Multivariable calculus: An ellipse has eccentricity e = 12/13 and vertices at (3, 2) and (3, 28). Find the foci of the ellipse and determine the length of string needed to trace out the ellipse from its foci.

1. Equation of a Parabola 1
2. Equation of a Parabola 2
3. Equation of an Ellipse 1
4. Equation of an Ellipse 2
5. Equation of a Hyperbola 1
6. Equation of Hyperbola 2
7. Example of Equation of a Sphere
8. Equation of a Sphere Given Diameter
9. Equation of Sphere Given Tangent Plane 1
10. Equation of Sphere Given Tangent Plane 2
11. Equation of Sphere Given Tangent Plane 3
12. Angle Between Two Vectors Using Dot Product
13. Vector Decomposition of (2,2,1) Along (1,1,1)
14. Unit Vector Perpendicular to Two Vectors
15. Area of Parallelogram in Three Space
16. Volume of a Parallelepiped
17. Diagonal Lengths of a Parallelepiped
18. Example of Symmetric Equations of a Line
19. Equation of a Parallel Line
20. Example of Intersecting Lines
21. Angle Between Two Planes
22. Planes: Parallel, Equal, or Intersecting?
23. Line of Intersection of Two Planes
24. Equation of a Plane Containing a Point and a Line
25. Equation of a Plane Through Three Points
26. Example of Plane-Line Intersections
27. Domain of a Vector-Valued Function
28. Limit and Derivative of Vector Function
29. Example of Position, Velocity and Acceleration in Three Space
30. Tangent Line to a Parametrized Curve
31. Angle of Intersection Between Two Curves
32. Unit Tangent and Normal Vectors for a Helix
33. Sketch/Area of Polar Curve r = sin(3O)
34. Arc Length along Polar Curve r = e^{-O}
35. Showing a Limit Does Not Exist
36. Contour Map of f(x,y) = 1/(x^2 + y^2)
37. Sketch of an Ellipsoid
38. Sketch of a One-Sheeted Hyperboloid
39. Sketch of a Double-Napped Cone
40. Example of Implicit Differentiation with Several Variables
41. Gradient of f(x,y) = yx^2 + cos(xy)
42. Tangent Plane to x^2 - xy - y^2 -z = 0
43. Lagrange Multiplier: Single Constraint
44. Optimization on Ellipse in R^3 1: Parametrization Method
45. Optimization on Ellipse in R^3 2: Lagrange Multipliers with Two Constraints
46. Example of Chain Rule for Partial Derivatives
47. Second Partials Test for f(x,y) = x^3 + 3xy + y^3
48. Directional Derivative of f(x,y,z) = xy + yz
49. Linear Approximation to f(x,y) = x^2y^2 + x
50. Taylor Polynomial of f(x,y) = ycos(x+y)
51. Conversion From Rectangular Coordinates
52. Conversion From Cylindrical Coordinates
53. Conversion from Spherical Coordinates
54. Examples of Double and Triple Integrals
55. Center of Mass for a Rectangle of Variable Density
56. Interchange of Limits of Integration
57. Integral in Polar Coordinates
58. Area Between Polar Curves r = 2/cos(θ) and r = 4cos(θ)
59. Integral of exp(-x^2) (HD Version)
60. Surface area of z = (x^2+y2)^1/2
61. Mass of Solid as a Triple integral in Rectangular Coordinates
62. Volume of Truncated Paraboloid in Cylindrical Coordinates
63. Volume of a Snow Cone in Cylindrical and Spherical Coordinates
64. Example of Vector Field
65. Example of Arc Length Along a Parametrized Curve
66. Sketching a Parametrized Curve
67. Line Integral of xy^3 over Unit Circle in Q1

In his final calculus series, Dr. Bob (Robert Donley) covers topics specific to multivariable calculus, including: conic sections; vectors in two and three space; dot and cross product; lines and planes; vector functions; functions of two variables and surfaces; coordinate systems; iterated integrals, area, and volume; line integrals.