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MATH 317 - Honors Advanced Calculus II (Winter 2012)

Time and Location

Time: MWF 10:00 - 10:50 am and R 5:00 - 5:50 pm
Room: CAB 281


Instructor

Dr. Arno Berger (CAB 683, aberger@math.ualberta.ca)


Office hours

MWF 2:00 - 3:00 pm or by appointment.


General information

Please see this PDF document for all relevant details concerning MATH 317.


Course notes

Be prepared to take careful notes in class, as no set textbook will be used.

The course will loosely follow Dr. Runde's notes (PDF,1.2MB) which you are very welcome to use. This year's version of MATH 317 will cover roughly Chapters 6-8 of these notes. Be aware that notation and terminology may differ from those used in class.


Material covered in class (Course Diary)

I plan to keep an up-to-date list of the topics, examples etc. covered in class.

Lecture # Date Material covered / special events Remarks/ additional material
    WELCOME TO
MATH 317 !!
  
1 Mon
9
Jan 		Motivating the Implicit Function Theorem (IFT): Level sets.
2 Wed
11
Jan 		Local behaviour of C1 functions.
3 Thu
12
Jan 		Local one-to-one-ness.
4 Fri
13
Jan 		Local openness.
5 Mon
16
Jan 		Homeo- and diffeomorphisms. Examples.
6 Wed
18
Jan 		The Inverse Function Theorem.
7 Thu
19
Jan 		The Implicit Function Theorem - geometric meaning.
8 Fri
20
Jan 		The Implicit Function Theorem - proof.
9 Mon
23
Jan 		Examples. Manifolds in Rd.
10 Wed
25
Jan 		Examples of manifolds.
11 Thu
26
Jan 		More examples.
12 Fri
27
Jan 		A fun example: O(d) and SO(d).
13 Mon
30
Jan 		Maxima and minima under constraints.
14 Wed
1
Feb 		Examples of Lagrange multipliers.
15 Thu
2
Feb 		The Transformation Formula for Riemann Integrals: Statement.
16 Fri
3
Feb 		Examples.
17 Mon
6
Feb 		Towards a proof of the Transformation Formula: Step I.
18 Wed
8
Feb 		Step II.
Thu
9
Feb 		MIDTERM TEST #1. Good luck!!
19 Fri
10
Feb 		Local distortion of Jordan content.
20 Mon
13
Feb 		Step III: Putting things together. Due date for Homework 3 changed to 27 February.
21 Wed
15
Feb 		Proof of the Transformation Formula.
22 Thu
16
Feb 		Examples.
23 Fri
17
Feb 		A taste of vector calculus. Paths.
Have a relaxing reading week.
24 Mon
27
Feb 		Integrating functions along paths.
25 Wed
29
Feb 		Basic properties of integrals along paths.
26 Thu
1
Mar 		Examples.
27 Fri
2
Mar 		Integrating vector fields along paths.
28 Mon
5
Mar 		Examples. Conservative fields.
29 Wed
7
Mar 		Characterising conservative fields.
30 Thu
8
Mar 		l-paths in Rd.
31 Fri
9
Mar 		Towards a notion of l-dimensional volume for l-paths. Parallelotopes.
32 Mon
12
Mar 		Integrating functions over l-paths.
33 Wed
14
Mar 		Examples.
Thu
15
Mar 		MIDTERM TEST #2. Good luck!!
34 Fri
16
Mar 		Integrating vector fields over (d-1)-paths. The exterior product.
35 Mon
19
Mar 		Examples.
36 Wed
21
Mar 		The classical theorems of vector calculus: Green's Theorem.
37 Thu
22
Mar 		Green's Theorem: Proof. Examples.
38 Fri
23
Mar 		Stokes' Theorem.
39 Mon
26
Mar 		Gauss' Theorem.
40 Wed
28
Mar 		Example.
Sequences of functions.
41 Thu
29
Mar 		Pointwise vs. uniform convergence.
42 Fri
30
Mar 		More on uniform convergence.
43 Mon
2
Apr 		A quick review of series.
44 Wed
4
Apr 		More on series.
45 Thu
5
Apr 		Power series basics.
Fri/Mon
6/9
Apr 		No class. Happy Easter!!
Wed
11
Apr 		Class cancelled. I am here.
46 Thu
12
Apr 		More on power series. Examples.
47 Fri
13
Apr 		A final example: the exponential function. e is transcendental (Thm.3).
Good bye and good luck !!
Fri
20
Apr 		Final review/question time: 12:30 - ?? in CAB 281.
Mon
23
Apr 		Final exam !

Please see box on the left for details. 		Good luck !!

Homework

Fortnightly homework assignments will be posted here. Unless stated otherwise, the deadline for homework submission is 5:00 pm on Friday. Please submit your solutions into the designated MATH 317 assignment box on the third floor of CAB.

Three words about cheating:

    Don't Do It !!

Midterm tests

There will be two midterm tests during the semester. These tests will be held in class, on Thursday, February 9, 2012, and on Thursday, March 15, 2012.

Some details about the first midterm:

  • Duration: 50 minutes.
  • Material covered: up to, and including applications of the transformation formula
  • NO textbooks, notes, calculators, formula sheets etc.!
  • NO cell-phones, i-pods, or other electronics!
  • Please bring a valid ID with you.
  • Good luck!

To help you prepare for the midterm test, here is a practice version. The real test will be very similar.

And now for the real thing ...

The format of the second midterm will be identical with the first. This test may contain applications of the transformation formula but will mainly focus on paths in Rd. To help you prepare for the second midterm test, here is again a practice version. As always, the real test will be very similar.

  • Practice Midterm #2 - Solutions
    (As always, it is strongly recommended that you look at the solutions only after you have tried the practice problems on your own.)

Once again, here is the real thing ...

Final exam

The final exam will be held on Monday, April 23, 2012 at 9:00 am, in CAB 281 (our usual classroom).

Some details about the final:

  • Duration: 3 hours.
  • Material covered: Basically everything, but with a clear emphasis on Chapter IV.
  • NO textbooks, notes, calculators, formula sheets etc.!
  • NO cell-phones, i-pods, or other electronics!
  • Please bring a valid ID with you.
  • Good luck!

To help you prepare for the final, here is a practice version. The real exam will be very similar.

A special question time session will be held on Friday, April 20, at 12:30 pm, in CAB 281 (our usual classroom). Please remember that the quality and usefulness of this event completely depends on YOU - the more numerous and precise your questions, the more you will benefit from this session. All MATH 317-related (in a liberal sense) questions are welcome.

Other material

Dr. Muldowney's classical notes (PDF,16.8MB) are a great additional resource. They contain many practice problems.

Feeling the need to review some first-year stuff? Dr. Bowman's MATH 117/118 notes (PDF,5.3MB) are a good place to start.

This online Introduction to Real Analysis may also be useful.

General information about the department's honors program is available here.