|13:30 - 14:50||18:00 - 18:50|
My own lecture note is posted on-line. No textbook from the market will be used.
The minimal requirement is the knowledge of multivariable calculus and linear algebra. More advanced knowledge from mathematical analysis also helps.
Integration on Submanifold of Rn
length of curve, integral along curve, area of surface, integral along surface, volume of submanifold, integral along submanifold
Stokes' Theorem in Rn
Green's theorem, antiderivative in R2, Stokes' theorem, antiderivative in Rn, Gauss' theorem
Differentiation on Manifold
differentiable manifold, tangent vector, differential of map between differentiable manifolds, differentiation theory on manifold, orientability
Integration on Manifold
multilinear algebra, cotangent vector, partition of unity, integration
Stokes' Theorem on Manifold
differentiation of form, Poincaré lemma, deRham cohomology
No hard copies of the homework will be distributed. Please check my web page for the latest assignments. Usually you have one week to do the homework. The answer will be put on my web page after the homework is collected. Absolutely no late homework will be accepted.
Exam and Grade
There will be NO midterm and one final exam. The homework is counted as 20% of the final grade and the exam is 80%.
The syllabus is subject to change as circumstances arise.