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How to use this page:
- Click the chapter we are working on.
- Review notes/examples as you do homework in an organized handwritten notebook.
- Use review sheets and ask questions, then try test preps to check understanding.
- Use exam review archive before tests working through several old exams.
Reference
Chapter 12 - Vectors and Geometry in 3D
Course Materials by Section:
- 12.1 - Coordinates and Spheres
- 12.2 - Vectors
Desmos & Visualizations
Supplemental Videos
Try the homework first, then use these if you want another explanation or example.
The Vector Concept (12 min)
Scalar Multiplication (7 min)
Vector Addition (12 min)
2D Vectors: Angles & Slope (10 min) - 12.3 - Dot Products and Projections
Autumn 2026 Lecture Outline — Dot Products and Projections
12.3 Two-Page Review — Key Ideas and FormulasDesmos & Visualizations
Supplemental Videos
Try the homework first, then use these if you want another explanation or example.
Dot Product Concept, Proof & Key Formula (15 min)
Angle of Intersection (10 min)
Dot Products & Projections (12 min)
Projections, Projections and More Projections (8 min) - 12.4 - Cross Product and Area
Desmos & Visualizations
Supplemental Videos
Try the homework first, then use these if you want another explanation or example.
Cross Product Concept, Formula & Computation (13 min)
Right-Hand Rule (7 min)
Right-Hand Rule — Goofy Version
Cross Product Length & Parallelogram Area (14 min)Optional Extension
- 12.5 - Lines and Planes
Autumn 2026 Lecture Outline — Lines and Planes, Lecture 1
Autumn 2026 Lecture Outline — Lines and Planes, Lecture 2
12.5 Review Sheet — Key Ideas and FormulasDesmos & Visualizations
Supplemental Videos
What are you GIVEN, and what do you WANT? These four short videos help develop this essential problem-solving skill.
Lines — What Do We WANT? (6 min)
Planes — What Do We WANT? (8 min)
What Are We GIVEN? Translation Skills (8 min)
Line Notation — Vector and Parametric (5 min)Extra Practice & Problem-Solving Guides
- 12.6 - Quadric Surfaces: Summary Notes
- TP - Calculus Skills - solns - video
- TP - 12.1 - solns - video
- TP - 12.2-12.4 - solns - video
- TP - 12.4 & 12.5 - solns - video
- TP - 12.5 & 12.6 - solns - video
- TP - Ch 12 - solns - video
Chapter 13 - Curves in 3D and Motion in Space
Lecture Outlines and Old Notes:
- 13.1 - Vector Functions and Space Curves: Lecture Outline | Notes
- 13.2 - Derivatives and Integrals of Vector Functions: Lecture Outline | Notes
- 13.3 - Arc Length and Curvature: Lecture Outline | Notes
- 13.4 - Motion in Space: Lecture Outline | Notes
Chapter 14 - Partial Derivatives and Optimization
Lecture Outlines and Old Notes:
- 14.1 / 14.3 - Functions of Several Variables, Surfaces, Level Curves, and Partial Derivatives: Lecture Outline | Notes
- 14.3 / 14.4 - Tangent Planes and Linear Approximation: Lecture Outline | Notes
- 14.4 / 14.7 - Critical Points and Local Extrema: Lecture Outline | Notes 1
- 14.7 - Global Extrema on Regions: Lecture Outline | Notes 2
Chapter 15 - Double Integrals and Polar Coordinates
Lecture Outlines and Old Notes:
- 15.1 - Double Integrals over Rectangles: Lecture Outline | Notes
- 15.2 - Double Integrals over General Regions: Lecture Outline | Notes
- Polar Coordinates Review: Lecture Outline | Notes
- 15.3 - Double Integrals in Polar Coordinates: Lecture Outline | Notes
- 15.4 - Center of Mass: Lecture Outline | Notes
Taylor Polynomials and Series
Lecture Outlines and Old Notes:
- TN 1 - Tangent Lines and Intro to Error Bounds: Lecture Outline | Notes
- TN 2-3 - Higher Order Taylor Polynomials and Taylor's Inequality: Lecture Outline | Notes
- TN 4 - Taylor Series: Lecture Outline | Notes
- TN 5 - Manipulating Taylor Series: Lecture Outline | Notes
- TP - TN 1-3 - solns - video
- TP - TN 4-5 - solns