MATH 212 Multivariable Calculus II, Spring 2008

Course notes: Jerry Shurman: Multivariable Calculus

Lectures: Section 1: MTWF 9-9:50, Section 2: 11-11:50am, both in Library 389
  • Monday, 28 January: Overview
  • Tuesday, 29 January: 6.1: Machinery: boxes, partitions, and sums
  • Wednesday, 30 January: 6.1
  • Friday, 1 February: Go over homework, start 6.2: definition of the integral

  • Monday, 4 February: Finish 6.2.
  • Tuesday, 5 February: Go over homework. 6.3: Continuity and integrability.
  • Wednesday, 6 February: 6.3
  • Friday, 8 February: Go over homework. Start 6.4: Integration of functions of one variable. Quiz over 6.1.

  • Monday, 11 February: 6.4: Integration of functions of one variable.
  • Tuesday, 12 February: 6.4, go over homework.
  • Wednesday, 13 February: 6.5: Integration over non-boxes.
  • Friday, 15 February: Go over homework. 6.5.

  • Monday, 18 February: Finish 6.5
  • Tuesday, 19 February: 6.6: Fubini's theorem. Go over homework.
  • Wednesday, 20 February: 6.6.
  • Friday, 22 February: Go over homework. 6.6. Quiz.

  • Monday, 25 February: 6.7: Change of variable.
  • Tuesday, 26 February: 6.7: Change of variable. Go over homework.
  • Wednesday, 27 February: 6.7.
  • Friday, 29 February: 6.7: Change of variable. Review. Go over homework.

  • Monday, 3 March: 6.8: Topological preliminaries for the change of variable theorem.
  • Tuesday, 4 March: 6.9: Proof of the change of variable theorem
  • Wednesday, 5 March: Pass out exam on Chapter 6. Overview of Chapter 6.
  • Friday, 7 March: More details on 6.8 and 6.9.

  • Monday, 10 March: Exam due in class. 6.9.
  • Tuesday, 11 March: Finish 6.9. 7.1
  • Wednesday, 12 March: Start Chapter 8. Overview. 8.1. Smooth maps. Surfaces, curves. Perpendicular vectors.
  • Friday, 14 March: 8.1: Volumes revisited; integrals over surfaces.

  • Spring break

  • Monday, 24 March: Curves, parameterized curves.
  • Tuesday, 25 March: Curves, parameterized curves. Go over homework.
  • Wednesday, 26 March: Curves, parameterized curves.
  • Friday, 28 March: 8.2: Flow and flux integrals. Go over homework.

  • Monday, 31 March: Section 8.3: Differential forms syntactically and operationally.
  • Tuesday, 1 April: Go over homework. Section 8.4: 1-forms.
  • Wednesday, 2 April: Section 8.5: 2-forms on R^3.
  • Friday, 4 April: Sections 8.6, 8.7: Algebra of forms. Quiz.

  • Monday, 7 April: Section 8.8: Algebra of forms: differentiation.
  • Tuesday, 8 April: Section 8.9: Algebra of forms: the pullback.
  • Wednesday, 9 April: Review of curves, Chapter 8 through Section 8.7.
  • Friday, 11 April: In-class exam.

  • Monday, 14 April: Algebra of forms.
  • Tuesday, 15 April: Section 8.10: Change of variable for differential forms.
  • Wednesday, 16 April: Section 8.11: Cubes and chains.
  • Friday, 18 April: Section 8.12: The geometry of chains: the boundary operator.

  • Monday, 21 April: Section 8.13: The generalized Fundamental Theorem of Integral Calculus
  • Tuesday, 22 April: Section 8.14: The classical theorems
  • Wednesday, 23 April: Section 8.14: The classical theorems
  • Friday, 25 April: Differential equations. Quiz on Sections 8.9-8.11

  • Monday, 28 April: Differential equations. Improper integrals.
  • Tuesday, 29 April: Improper integrals.
  • Wednesday, 30 April: Review, more examples
  • Friday, 2 May: Review, more examples

    Assignments (due at the beginning of class):
  • Friday, 1 February: Section 6.1: 1, 2, 3, 4 (a), 5
  • Tuesday, 5 February: Section 6.2: 2, 4, 5, 6
  • Friday, 8 February: Section 6.2: 7. Section 6.3: 1, 2, 3, 4
  • Tuesday, 12 February: Section 6.3: 5, 6
  • Friday, 15 February: Section 6.4: 3, 4, 5, 6. Integration by substitution handout
  • Tuesday, 19 February: Section 6.5: 1, 3, 6, 7
  • Friday, 22 February: Section 6.5: 9. Section 6.6: 1, 2, 3, 4, 5
  • Tuesday, 26 February: Section 6.6: 6, 8, 9, 12
  • Friday, 29 February: Section 6.7: 1, 3, 5, 6, 8, 12
  • Tuesday, 4 March: Section 6.8: 2, 5
  • Monday, 10 March: Take-home exam due
  • Tuesday, 25 March: Section 8.1: 1.
  • Friday, 28 March: Section 8.1: 2, 3. Find a parameterization of a curve that loooks like a heart, and draw/graph your parameterization. Set up the integral for the arc length of the ellipse {x^2 \over a^2} + {y^2 \over b^2} = 1, and at least try to integrate.
  • Tuesday, 1 April: 1. Evaluate the flow of the vector field F(x,y) = (-x,y) along the curves (i) f(t) = (t,t+1), t from 1 to 8; (ii) g(t) = (t, t^2), t from 2 to 3; (iii) h(t) = (cos t, sin t), t from 0 to pi; (iv) k(t) = (sin t, cos t), t from 0 to pi.
  • Friday, 4 April: Section 8.3: 1, 2. Section 8.4: 1, 3.
  • Tuesday, 8 April: Section 8.5: 1, 2, 4. Section 8.6: 1. Section 8.7: 2.
  • Friday, 11 April: In-class exam.
  • Tuesday, 15 April: Section 8.8: 1, 2, 3, 4, 6. Read 5.
  • Friday, 18 April: Section 8.9: 1, 2, 3.
  • Tuesday, 22 April: Section 8.10: 1. Section 8.11: 1.
  • Friday, 25 April: Section 8.12: 2, 3, 4. Section 8.13: 3. Section 8.14: 3.
  • Tuesday, 29 April: Section 8.14: 5.
  • Friday, 2 May: Homework handout.




    Created: 28 January 2008