Class

lecture | tutorial | |

Time | Tue, Thu | Mon |

9:00 - 10:20 | 13:30 - 14:20 | |

Venue | 2504 | 3588 |

Instructor | YAN Min | |

Office | 3484 | |

Phone | 23587442 |

Textbook

My own lecture note is posted on-line. No textbook from the market will be used.

Prerequisite

The minimal requirement is the knowledge of multivariable calculus and linear algebra. More advanced knowledge from mathematical analysis also helps.

Topics

Integration on Submanifold of **R**^{n}

length of curve, integral along curve, area of surface, integral along surface, volume of submanifold, integral along submanifold

Stokes' Theorem in **R**^{n}

Green's theorem, antiderivative in **R**^{2}, Stokes' theorem, antiderivative in **R**^{n}, 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

Homework

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%.

Note

The syllabus is subject to change as circumstances arise.