Lecture Materials

Below you will find copies of the overheads that I use in lecture. Most of lecture I write out during class, so if you missed class, then you will want to get a copy of the notes from a classmate.

12-1 Notes: Intro to 3D, axes, coordinate planes, distance, and spheres.
12-2 Notes: Intro to vectors; addition, magnitude, scalar multiplication, unit vector, dot product.
12-3 Notes: Dot product facts; angle between vectors, orthogonality, projections.
12-4 Notes: Cross product facts; computation, orthogonal to the given vectors, areas of parallelograms/triangles.
12-5 Notes: Lines; Finding a point and a direction vector. Planes; Finding a point and a normal vector.
12-5 Many, Many Practice Problems and Solutions.
12-6 Lecture Outline and Notes: Discussion of seven special 3D Surfaces that you need to know:
1. Cylinders, 2. Spheres/Ellipsoids, 3/4. Paraboloids (Circular or Hyperbolic), 5. Cones, 6/7. Hyperboloids (of One Sheet or Two Sheets)
13.1 Notes: Intro to 3D and vector curves: how to visualize (surface of motion), thinking in terms of points or position vectors.
13.2 Notes: Calculus on vector curves: Tangent/Derivative Vector, Unit Tangent, Tangent line, Integral/Antiderivative.
13.3 Notes: Measurements on 3D curves: Unit Tangent, Principal Unit Normal, Arc Length, Curvature.
13.4 Lecture Outline - 13-4 Notes: Acceleration and Velocity in 3D: Antiderivatives to go from acceleration to position, tangential and normal components of acceleration.
Exam 1 Fact Sheet
Exam 1 Rules and Quick Review

14.1/3 Notes: Intro to 3D Surfaces and Partial Derivatives; Domain, Traces, Level Curves, Contour Map, partial derivatives and interpretting.
14.3/4 Notes: More on partial derivatives as well as Tangent Planes and linear approximation
14.7 Local Max/Min Notes: Discussion of Critical Points and Local Max/Min
14.7 Global Max/Min Notes: Discuss of Global Max/Min (boundaries of a region)
15.1 Notes: Intro to double integrals.
15.2 Notes: Double integrals over general regions, reversing order, setting up, evaluating.
10.3 Notes: Polar Coordinates (a tool we need in order to work with circular regions.
15.3 Notes: Double integrals over polar regions, how to integral above circular regions!
Exam 2 Review
Exam 2 Fact Sheet

15-4 Notes - Center of Mass
TN 1 Notes - Taylor Notes 1: tangent lines and intro to error bounds
TN 2-3 Notes - Taylor Notes 2-3: higher order Taylor polynomials and Taylor's inequality
TN 4-5 Outline - Taylor Notes 4-5: Taylor Series
TN 4 Notes
TN 5 Notes
Final Revew Lecture Outline - Final Review Notes
Last Day Lecture Outline
Final Exam Fact Sheet

back to Math 126