Syllabus for MA  426, Spring 2010

1.    Instructor:  J. E. Franke
Office:  SAS 3222
Office Hours:  9:00 - 10:00  M, W, F  or by appointment
Phone Number:  515-2381
E-mail address:  franke@math.ncsu.edu
Homepage:  http://www.math.ncsu.edu/~franke
2. Goals and Objectives:
 MA 426 is the second semester of mathematical analysis. Students will
3. Textbook:
Elementary Classical Analysis by Jerrold E. Marsden and Michael J. Hoffman, Second Edition, W. H. Freeman and Company
   $140
4. Topics and estimated days allocated to each topics:
 
 
 Chapter  Sections Lectures   Topics
1 & 2  1.6-1.7, 2.1, 2.3-2.5,
 2.7-2.9		 8 Topology of n-space
3  3.1-3.5 5 Compact and Connected sets
4 4.1-4.6 6 Continuous Mappings
5 5.1 2 Uniform Convergence
6 6.1-6.9 9 Differentiable Mapppings
7 7.1-7.2, 7.7(optional) 3 Inverse and Implicit Function Theorems
8 8.1-8.4 6 Integration
9 9.1-9.2 2 Fubini's Theorem, Change of Variables

 
 
 
 

5. Tentative schedule of reading assignments
 

Read the sections to be covered for the week.
6. Tentative schedule of homework due dates, quizzes and tests
Homework will be done in groups and is due on Friday.

There will be two tests, scheduled depending on class progress.

The final is on Wednesday, May 12 at 1:00 pm. It is a 3 hour test.

7. Determination of grades:
 
 
Homework: 15%
Test 1 25%
Test 2 25%
Final: 35%


Range Grade
97.6 <= X <= 100    A+ 
92.3 <= X < 97.6    A 
90.0  <= X < 92.3    A- 
87.6 <= X < 90.0    B+ 
82.3 <= X < 87.6    B 
80.0 <= X < 82.3    B- 
77.6 <= X < 80.0    C+ 
72.3 <= X < 77.6    C 
70.0 <= X < 72.3    C- 
67.6 <= X < 70.0    D+ 
62.3 <= X < 67.6    D 
60.0 <= X < 62.3    D- 
X < 60    F 

8. Policy on incomplete grades and late assignments:
Late homework assignments will not be graded.

The policy on incomplete grades is consistent with Grading Policies in Chapter 5 of the Handbook on Advising at
http://www.ncsu.edu/provost/academic_policies/grading/reg.htm


 

9. Policy on absences (excused and unexcused) and scheduling makeup work:

The attendance policy is consistent with the Academic Regulations which can be found at http://www2.ncsu.edu/unity/project/www/ncsu/provost/info/academic_regulations/attend/reg.htm (link)

In addition, the following clarifications are used in this course:  Excused absences are required for making up a missed test.

10. Course Prerequisites / Restrictive Statements:

        MA 425 and MA 405
        More information is available at : http://www2.acs.ncsu.edu/reg_records/crs_cat/MA.html (link)

11. Academic Integrity Statement:

Students are expected to follow university guidelines available at http://www.ncsu.edu/provost/academic_regulations/integrity/reg.htm (link)
12. NC State policy on working with students with disabilities:
Information can be found at http://www2.ncsu.edu/ncsu/stud_affairs/counseling_center/dss/ (link)
13. Statement on laboratory safety or risk assumption in courses requiring physical activity or field trips:
None
14. Statement on "pass-through" charges e.g. , lane rental at bowling alley, field trip costs, etc.:
None
Further Information:
NCSU Academic Regulations can be found at http://www2.ncsu.edu/unity/project/www/ncsu/provost/info/academic_policies/ (link)
Homework
 
Individual Turn in Group Turn in
 Extra not turned in
 Date
P. 63 # 5
P. 70 # 1
P. 98 # 19
 Show that the sup norm on Rn does not come from any inner product.
P. 70 # 4
P. 98 # 10, 13, 27
 P. 64 #1, 3,  5
P. 70 # 3
P. 98 # 12, 14b,16, 20, 30
 1/22
P. 108 # 6
P. 109 # 2
P. 112 #
P. 108 #
P. 110 # 4
P. 112 # 4
 P. 108 # 2, 3, 5
P. 109 #  3, 5
P. 112 #1, 2, 5, 6
 1/29
P. 115  # 4
P. 117  # 5
P. 120 #
P. 123 #
 P. 115 # 3c
P. 117 # 4
P. 120 # 4
P. 123 # 2
 P. 115 # 6
P. 117 # 3
P. 120 # 5, 6
P. 123 # 3, 5
 Note
Mon.
2/8
P. 125 #
P. 143 # 20a
P. 155 #
P. 156 # 5
P. 172 #
 P. 125 # 2
P. 143 # 9b, 43
P. 155 # 4a) Change to: Show directly that A is sequentially compact. (b)
P. 156 #
P. 172 # 5
 P. 125 # 3, 4, 5
P. 143 # 1c, 11, 12c, 13, 14b, 15b
26, 40
P. 155 # 2, 5
P. 156 # 1, 3, 4
P. 172 # 4, 8, 16
 2/12
P. 159 #
P. 162 # 3
P. 174 # 19
P. 181 #
P . 232 #
 P. 159 # 2 do this in Rn.
P. 162 #
P. 172 # 2, 22
P. 181 #
P. 232 # 10
 P. 159 # 1, 4
P. 162 # 1a,c
P. 164 # 1, 2, 4
P. 174 # 6, 7, 15, 24
P. 181 # 1b, 3
P. 232 # 2, 9 Here [a, b[ equals [a, b)
 2/19
P. 184 #
P. 233 # 18
P. 234 # 28 prove
P. 244 # 3

 P. 184 #
P. 233 # 33
P. 196 # 4 give a proof or a counter example
P. 234 # 24b
P. 244 # 2
P. 316 # 1, 8
 P. 184 # 3, 5
P. 187 # 2, 3
P. 191 # 1
P. 193 # 3 f(x0)=x0
P. 196 # 2, 4
P. 231 # 3, 7, 13, 19, 34
P. 233 # 16, 26
P. 244 # 1, 4
P. 316 # 2, 5, 6
 2/26
P. 330 # 4
P. 383 # 4
P. 334
P. 389
P. 338 # 5
P. 344
P. 387 # 27
 P. 330 #
P. 383 # 1,
P. 334 # 3
P. 389 # 40a
P. 338
P. 344# 1, 5
 P. 330 # 2, 3
P. 383 # 2
P. 334 # 1, 2
P. 389 # 38c
P. 338 # 1, 3, 4
P. 344 # 3, 4
 3/12
P. 349 #
P. 386 # 13c
P. 355 # 3
Special HandOut
P. 362 # 1
P. 367 # 2
 P. 349 # 2
P. 355 # 5
P. 384 # 6a
P. 362 # 5
P. 367 # 3
 P. 349 #
P. 355 # 6
 3/31
P. 396 # 5
P. 401 # 1
 P. 396 # 1, 2
P. 439 # 5 c,d There is a mistake in z = rcos(phi)
P. 401 # 5
 P. 396 # 3
P. 401 # 3
 4/9
P. 450 # 1
P. 454 # 2, 5
P. 490 # 10
 P. 450 # 2
P. 454 # 3, 4, 6
P. 490 # 11a
 P. 450 # 4, 6
P. 454 # 1
P. 490 # 5, 7
 4/16


P. 456 # 1, 2, 3, 4
P. 459 # 1, 4
P. 491 # 11b, 12, 17, 18, 24
P. 505 # 2, 3
P. 508 # 2, 3
P. 510 # 2
P. 512 # 2, 3, 5
 end
of
semester