# Old Lecture Materials

Below are outlines and notes for lectures from a pervious quarter. I will give the most up-to-date outlines on Canvas, but use these old notes if you want to read ahead or see more examples. Note that in my in-class session will also have animations and extra examples (that you won't find in these old notes), but these work as quick notes if you ever miss a day.12.1 Lecture Outline - 12.1 Notes: Intro to 3D, axes, coordinate planes, distance, and spheres.

12.2 Lecture Outline - 12.2 Notes: Intro to vectors: addition, magnitude, scalar multiplication, unit vector; Then Intro to dot products.

12.3 Lecture Outline - 12.3 Notes: Dot Products: Definition, Big Theorems/Facts, Orthogonality, Angle between vectors, Projections; Then Intro to Cross-Product.

12.4 Lecture Outline - 12.4 Notes: Cross Products: Defintion, Computing/Checking, Big Facts, Right-Hand Rules, Area of Parallelogram; Then intro to Lines.

12.5 Lecture Outline - 12.5 Notes 1: 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.

Ch. 12 - Quick Fact Sheet

13.1 Lecture Outline - 13.1 Notes: Intro to vector curves: how to visualize (surface of motion), thinking in terms of points or position vectors.

13.2 Lecture Outline - 13.2 Notes: Calculus on vector curves: Tangent/Derivative Vector, Unit Tangent, Tangent Line, Intergral/Antidervative.

13.3 Lecture Outline - 13.3 Notes: Measurement on 3D curves: Unit Tangent, Principal Unit Normal, Arc Length, Curvature.

13.4 Lecture Outline - 13.4 Notes: Acceleration and Velocity in 3D: Antidertivative to go from acceleration to velocity to position, tangent and normal components of acceleration.

Ch. 12 & 13 Fact Sheet - Vector Tools and Vector Calculus on 3D curves

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 Notes 1: Discussion of Critical Points and Local Max/Min

14.7 Lecture 2 Outline - 14.7 Notes 2: Discussion of Global Max/Min (boundaries of a region)

Ch. 14 Full Review

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 Facts - Ch. 15 Review

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

Taylor Notes Fact Sheet

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