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MATH 217 - Honors Advanced Calculus I (Fall 2011)

Time and Location

Time: MWF 10:00 - 10:50 am and R 5:00 - 5:50 pm
Room: CAB 269


Instructor

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


Office hours

MWF 2:30 - 4:00 pm or by appointment.


General information

Please see this PDF document for all relevant details concerning MATH 217.


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 217 will cover roughly Chapters 1-4 and parts of Chapter 6 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 217 !!
  
1 Wed
7
Sep 		Review of basic concepts:
Logic, Sets. 		Handout:
Review of basic concepts (PDF,135kB)
2 Thu
8
Sep 		Review of basic concepts:
Relations. 		 
3 Fri
9
Sep 		Review of basic concepts:
Functions. 		 
4 Mon
12
Sep 		Review of basic concepts:
Groups. 		 
5 Wed
14
Sep 		Welcome to the real line:
Fields. 		 
6 Thu
15
Sep 		Properties of ordered fields.  
7 Fri
16
Sep 		Complete ordered fields.  
8 Mon
19
Sep 		Dedekind cuts.  
9 Wed
21
Sep 		Introducing the real numbers.  
10 Thu
22
Sep 		Countable and uncountable sets.  
11 Fri
23
Sep 		Introducing Rd: dot product and length.  
12 Mon
26
Sep 		More on dot product and length; the Cauchy-Schwarz inequality.  
13 Wed
28
Sep 		Some basic topology: interior, cluster, boundary, and isolated points.  
14 Thu
29
Sep 		Examples. Open sets.  
15 Fri
30
Sep 		Properties of open and closed sets.  
16 Mon
3
Oct 		Open covers. Compact sets. Congratulations Josh!
17 Wed
5
Oct 		The Heine-Borel Theorem and its consequences.  
18 Thu
6
Oct 		Connected, star-shaped, and convex sets.  
19 Fri
7
Oct 		Introducing sequences. Basic properties.  
Mon
10 Oct 		No class. Happy Thanksgiving!
20 Wed
12
Oct 		Subsequences. Characterizing closed and compact sets.  
21 Thu
13
Oct 		Cauchy sequences. Limits of functions.  
22 Fri
14
Oct 		Continuous functions. Basic properties.  
23 Mon
17
Oct 		More on continuous functions. Due date for Homework 5 changed to 21 October.
24 Wed
19
Oct 		Uniform continuity.  
25 Thu
20
Oct 		Differentiability on R - A review.  
26 Fri
21
Oct 		Differentiability.  
27 Mon
24
Oct 		Directional and partial derivatives.  
28 Wed
26
Oct 		Examples.  
Thu
27
Oct 		MIDTERM TEST. Good luck!!
29 Fri
28
Oct 		More examples.  
30 Mon
31
Oct 		The Chain Rule. Schwarz's Theorem.  
31 Wed
2
Nov 		Multiindices. Taylor's Theorem on R.  
32 Thu
3
Nov 		Stationary points and extrema.  
33 Fri
4
Nov 		The second-derivative test.  
34 Mon
7
Nov 		Examples of local extrema. Constraints.  
35 Wed
9
Nov 		A preview of Lagrange multipliers.  
Thu/Fri
10/11 Nov 		No classes. Remembrance Day Weekend.
36 Mon
14
Nov 		d-boxes and their partitions.  
37 Wed
16
Nov 		The Riemann integral.  
38 Thu
17
Nov 		Characterizing integrability.  
39 Fri
18
Nov 		Riemann integrals on the real line - a review.  
40 Mon
21
Nov 		Some fun with integrals - Wallis' product.  
41 Wed
23
Nov 		Jordan (measurable) sets.
Integrating over general domains. 		 
42 Thu
24
Nov 		Basic properties of the Riemann integral.  
43 Fri
25
Nov 		Fubini's Theorem.  
44 Mon
28
Nov 		Applications of Fubini's Theorem.
Cavalieri's principle. 		 
45 Wed
30
Nov 		The transformation formula for Riemann integrals.  
46 Thu
1
Dec 		Polar coordinates.  
47 Fri
2
Dec 		Cylindrical coordinates.
Guldin's rule. 		 
48 Mon
5
Dec 		Spherical coordinates.  
49 Wed
7
Dec 		Examples.  
Good bye and good luck !!
Wed
14
Dec 		Special office hours:
10am - 3pm in CAB 683.
Sat
17
Dec 		Ooooops ... a correction. Do not forget:
Final question time,
1-?? pm in CAB 269.
Mon
19
Dec 		Final exam !

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

Homework

Weekly homework assignments will be posted here. Unless stated otherwise, the deadline for homework submission is 5:00 pm on Wednesday. Please submit your solutions into the designated MATH 217 assignment box on the third floor of CAB.

Three words about cheating:

    Don't Do It !!

Midterm test

The midterm test will be held on Thursday, October 27, 2011, in class.

Some details about the midterm:

  • Duration: 50 minutes.
  • Material covered: Chapters I and II.
  • 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 ...

Final exam

The final exam will be held on Monday, December 19, 2011 at 9:00 am, in CAB 269 (our usual classroom).

Some details about the final:

  • Duration: 3 hours.
  • Material covered: Basically everything, but with more emphasis on Chapters III and 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.

As agreed upon in class, a special question time session will be held on Saturday, December 17 at 1:00 pm, in CAB 269. 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 217-related (in a liberal sense) questions are welcome.

Here is what really happened ...

Other material

Dr. Muldowney's classical notes (PDF,19.7MB) 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.

Still looking for something to read for Christmas??
A suggestion for the calculus-minded Santa Claus can be found here (see also here) ...