Math 114-004 Class Notes

• Review
• § 10.5, 10.6 : Linear Equations and Predator-Prey Systems
• § 13.1, 13.2 : Three-Dimensional Coordinate Systems and Vectors
• § 13.3 : Dot Products
• § 13.4 : Cross Products
  Sketches on SMART board
• § 13.5 : Equations of Lines and Planes
• § 13.6: Cylinders and Quadric Surfaces
  Maple demonstration of traces
• § 14.1: Vector Functions and Space Curves
  Helix; Example 3; Toroidal Spiral; Trefoil Knot
• § 14.2:Derivatives and Integrals of Vector Functions
  animation of the definition of derivative; tangent vectors
• § 14.3: Arc Length and Curvature
  Tangent, Normal, Binormal Vectors
• § 14.4: Motion in space
• Midterm 1 Review
• § 15.1: Functions of Several Random Variables
  graphs of some two-variable functions
• § 15.2: Limits and Continuity
  graphs with a hole or a break
• § 15.3: Partial Derivatives
• § 15.4: Tangent Planes and Linear Approximations
• § 15.5: The Chain Rule
• § 15.6: Directional Derivatives and The Gradient Vector
• § 15.7: Maximum and Minimum Values
• § 15.8: Lagrange Multipliers
• § 16.1 and 16.2: Double Integrals over Rectangles and Iterated Integrals
• § 16.3: Double Integrals over General Regions
• § 16.4: Double Integrals in Polar Coordinates
  Sketches on the SMART board
• § 16.5: Applications of Double Integrals
  Sketches on the SMART board
• § 16.6: Triple Integrals
  Sketches on the SMART board
• § 16.7: Triple Integrals in Cylindrical Coordinates
  Sketches on the SMART board
• § 16.8: Triple Integrals in Spherical Coordinates
• § 16.9: Change of Variables in Multiple Integrals
  Sketches on the SMART board
• § 17.1: Vector Fields
• § 17.2: Line Integrals
  Sketches on the SMART board
• § 17.3: The Fundamental Theorem for Line Integrals
• § 17.4: Green's Theorem
  Sketches on the SMART board