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Flashcards in Calc2 Deck (66):
1

vectors in 3-space

1
octants, vector, properties

2

magnitude/norm

2

3

distance

3

4

dot product

4
defn, calculating it

5

properties of dot product

5
5 of em

6

projection, proj_A(B)

6

7

orthogonal dot product relation

7

8

cross product

8
defn, RHR, calculating it

9

properties of cross product

9
6 of em

10

cross product relation

10

11

triple scalar product, (AxB)•C

11

12

lines in 3-space

12
requirements, parametric equations

13

plane in 3-space

13

14

cylinder

14

15

surfaces of revolution

15
defn, if the curve __ is revolved around the _axis then replace _ by __ to get surface of revolution

16

level curves

16

17

cylindrical coordinates

17

18

spherical coordinates

18

19

conversions of spherical to polar

19

20

partial derivative

20

21

higher order partial derivatives

21

22

tangent plane to a surface

22

23

linear approximations

23

24

dependent, intermediate and independent variables

24

25

chain rule for partial derivatives

25

26

directional derivative

26

27

gradient of f, ∇f

27

28

directional derivative of f at P in the direction of u

28

29

direction f increases most rapidly

29

30

gradient, level surface/curve

30
perpendicular, perpendicular, tangent plane

31

critical point

31

32

saddle point

32

33

second-derivative test

33

34

max/min problems with a constraint

34
maximize f(x,y) = xy given x^2+y^2 = 1

35

Lagrange multiplier method

35

36

double integral

36

37

double integrals in polar coordinates

37

38

transformation

38

39

Jacobian

39

40

change of variables for double integral

40

41

change of variables for triple integral

41

42

surface area, 2D

42

43

parametric line equations

43
ellipse, circle, y=f(x), x=g(y), line segment

44

smooth curve

44

45

piecewise smooth curve

45

46

directed curve

46

47

line integral of f along C wrt arc length

47
defn, computation

48

line integral of f wrt x

48

49

vector field

49

50

integral of F along C

50

51

closed curve

51
defn, positive orientation

52

potential for F

52

53

conservative vector field

53

54

Fundamental theorem of calculus for line integrals

54

55

simple curve

55

56

Green's theorem

56

57

corollary of Green's theorem, area of R

57

58

simply connected

58

59

curl

59

60

divergence

60

61

path independence and conservative fields
TFAE: (6 of em)

61
TFAE (6 of em)

62

parametric surface equations

62

63

area of parametric surface

63

64

integral over surface

64

65

Stokes theorem

65

66

Divergence theorem

66