Calc2

Question 1

vectors in 3-space

Answer 1

1

octants, vector, properties

Question 2

magnitude/norm

Answer 2

2

Question 3

distance

Answer 3

3

Question 4

dot product

Answer 4

4

defn, calculating it

Question 5

properties of dot product

Answer 5

5

5 of em

Question 6

projection, proj_A(B)

Answer 6

6

Question 7

orthogonal dot product relation

Answer 7

7

Question 8

cross product

Answer 8

8

defn, RHR, calculating it

Question 9

properties of cross product

Answer 9

9

6 of em

Question 10

cross product relation

Answer 10

10

Question 11

triple scalar product, (AxB)•C

Answer 11

11

Question 12

lines in 3-space

Answer 12

12

requirements, parametric equations

Question 13

plane in 3-space

Answer 13

13

Question 14

cylinder

Answer 14

14

Question 15

surfaces of revolution

Answer 15

15

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

Question 16

level curves

Answer 16

16

Question 17

cylindrical coordinates

Answer 17

17

Question 18

spherical coordinates

Answer 18

18

Question 19

conversions of spherical to polar

Answer 19

19

Question 20

partial derivative

Answer 20

20

Question 21

higher order partial derivatives

Answer 21

21

Question 22

tangent plane to a surface

Answer 22

22

Question 23

linear approximations

Answer 23

23

Question 24

dependent, intermediate and independent variables

Answer 24

24

Question 25

chain rule for partial derivatives

Answer 25

25

Question 26

directional derivative

Answer 26

26

Question 27

gradient of f, ∇f

Answer 27

27

Question 28

directional derivative of f at P in the direction of u

Answer 28

28

Question 29

direction f increases most rapidly

Answer 29

29

Question 30

gradient, level surface/curve

Answer 30

30

perpendicular, perpendicular, tangent plane

Question 31

critical point

Answer 31

31

Question 32

saddle point

Answer 32

32

Question 33

second-derivative test

Answer 33

33

Question 34

max/min problems with a constraint

Answer 34

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

Question 35

Lagrange multiplier method

Answer 35

35

Question 36

double integral

Answer 36

36

Question 37

double integrals in polar coordinates

Answer 37

37

Question 38

transformation

Answer 38

38

Question 39

Jacobian

Answer 39

39

Question 40

change of variables for double integral

Answer 40

40

Question 41

change of variables for triple integral

Answer 41

41

Question 42

surface area, 2D

Answer 42

42

Question 43

parametric line equations

Answer 43

43

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

Question 44

smooth curve

Answer 44

44

Question 45

piecewise smooth curve

Answer 45

45

Question 46

directed curve

Answer 46

46

Question 47

line integral of f along C wrt arc length

Answer 47

47

defn, computation

Question 48

line integral of f wrt x

Answer 48

48

Question 49

vector field

Answer 49

49

Question 50

integral of F along C

Answer 50

50

Question 51

closed curve

Answer 51

51

defn, positive orientation

Question 52

potential for F

Answer 52

52

Question 53

conservative vector field

Answer 53

53

Question 54

Fundamental theorem of calculus for line integrals

Answer 54

54

Question 55

simple curve

Answer 55

55

Question 56

Green’s theorem

Answer 56

56

Question 57

corollary of Green’s theorem, area of R

Answer 57

57

Question 58

simply connected

Answer 58

58

Question 59

curl

Answer 59

59

Question 60

divergence

Answer 60

60

Question 61

path independence and conservative fields

TFAE: (6 of em)

Answer 61

61

TFAE (6 of em)

Question 62

parametric surface equations

Answer 62

62

Question 63

area of parametric surface

Answer 63

63

Question 64

integral over surface

Answer 64

64

Question 65

Stokes theorem

Answer 65

65

Question 66

Divergence theorem

Answer 66

66