Latest news
URGENT!!!The building is locked.
Lectures on 30th April and 2th May are cancelled.
For the next meeting, on 5th May, you are asked to
read yourselves Sect. 4
of Spivak's book,
pages 82-97, with special attention to Th. 4-6, definition of df, d\omega,
Th. 4-9, 4- 10,
Study the proof of Th. 4-11 (the Poincare lemma).
The next assignment will be placed tomorrow!
See more old exams
below!
Welcome to the course.
The schedule for the course can be found via the link to webTimeEdit
top of the page.
A change in Assignment 2. Turn-in time moved to Week
5. Use English version only!!
More additional
literature.
Read about the degree of
the mapping and its applications here
(DJVUReader
can be downloaded from )
The last section of the
course will be based upon Ch.1,2 of the book
(very) old exams exam 1 , Exam 2
(too complicated, by my
opinion)
Teachers
Course coordinator:
Grigori Rozenblioum, grigori@chalmers.se,
7725309, MVL2071
Course litterature
M. Spivak,
Calculus on Manifolds, Benjamin/Cummings Publishing Company, NY – can be bought
in Cremona
L. Hörmander, Advanced Differential Calculus, Lecture
Notes, Matematisk inst., Lund Univ..(can
be downloaded)
Additional literature
Kuttler. Calculus,
Applications
Kuttler. Advanced
Calculus
Kuttler. Topics in Analysis
Shurman Advanced Calculus
Gelbaum
B., Olmsted J. Counterexamples in analysis (Dover, 2003)
S. Lang, Introduction
to differential manifolds, 2003
[S] Ch.1-5
[H] Ch.4,11,12
Contents: Basics of Calculus.The inverse and implicit function theorems, Sets
of measure zero, Sard’s theorem, Degree of mapping.
Manifolds. Vector fields and differential forms. Differential mappings and
their derivatives. Integation of differential forms. DeRham cohomology. Stokes’
theorem. Elliptic operators.
Theory. The proofs of the following theorems are required
[S] Theorems
2-11,2-12,2-13,3-13,3-14,4-5,4-6,4-10,4-12,4-13,5-2,5-7,5-8,5-9
[H]Th. 4.2, Corr. 4.4, Th. 12.2,12.3
Recommended exercises
[S] Ch 1. 1-5, 7,8,10, 12,14,19,21,22,26,29
Ch.2:
1,2,4,5,8,13,15,25,34,35,36,39
Ch.3: 7,11,38,40
Ch.4: 1,2,3,13,16,17,19,21,24,26,28,30,34
Ch.5: 4,6,10,14,15,19,20,23,27,28,31,32,33,36
(more exercises and homework will be handed during the lectures)
English-Swedish mathematical dictionaries
Course requirements
Assignments
Week 2-3 (in English) (turn in week 3)
Week
3-4 (in English) (turn in week 5)
Week 4-5 (in English)
Turn in week 5
week
5-6 Turn in week 7
!!! The text of Ass. 4
is correct, just remove the word ‘closed’!! Anad the lasty factor in the first product in the formula is $dx^d$
week 6-7 Turn in week 8, in
English
Additional questions.
Study the proofs of the inverse mapping
theorem in S and the one given in the
lecture. Investigate, for each proof,, how the conditions
of the theorem can be relaxed so that the
proofs still are valid.
It is proved that a
continuous mapping maps compact sets to compacts. Is the converse statement
true: if a mapping maps any compact set to a compact one,
is it necessarily
continuous?,
Examination
The
examination consists of a written exam and week assignments. For ‘godkänt’ one needs at least 40% of both parts approved.
Examination procedures
In Chalmers Student Portal you can read about when
exams are given and what rules apply on exams at Chalmers.
At the link Scedule you can find when exams
are given for courses at University of Gothenburg.
At the exam, you should be able to show valid identification.
Before the exam, it is important that you report that you want to take the
examination. If you study at Chalmers, you will do this by the Chalmers Student Portal, and if you study at
University of Gothenburg, so sign up via GU's Student Portal.
You can see your results in Ladok by logging on to
the Student portal.
At the annual examination:
When it is practical a separate review is arranged. The date of the review will
be announced here on the course website. Anyone who can not participate in the
review may thereafter retrieve and review their exam on Mathematical sciences
study expedition, Monday through Friday, from 9:00 to 13:00. Check that you
have the right grades and score. Any complaints about the marking must be
submitted in writing at the office, where there is a form to fill out.
At re-examination:
Exams are reviewed and picked up at the Mathematical sciences study expedition,
Monday through Friday, from 9:00 to 13:00. Any complaints about the marking
must be submitted in writing at the office, where there is a form to fill out.
Will be shown.