PDF Notes

The following calculus notes are sorted by chapter and topic, provided as downloadable PDFs. If you prefer interactive HTML5 slideshows, click here.

• Ref
  Formula Sheet: Calculus BC Quick reference formula sheet
• 1
  Lesson 1: Parametric Plotting Parametrically plotting curves, circles, and ellipses; parametric equations for curves, surfaces, and solids ▹ Watch videos
• 2
  Lesson 2: Vectors Vector addition, subtraction, scalar multiplication; dot products and projection; magnitude and unit vectors ▹ Watch videos
• 3
  Lesson 3: Perpendicularity XYZ and parametric equations for a plane; parallel/perpendicular planes; cross product ▹ Watch videos
• 3b
  Lesson 3 (Continued): Linearization 2D linearization (tangent lines); 3D linearization (tangent planes); parametric paths on surfaces ▹ Watch videos
• 4
  Lesson 4: Gradient Vectors Double integrals; changing the order of integration; Gauss-Green Formula ▹ Watch videos
• 4b
  Lesson 4 (Continued): Lagrange Multipliers Lagrange multipliers; constrained optimization; critical points on level curves ▹ Watch videos
• 5
  Lesson 5: Double Integrals Double integrals over rectangular and non-rectangular regions; Gauss-Green formula; area and volume ▹ Watch videos
• 6
  Lesson 6: Vector Fields Acting on a Curve Vector fields; gradient fields, slope fields; trajectories; net flow along and across a curve ▹ Watch videos
• 7
  Lesson 7: Flow Measurements Path integrals; net flow; flux; path independence; Fundamental Theorem of Line Integrals ▹ Watch videos
• 8
  Lesson 8: Sources, Sinks, and Singularities Green's Theorem; rotation; divergence; sources and sinks; singularities; del operator; Laplacian ▹ Watch videos
• 9
  Lesson 9: Change of Variables (2D Integrals) Change of variables; Jacobian determinant; double integrals in polar coordinates ▹ Watch videos
• 10
  Lesson 10: Change of Variables (3D Integrals) Change of variables for triple integrals; 3D Jacobian; volume and mass ▹ Watch videos
• 11
  Lesson 11: Spherical and Cylindrical Coordinates Spheres; cylinders; Jacobian for spherical/cylindrical; triple integrals ▹ Watch videos
• 12
  Lesson 12: Surface Integrals Flux across a surface; Divergence Theorem; substitute surfaces; surface area ▹ Watch videos
• 13
  Lesson 13: Stokes' Theorem Curl; path integrals in 3D; Stokes' Theorem; orientable surfaces ▹ Watch videos