Slideshows

The following calculus notes are sorted by chapter and topic. They are interactive HTML5 slideshows that can be viewed in any web browser. If you prefer notes in PDF form, click here.

• 1
  Lesson 1: Parametric Plotting Parametrically plotting curves, circles, and ellipses; parametric equations for curves, surfaces, and solids; calculus with parametrically-defined curves; collision vs. intersection; surfaces of revolution ▹ Watch videos
• 2
  Lesson 2: Vectors Vector addition, subtraction, scalar multiplication; dot products and projection; magnitude and unit vectors; parametric equations for lines; position, velocity, speed, and acceleration ▹ Watch videos
• 3
  Lesson 3: Perpendicularity XYZ and parametric equations for a plane; parallel/perpendicular planes; line of intersection; cross product and its magnitude ▹ Watch videos
• 3b
  Lesson 3 (Continued): Linearization 2D linearization (tangent lines); 3D linearization (tangent planes); parametric paths on surfaces; mapping onto linearization ▹ Watch videos
• 4
  Lesson 4: Gradient Vectors Double integrals over rectangular and non-rectangular regions; changing the order of integration; area via double integrals; Gauss-Green Formula and proof ▹ Watch videos
• 4b
  Lesson 4 (Continued): Lagrange Multipliers Using Lagrange multipliers to find extrema on parametric paths; critical points where path is tangent to level curve ▹ Watch videos
• 5
  Lesson 5: Double Integrals Double integrals over rectangular and non-rectangular regions; Gauss-Green formula; computing area and volume; changing the order of integration ▹ Watch videos
• 6
  Lesson 6: Vector Fields Acting on a Curve Definition and examples of 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 along/across a curve; flux; path independence for gradient fields; Gradient Test; Fundamental Theorem of Line Integrals ▹ Watch videos
• 8
  Lesson 8: Sources, Sinks, and Singularities Gauss-Green formula (Green's Theorem); rotation and divergence; sources and sinks; singularities; del operator; Laplacian ▹ Watch videos
• 9
  Lesson 9: Change of Variables (2D Integrals) Change of variables; non-area-preserving maps; Jacobian determinant; double integrals in polar coordinates; Mathematica-aided coordinates ▹ Watch videos
• 10
  Lesson 10: Change of Variables (3D Integrals) Change of variables for triple integrals; 3D Jacobian; volume and mass calculations; Mathematica-aided coordinates ▹ Watch videos
• 11
  Lesson 11: Spherical and Cylindrical Coordinates Parameterizing spheres and cylinders; Jacobian for spherical/cylindrical coordinates; triple integrals in both systems ▹ Watch videos
• 12
  Lesson 12: Surface Integrals Flux across a surface; Divergence Theorem (Gauss' Theorem); substitute surfaces; surface area ▹ Watch videos
• 13
  Lesson 13: Stokes' Theorem Curl of a vector field; path integrals in 3D; Stokes' Theorem; orientable surfaces; gradient fields and path independence in 3D ▹ Watch videos