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