21-268 Multidimensional Calculus - CMU Spring 2016 (Sec. A and B)

This is the webpage for Lecture 1 of 21-268 at CMU Spring 2016 semester. I will try to keep it clear and simple.


Laurent Dietrich
Office: Wean Hall 7128
Office Hours: Mondays 4:30-6:00pm


Christopher Cox
Office: Wean Hall 6201
e-mail: cocox at andrew dot cmu dot edu
Office Hours:


Can be downloaded here.

Schedule and Assignment

Lectures take place on MWF 3:30-4:20pm in Scaife Hall 219.
Recitations for Sec. A on Tuesday 1:30-2:20pm in Wean Hall 6423 and for Sec. B on 3:30-4:20pm in Wean Hall 6423.

If I find a perfect solution among your Assignment, I will sometimes scan it, make it anonymous, and upload it. If you recognize your solution and don't want it to be on my webpage, you can just contact me and I'll take it off.

Week #1
Jan. 16 - Jan. 20
Assignment | Sol.
M: Martin Luther King day, no class.
W: Geometry and topology of R^n.
F: Level sets. Limits.
Week #2
Jan. 23 - Jan. 27
Assignment | Sol.
M: Continuity.
W: Partial derivatives (+ handout).
F: Implicit differentiation. Total differential.
Week #3
Jan. 30 - Feb. 3
Assignment | Sol.
M: Continuity of partial derivatives implies differentiable. Digression: determinant.
W: The Jacobian matrix. Composition d/dt [f(g1(t),...,gn(t))].
F: The general chain rule. The implicit function theorem (n=2).
Week #4
Feb. 6 - Feb. 10
Assignment | Sol.
M: General implicit function theorem. Inverse functions and determinant.
W: The inverse function theorem. Directional derivatives. Gradient.
F: Laplacian. Minima and maxima.
Week #5
Feb. 13 - Feb. 17
Review Q. | Sol.
M: Necessary and sufficient conditions for local extrema.
W: Minima and maxima for continuous functions on compact subsets.
F: Scalar and vector fields. Divergence, gradient, curl and what they measure (+ handout).
Week #6
Feb. 20 - Feb. 24
Assignment | Sol.
M: Vectorial calculus identities. Reminder about integration on [a,b].
W: Midterm 1 and a short solution.
F: Integration on the plane. Properties.
Week #7
Feb. 27 - Mar. 3
Assignment | Sol.
M: Iterated integrals. Areas of some shapes.
W: 3D integrals.
F: More 3D integrals. The change of variable formula.
Week #8
Mar. 6 - Mar. 10
Assignment | Sol.
M: Polar and linear changes of variables.
W: More changes of variables (spherical).
F: Mid-semester break, no class.
Week #9
Mar. 13 - Mar. 17
M: Spring break, no class.
W: Spring break, no class.
F: Spring break, no class.
Week #10
Mar. 20 - Mar. 24
Assignment | Sol.
M: Arc length. Surface area.
W: Surface area. Improper integrals.
F: Improper integrals, Leibniz rule.
Week #11
Mar. 27 - Mar. 31
No assignment.
M: Curve integrals 1/2.
W: Curve integrals 2/2.
F: Green's theorem 1/2.
Week #12
Apr. 3 - Apr. 7
Assignment | Sol.
M: Green's theorem 2/2. Path independence.
W: Midterm 2 and solution.
F: Characterizations of path independence in the plane.
Week #13
Apr. 10 - Apr. 14
Assignment | Sol.
M: Line integrals in space. Oriented surfaces.
W: Surface integrals.
F: The divergence theorem 1/2.
Week #14
Apr. 17 - Apr. 21
Assignment | Sol.
M: Divergence theorem 2/2, applications to physics.
W: Stokes theorem 1/2.
F: Spring carnival, no class.
Week #15
Apr. 24 - Apr. 28
M: Stokes theorem 2/2.
W: What is the magnetic field induced by an electrical wire ?
F: Path independence. Maxwell's equations.
Week #16
May 1 - May 5
M: Review week 1/4
T: Review week 2/4
W: Review week 3/4
F: Review week 4/4
Week #17
May 8 - May 12
T: Final exam 5:30 - 8:30 p.m. in HH B131
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