David Drasin

Professor Emeritus

drasin@purdue.edu

Research Interest(s):

complex variables, potential theory

Courses

Courses I am teaching:

• Spring 2008
  • MATH 525
  • MA 261
• Summer 2008
  • MA 511

MA-261 Spring 2008, Instructor: D. Drasin

My Office hours (MATH 622) are daily 9:30AM, daily 11 AM or by appointment. After each lecture I usually spend some time answering questions as well, or via wmail. The updated schedule will be posted here. For all other info about this class, go to the departmental MA-261 web page.

This table shows the lesson covered in class. For example, on 1/7, Lesson 1 ( L1 ) was covered. The corresponding HW assignment is then due in the following schedule: Monday lecture due in Tuesday recitation, Wednesday lecture handed in Friday, Friday handed in Monday (all after class).

I have prepared my own notes on Lecture 18, section 14.8.

ANNOUNCEMENT: In order to have a comfortable atmosphere during lecture I am no longer collecting homework at lecture; homework from Wed/Fri/Mon lecture will be collected on Tuesday recitation. In order to keep up with the pace of the class, DO NOT leave the assignment for the Monday before recitation; it is doubtful that you will succeed in the final exam. DO COME TO LECTURE AND ASK QUESTIONS!

FOR FINAL etc. In order to have review time, I plan to have finshed the course material by MONDAY lecture. Wednesday and Friday will be review, although I will be reviewing during each regular lecture. I have also scheduled an EXTRA help session for Sunday night, April 27, 7-9 PM in LILY 2102. Please come with questions to these classes.

ADDED 4/26--information on FINAL and SUNDAY REVIEW : NO FORMULAS will be given in the final, so know those for Green's theorem, Divirgence, Stokes, etc. No table of integrals will be provided, and you are expected to remember things from MA 162 such as integration by parts, trig. identities since as (sin t)*2=(1/2)(1- cos 2t), (cos t)*2=(1/2)(1+ cos 2t) . I will outline and review the course and discuss the kinds of questions we have asked in earlier exams.

REVIEW LECTURES We will do the Spring 2006 and Fall 2005 Finals in classes 4/23 and 4/25 as well as other issues that may arise. These old exams are on the course web pages. RECITATION on April 22 will be review for the final. Homework will be collected and checked, but this is dead week for the recitation instructors too!

Last updated: Saturday, April 26, 2008

MA 511

This page will contain material for the Spring 2010 semester of MATH 511, Drasin Section
We meet Tues-Th 9-10:15, UNIV 317
Evening exams: March 10, BRNG 2280, 7 PM

CHANGE!-- No evening Exam April 21; we will have a class quiz

April 29 meeting at 7 PM April 28, BRNG 1245

Course outline

(regularly updated)

Outline April 13

FINAL EXAMINATION: Lawson B155, May 5, 7-9 PM

PRELIMIARY SCORES on Final (5/10): 192(1), 184(3), 176(3), 168(4), 160(7), 152(7), 144(2), 136(2), 128(1), 120(1), 112(1), 104(1), FINAL GRADES have been determined.

EXTRA OFFICE HOURS
WEDNESDAY MAY 12, 1-3 PM in my office, MA 622.

• SOLUTIONS TO March 11 Exam 1 Please consult
• SOLUTIONS TO Jan 21 quiz Please consult
• SOLUTIONS TO Feb 8 quiz (Error: in 3a we have y3 is free variable)
• SOLUTIONS TO April 8 quiz (April 8 solutions)
• SOLUTIONS TO April 22 quiz (April 22 solutions)
• A homework solution p.216 #9
• Hint for Nos. 6 and 8 of section 6.3. Look at remarks 3 and 4 on page 331. Then that should tell you that the matrix Sigma is very simple in this situation.
• Another homework solution (on request) p.344 #2
• Homework for week of April 26. NO HOMEOWRK DUE 4/27, but for 4/29 do (sec 6.3) 1, 2, 3, 6, 8 (only first sentence) and 7.2: 1, 2, 5 (use def. on norm!), 11a, 12. We will distribute a practice final exam.
• Last class: April 29 modification: Class will be 2 hours the previous night, Wed. April 28, starting at 7 PM (BRNG 1245). We will review practice exam and be open for questions.
• REVIEW SESSION: May 3 (Mon)-- 6-8 PM BRNG 1235

CV

EDUCATION

B.S. Temple University 1962

Ph.D. Cornell University 1966

PROFESSIONAL EXPERIENCE

Assistant Professor Purdue University 1966-69

Associate Professor Purdue University 1969-74

Professor Purdue University 1974-

Program Director (Analysis) National Science Foundation 2002-04

PROFESSIONAL SOCIETIES AND HONORS

Associate Editor, American Mathematical Monthly 1968-71

Reviewer, Math Reviews, Zentralblatt

Associate Editor, Serdica (Bulgarian Journal) 1995-2004

Associate Editor, Annals of the Finnish Academy

(Annales Academiae Scientiarum Fennicae) 1996-

Associate Editor, Computational Methods in Function Theory 2001-

Guest Professor, University of Kiel May 2005

Guest Professor, University of Helsinki 2005-06

Papers

Below are links to some of my papers and preprints:

On Nevanlinna's Inverse Problem

A Function in Class S of Irregular Growth (appeared 2008)

Publications listed in MathSciNet

1. V. Azarin, D. Drasin, and P. Poggi-Corradini. A generalization of trigonometric convexity and its relation to positive harmonic functions in homogeneous domains. J. Anal. Math. , 95:173-220, 2005.
2. D. Drasin, A. A. Goldberg, and P. Poggi-Corradini. Quasiconformal mappings in value-distribution theory. In Handbook of complex analysis: geometric function theory. Vol. 2 , pages 755-808. Elsevier, Amsterdam, 2005.
3. David Drasin and Swati Sastry. Periodic quasiregular mappings of finite order. Rev. Mat. Iberoamericana , 19(3):755-766, 2003.
4. David Drasin and Jang-Mei Wu. The sharpness of a criterion of MacLane for the class A . J. London Math. Soc. (2) , 67(2):433-447, 2003.
5. Vladimir Azarin and David Drasin. A generalization of completely regular growth. In Entire functions in modern analysis (Tel-Aviv, 1997) , volume 15 of Israel Math. Conf. Proc. , pages 21-30. Bar-Ilan Univ., Ramat Gan, 2001.
6. David Drasin. Approximation of subharmonic functions with applications. In Approximation, complex analysis, and potential theory (Montreal, QC, 2000) , volume 37 of NATO Sci. Ser. II Math. Phys. Chem. , pages 163-189. Kluwer Acad. Publ., Dordrecht, 2001.
7. David Drasin. On Nevanlinna's inverse problem. Complex Variables Theory Appl. , 37(1-4):123-143, 1998.
8. David Drasin. The works of Sunyer i Balaguer and contemporary mathematics. Gac. R. Soc. Mat. Esp. , 1(3):364-371, 1998.
9. J. Milne Anderson, David Drasin, and Linda R. Sons. Wolfgang Heinrich Johannes Fuchs (1915-1997). Notices Amer. Math. Soc. , 45(11):1472-1478, 1998.
10. David Drasin. On a method of Holopainen and Rickman. Israel J. Math. , 101:73-84, 1997.
11. D. Drasin and J. K. Langley. On deficiencies and fixpoints of composite meromorphic functions. Complex Variables Theory Appl. , 34(1-2):63-82, 1997.
12. David Drasin. The minimum modulus of subharmonic functions of order one and a method of Fryntov. J. London Math. Soc. (2) , 54(2):239-250, 1996.
13. David Drasin. Meromorphic functions: progress and problems. In Proceedings of the International Congress of Mathematicians, Vol.1, 2 (Zürich, 1994) , pages 828-835, Basel, 1995. Birkhäuser.
14. David Drasin. On Ahlfors's theory of covering surfaces. In Proceedings Symposium on Value Distribution Theory in Several Complex Variables (Notre Dame, IN, 1990) , volume 12 of Notre Dame Math. Lectures , pages 54-68, Notre Dame, IN, 1992. Univ. Notre Dame Press.
15. Chong Ji Dai, David Drasin, and Bao Qin Li. Correction to: “On the growth of entire and meromorphic functions of infinite order” [J. Analyse Math. 55 (1990), 217-228; MR1094716 (92a:30031)]. J. Anal. Math. , 57:299, 1991.
16. David Drasin. Asymptotic periods of entire and meromorphic functions. In International Symposium in Memory of Hua Loo Keng, Vol.II (Beijing, 1988) , pages 89-106. Springer, Berlin, 1991.
17. Chong Ji Dai, David Drasin, and Bao Qin Li. On the growth of entire and meromorphic functions of infinite order. J. Analyse Math. , 55:217-228, 1990.
18. David Drasin and Allen Weitsman. Bounds on the sums of deficiencies of meromorphic functions of finite order. Complex Variables Theory Appl. , 13(1-2):111-131, 1989.
19. David Drasin. The impact of Lars Ahlfors's work in value-distribution theory. Ann. Acad. Sci. Fenn. Ser. A I Math. , 13(3):329-353, 1988.
20. D. Drasin, C. J. Earle, F. W. Gehring, I. Kra, and A. Marden, editors. Holomorphic functions and moduli. II , volume 11 of Mathematical Sciences Research Institute Publications , New York, 1988. Springer-Verlag.
21. D. Drasin, C. J. Earle, F. W. Gehring, I. Kra, and A. Marden, editors. Holomorphic functions and moduli. I , volume 10 of Mathematical Sciences Research Institute Publications , New York, 1988. Springer-Verlag.
22. D. Drasin. Some recent successes in value-distribution theory. In Complex analysis, III (College Park, Md., 1985-86) , volume 1277 of Lecture Notes in Math. , pages 1-14. Springer, Berlin, 1987.
23. David Drasin. Proof of a conjecture of F. Nevanlinna concerning functions which have deficiency sum two. Acta Math. , 158(1-2):1-94, 1987.
24. David Drasin, Peter Duren, and Albert Marden, editors. The Bieberbach conjecture , volume 21 of Mathematical Surveys and Monographs , Providence, RI, 1986. American Mathematical Society.
25. D. Drasin. On the Teichmüller-Wittich-Belinski\itheorem. Results Math. , 10(1-2):54-65, 1986.
26. D. Drasin and E. Seneta. A generalization of slowly varying functions. Proc. Amer. Math. Soc. , 96(3):470-472, 1986.
27. D. Drasin and W. K. Hayman. Value distribution of functions meromorphic in an angle. Proc. London Math. Soc. (3) , 48(2):319-340, 1984.
28. David Drasin. Some problems related to MacLane's class. J. London Math. Soc. (2) , 23(2):280-286, 1981.
29. David Drasin, Guang Hou Zhang, Lo Yang, and Allen Weitsman. Deficient values of entire functions and their derivatives. Proc. Amer. Math. Soc. , 82(4):607-612, 1981.
30. David Drasin. Quasiconformal modifications of functions having deficiency sum two. Ann. of Math. (2) , 114(3):493-518, 1981.
31. D. Drasin. On equality in convolution inequalities. J. Math. Anal. Appl. , 78(1):144-160, 1980.
32. David Drasin. An application of quasiconformal methods to a problem in value-distribution theory. In Complex analysis Joensuu 1978 (Proc. Colloq., Univ. Joensuu, Joensuu, 1978) , volume 747 of Lecture Notes in Math. , pages 92-100. Springer, Berlin, 1979.
33. David Drasin. The inverse problem of the Nevanlinna theory. Acta Math. , 138(1-2):83-151, 1976.
34. David Drasin. A note on functions with deficiency sum two. Ann. Acad. Sci. Fenn. Ser. A I Math. , 2:59-66, 1976.
35. D. Drasin. An introduction to potential theory and meromorphic functions. In Complex analysis and its applications (Lectures, Internat. Sem., Trieste, 1975), Vol. I , pages 1-93. Internat. Atomic Energy Agency, Vienna, 1976.
36. David Drasin and Daniel F. Shea. Convolution inequalities, regular variation and exceptional sets. J. Analyse Math. , 29:232-293, 1976.
37. David Drasin and Allen Weitsman. On the Julia directions and Borel directions of entire functions. Proc. London Math. Soc. (3) , 32(2):199-212, 1976.
38. David Drasin and Allen Weitsman. Meromorphic functions with large sums of deficiencies. Advances in Math. , 15:93-126, 1975.
39. David Drasin. A meromorphic function with assigned Nevanlinna deficiencies. In Proceedings of the Symposium on Complex Analysis (Univ. Kent, Canterbury, 1973) , pages 31-41. London Math. Soc. Lecture Note Ser., No. 12, London, 1974. Cambridge Univ. Press.
40. David Drasin. Value distributions of entire functions in regions of small growth. Ark. Mat. , 12:281-296, 1974.
41. David Drasin. A flexible proximate order. Bull. London Math. Soc. , 6:129-135, 1974.
42. David Drasin. A meromorphic function with assigned Nevanlinna deficiencies. Bull. Amer. Math. Soc. , 80:766-768, 1974.
43. David Drasin. On asymptotic curves of functions extremal for Denjoy's conjecture. Proc. London Math. Soc. (3) , 26:142-166, 1973.
44. David Drasin and Daniel F. Shea. Pólya peaks and the oscillation of positive functions. Proc. Amer. Math. Soc. , 34:403-411, 1972.
45. David Drasin and Allen Weitsman. The growth of the Nevanlinna proximity function and the logarithmic potential. Indiana Univ. Math. J. , 20:699-715, 1970/1971.
46. David Drasin and Daniel F. Shea. Complements to some theorems of Bowen and Macintyre on the radial growth of entire functions with negative zeros. In Mathematical Essays Dedicated to A. J. Macintyre , pages 101-121. Ohio Univ. Press, Athens, Ohio, 1970.
47. David Drasin. An application of Tauberian methods to a problem in series. Amer. Math. Monthly , 77:152-156, 1970.
48. David Drasin. Normal families and the Nevanlinna theory. Acta Math. , 122:231-263, 1969.
49. David Drasin and Daniel F. Shea. On the Valiron deficiencies of integral functions. Bull. London Math. Soc. , 1:174-178, 1969.
50. Harold Widom. Lectures on integral equations . Notes by David Drazin and Anthony J. Tromba. Van Nostrand Mathematical Studies, No. 17. Van Nostrand, 1969.
51. David Drasin and Daniel F. Shea. Asymptotic properties of entire functions extremal for the cos πρ theorem. Bull. Amer. Math. Soc. , 75:119-122, 1969.
52. David Drasin and C. J. Earle. On the boundedness of automorphic forms. Proc. Amer. Math. Soc. , 19:1039-1042, 1968.
53. David Drasin. Cusp forms and Poincaré series. Amer. J. Math. , 90:356-365, 1968.
54. David Drasin. Tauberian theorems and slowly varying functions. Trans. Amer. Math. Soc. , 133:333-356, 1968.

Relevant Files

• Vita
• Rick5.eps
• Rick5.fig
• Rick5.fig.bak