Description
This course continues from Analysis I (18.100B), in the direction of manifolds and global analysis. The first 16 lectures are devoted to multivariable calculus, following carefully the approach in Munkres' book (see below). The rest of the course covers the theory of differential forms in n-dimensional vector spaces and manifolds.
Topics include: Differentiable maps, inverse and implicit function theorems, n-dimensional Riemann integral, change of variables in multiple integrals, manifolds, differential forms, and n-dimensional version of Stokes' theorem.
Prerequisites
Analysis I (18.100B) and one of the following: Linear Algebra (18.06), Linear Algebra with Theory (18.700), or Algebra I and II (18.701/18.702), or Modern Algebra (18.703). Introduction to Topology (18.901) is helpful but not required.
Textbooks
Munkres, James R. Analysis on Manifolds. Boulder, CO: Westview Press, June 1997. ISBN: 0201315963.
Spivak, Michael. Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus. Boulder, CO: Westview Press, June 1, 1965. ISBN: 0805390219.
Assignments
There are two kinds of assignments for this course: Daily Homework and Problem Sets. The daily homework assignments will not be handed in, but some problems will show up in the midterm and the final. The problem sets will be handed in and graded.
Grading
| Four Problem Sets |
50% |
| Exams |
50% |
Problem Sets (50%): There will be 4 problem sets.
Exams (50%): A midterm exam and a final exam.