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45

Theorem: polar coordinates

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46

Triple Integral

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47

Volume (using triple integral)

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48

Volume (using double integral)

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49

Cylindrical coordinates

same as polar coord. except z=z and integrate by z first (also has same jacobian of R)

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50

Spherical coordinates

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51

Spherical coordinates jaacobian

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52

Jacobian of T

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53

Jacobian Theorem

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54

Theorem: change of variables

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55

Area (with double integral)

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56

Vector field notation

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57

Theorem: conservative vector field in 2-space

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58

Divergence

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59

Curl of F (vector field)

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60

Parametric Curve

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61

Line Integral

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62

Line integral of vector valued function

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63

Conservative vector field (3-space)

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64

Potential function

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65

Theorem: line integral

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66

Greenâ€™s Theorem

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