Advanced Calculus 322

Spring 2013


Class days are Tue, Thu, Fri

Week 1: Jan 21 - Jan 25

  • 9.1 Sequences and Series of Nums
  • 9.2 Pointwise convergence of fn seqs
  • 9.3 Unif conv of fn seqs

Week 2: Jan 28 - Feb 1

  • 9.4 Uniform limit
  • 9.5 Power Series
  • 9.6 Cont. not differ example

Week 3: Feb 4 - Feb 8

  • 10.1/10.2 R^n as VS, Basic topology
  • 10.2/10.3
  • 11.1 Continuity

Week 4: Feb 11 - Feb 15

  • 10.3 Topology
  • 11.1 Continuity
  • 11.2 Seq Compactness

Week 5: Feb 18 - Feb 22

  • 11.3 Path Connectedness an IVT
  • 13.1 Limits
  • 13.2 Partial Derivs

Week 6: Feb 25 - Mar 1

  • 13.3 MVT, Directional Derivs
  • 14.1 Linear Approx
  • Catchup

Week 7: Mar 4 - Mar 8

  • 14.2 Quadratic function basics
  • 14.3 Quadratic Approx
  • 15.1 More linear algebra

Week 8 : Mar 11 - Mar 15

  • 15.2 Derivative Matrix and Differential
  • 15.3 Chain Rule
  • Catchup

Week 9: Mar 25 - Mar 29

  • 16.1 Maps in the plane
  • 16.2 Stability
  • 16.3 Inverse Function Theorem

Week 10: Apr 1-Apr 5

  • 17.1 Dini's Theorem
  • 17.2 Implicit Function Theorem
  • Catchup

Week11: Apr 8 - Apr 12 (Registration Week)

  • 17.3 Surfaces and paths in R^3
  • 17.4 Constrained optimization
  • 18.1 Ints on generalized rectangles

Week 12: Apr 15 - Apr 19

  • 18.2 Continuity and integrability
  • 18.3 Ints on Jordan domains
  • Catchup

Week 13: Apr 22 - Apr 26

  • 19.1 Fubini
  • 19.2 Change of variables (subst)
  • 19.3 Proof of above

Week 14: Apr 29 - May 3

  • 20.1 Line integrals
  • 20.2 Surface Integrals
  • Green and Stokes Theorems

Week 15: May 6 - May 10

  • Catchup
  • No Class (Reading Period)
  • No Class (Reading Period)

Notes

  1. 43 class days: 49 class hours