Interphase Calculus III

Course documents

Syllabus

In-class worksheets

27 June

29 June

01 July

06 July

08 July

11 July

13 July

15 July

20 July

22 July

25 July

27 July

29 July

01 August

Problem Sets

Problem Set 1 [solution]

Problem Set 2 [solution]

Problem Set 3 [solution]

Problem Set 4 [solution]

Problem Set 5 [solution]

Quizzes

Quiz 1 solutions

Quiz 2 solutions

Quiz 3 solutions

Exams

Practice Midterm [solutions]

Practice Final [answers]

Midterm

List of concepts for Midterm

List of concepts for Final

Notes

Notes on setting up triple integrals

Additional topics for ASE

  • Clairaut's theorem (which says that partial derivatives commute)
  • Differentials and the multivariable chain rule
  • Motion in space (velocity, acceleration, curvature, maybe binormal vector; recovering position from velocity or velocity from acceleration by integrating)
  • Second derivative test for classifying cricial points as local max/min or saddle points
  • Arc length of a parametrized curve
  • Integrals of scalar functions over curves, with respect to arc length
  • Integrals of scalar functions over surfaces, with respect to surface area
  • More practice with setting up bounds for double and triple integrals in Cartesian, polar, cylindrical, and spherical coordinates
  • Green's theorem
  • Relations between curl, div, & grad, like curl grad f = 0 for all f, or div curl F = 0 for all F