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; Then Intro to dot products.
12.3 Notes: Dot Products: Definition, Big Theorems/Facts, Orthogonality, Angle between vectors, Projections; Then Intro to Cross-Product.
12.4 Notes: Cross Products: Defintion, Computing/Checking, Big Facts, Right-Hand Rules, Area of Parallelogram; Then intro to Lines.
12.5 Notes 1: Intro to Lines and Planes in 3D.
12.5 Notes 2: Lines and Planes in 3D - How to approach problems.
12.6 Summary: Intro to Surfaces in 3D, traces, then 7 important names: Cylinders, Paraboloids (Two Types: Elliptical or Hyperbolic), Hyperboloids (Two Types: One Sheet or Two Sheets), Cones, Spheres/Ellipsoids. You must know how to identify all these shapes and generally know what they look like.
EXAM 1 - on Chapter 12.

13.1 Notes: Intro to 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, Intergral/Antidervative.
13.3 Notes:: Measurement on 3D curves: Unit Tangent, Principal Unit Normal, Arc Length, Curvature.
13.4 Notes: Acceleration and Velocity in 3D: Antidertivative to go from acceleration to velocity to position, tangent and normal components of acceleration.
Exam 2 Rules - Ch. 13 Review
EXAM 2 - on Chapter 13.

14.1/3 Lecture Outline - 14.1/3 Notes: Intro to 3D Surfaces and Partial Derivatives; Domain, Traces, Level Curves, Contour Map, partial derivatives and interpretting.
14.3/4 Lecture Outline - 14.3/4 Notes: More on partial derivatives as well as Tangent Planes and linear approximation
14.4/7 Lecture Outline -14.7 Local Max/Min Notes: Discussion of Critical Points and Local Max/Min
14.7 Lecture 2 Outline -14.7 Global Max/Min Notes: Discussion of Global Max/Min (boundaries of a region)
Exam 2 Rules and Ch. 14 Quick Review
Ch. 14 Full Review
EXAM 3 - on Chapter 14.


15.1 Lecture Outline - 15.1 Notes: Intro to double integrals.
15.2 Lecture Outline - 15.2 Notes: Double integrals over general regions, reversing order, setting up, evaluating.
10.3 Lecture Outline - 10.3 Notes: Polar Coordinates (a tool we need in order to work with circular regions).
15.3 Lecture Outline - 15.3 Notes: Double integrals over polar regions, how to integral above circular regions!
15.4 Lecture Outline - 15.4 Notes: Center of Mass
EXAM 4 - on Chapter 15.

TN 1 Lecture Outline - TN 1 Notes: tangent lines and intro to error bounds

TN 2-3 Lecture Outline - TN 2-3 Notes: higher order Taylor polynomials and Taylor's inequality

TN 4 Lecture Outline - TN 4 Notes: Taylor Series

TN 5 Lecture Outline - TN 5 Notes: Manipulating Taylor Series

EXAM 5 - on Tayloy Polynomials/Series

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