Math 535   Applied Functional Analysis   Spring, 2006

Meetings:  TR 12:15-1:30, Engr 105 (NOTE ROOM CHANGE)

Instructor:  Greg Morrow

Office:  Engr 271, (719) 262-3184

E-mail: gjmorrow@math.uccs.edu

Hours:  TR: 10:15-10:45, 2:00-2:50, or by appointment

Video Lectures:  Click here for the live and archived video lectures

Prerequisite:  Advanced Calculus in one real variable (Math 431)

Text: Introductory Functional Analysis with Applications by Erwin Kreyszig, ISBN 0-471-50731-8, Wiley (1978).

Description: An introduction to the basic concepts, methods and applications of functional analysis. Topics covered include metric spaces, normed and Banach spaces,  linear operators, Hilbert spaces, representation of functionals on Hilbert space,  Hahn-Banach theorem , Uniform-boundedness theorem, weak* convergence, Open mapping theorem, Closed graph theorem,  spectral properties of bounded linear operators and bounded self-adjoint operators.

Homework and Tests: Homework will be assigned and collected weekly; see the assignments and due dates on the syllabus.  Late homework will not be accepted. The lowest homework score will be dropped.  There will be one mid-semester test and a final exam.  The final exam will cover material primarily from the material after the second midterm test.  The following percentages may be used to compute the final grade: homework, 50%; tests, 25% each.

Final Exam: Thursday, May 11, 10:50 – 1:20 pm

Grading:  90’s => grade of A , 80’s => grade of B or better, 70’s => grade of C or better.

Syllabus for Math 535, Spring 2006  (subject to change, revised 04/27/06) 

Week (Tu-Th)             reading                                    due date

1/17  – 1/19                                2.1-2.3                 Notes 1                                                                     

 1/24 – 1/26                                 2.4-2.6                 Notes 2                 HW I, Jan. 26         

 1/31 – 2/2                                   2.7-2.9              Notes 3                               HW II, Feb. 2              

2/7 – 2/9                                    2.10 , 3.1-3.2                                          HW III, Feb.9          

2/14 – 2/16                                  3.3-3.4                                                HW IV, Feb. 16    

2/21 – 2/23                                3.5 -3.7                                                HW V, Feb. 23

 2/28– 3/2                                   3.8-3.10                                             HW VI, Mar .2

3/7– 3/9                                         4.1-4.3      Exam 1                              HW VII, Mar. 9         

3/14–3/16                       Exam 1 over 2.1-3.10 is due on 3/21                                                               

3/21 – 3/23                                  4.4-4.6                                              HW VIII, April 4                              

3/28-3/30                                           Spring Break               

4/4 – 4/6                                          4.7-4.9                                       HW IX, Apr. 13

4/11 – 4/13                                      4.11-4.13                                      HW X, Apr. 20            

4/18– 4/20                                      7.1-7.3                                    HW XI, Apr. 27

4/25 – 4/27                                     9.1-9.3                                     HW XII, May 4

5/2 – 5/54                                       9.4-9.6     Final Exam                                            

5/11                              Final Exam Due:  5/11, 10:50am -1:20 pm

Homework (HW).

I.      2.1: 9, 10; 2.2: 9, 11; 2.3: 3, 7 (EC), 9.

II.            2.4: 2, 6; 2.5: 4; 2.6: 4, 12, 14 (EC)

III.          2.7: 6, 7, 8, 11; 2.8: 2, 3, 6; 2.9: 4, 6. 

      IV.   2.10: 6, 8; 3.1: 3, 6 11, 3.2:  4.

      V.   3.3: 1, 6, 8; 3.4: 6, 8, 9.

      VI.   3.5: 6, 8; 3.6: 4, 10;  3.7:  1, 3 (EC), 6 (EC).

     VII.   3.8: 3, 7;  3.9: 2, 4, 10;  3.10:  6.

     VIII.  4.1: 4, 6;  4.2: 6;  4.3:  9 (extra credit), 12, 14 (for a real normed space).

      IX.  4.5: 8, 9;  4.6: 2, 6, 8. 

      X.  4.7: 6, 8, 10;  4.8: 4;  4.9:  4.

     XI.  4.11: 8;  4.12: 6, 8;  4.13: 8, 9.

     XII. 7.1: 7, 15;  7.2: 5;  7.3: 1, 4, 9.