  # Calculus with Dr. Bob VII: Multivariable Calculus

### Course Description

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. Dr. Bob showing an example of implicit differentiation with several variables, in Lesson 40.
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### Video Lectures & Study Materials

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