Math 150B. Calculus on Manifolds - Spring 09 - Hans Lindblad

Text: Sjamaar Manifolds and Differential Forms See also website for Sjamaar's course
Other books: Flanders Differential forms with applications to the physical sciences, Lovelock & Rund Tensors,
Differential Forms, and Variational Principles., Spivak Calculus on Manifolds, Munkers Analysis on Manifolds.
Easier books: Hubbard & Hubbard, Vector Calculus, Linear Algebra, and Differential Forms.
Backman A Geometric Approach to Differential Forms,
Lectures MWF 2-3 Centr 201 Instr Hans Lindblad lindblad@math.ucsd.edu Office hour WF 1.30-2 Mandeville cafe
Syllabus Differential forms, Manifolds and Stokes theorem. (If time permit tensors)

Preliminary schedule. Since class is small there will be no TA. Instead Fridays lecture will be a problem session.
wk  date  Monday  Wednesday  Friday
  1  3/30  2.1 Differential Forms  2.2-3 Exterior Derivative  Problem set 1
  2  4/6  2.4 Hodge star operator,
 2.5 Grad, Div, Curl		  Problems 2.17-18 or Flanders 4.6
 Maxwell's equations		  Problem set 2
  3  4/13  3.1 Determinants  3.2 Pulling back forms  3.2, Problemset 3
  4  4/20  4.1-3 Integration of one-forms  5.1-2 Integration over chains  Problemset 4
  5  4/27  5.2-5.3 Cycles and boundaries  5.4 Stokes' theorem, Problemset 5  Problemset 5, Practice midterm
  6  5/4  Midterm Ch 2-5  6.1 Manifolds  6.2 Manifolds
  7  5/11  7.1-2 Differen. forms on manifold  7.2 Differential forms on manifold  7.2, Problemset 6
  8  5/18  8.1-2 Volume forms on subspace  8.2-3 Volume forms on manifold  Problemsets 7,8
  9  5/25  Holiday  9.1-2 Manifolds with boundary  9.2-3 Integration-Gauss,Stokes
 10  6/1  10.1  10.2  Problemsets 9,10
 11  6/1  No class   Review 3.30-4.30 Centr 203  Final 3-6pm
Practice Final One page (one side) of notes allowed in the midterm. Two pages of notes in the final.


wk  date  Homework (tentative)  Due 6pm in box 6th floor APM   Solutions
  1  4/2   2: 1, 2, 5, 6,     Solutions
  2  4/9   2: 11, 12, 13, 14, 15, 16, (17, 18),  
  3  4/16   3: 1, 2, 3, 6, 7, 11, 14, 16, 17,    
  4  4/23   4: 1, 3, 4, 5, 8, 9, 12, 13,    
  5  4/30   5: 1, 2, 3, 4, 5, 6,    
  6  5/7   6: 1, 2, 3, 4, 5, 6, 10, 11,    
  7  5/14   7: 1, 4, 5, 6, 7, 8,    
  8  5/21   8: 1, 2, 6, 7,    
  9  5/28   9: 2, 4,      
 10  6/4   10: 6, 7,    
Exams One midterm in class, a final Fri June 12, 3-6. Grade Midterm 40%, final 60%.