MATHEMATICS 463: COMPLEX VARIABLES FOR SCIENTISTS AND ENGINEERS

Professor Robert L. Ellis This information is available on the web at

Room 4417, Mathematics Building http://www.wam.umd.edu/~rle/webpage_463.html

Tel. (301) 405-5518 and

E-mail: rle@math.umd.edu http://www.math.umd.edu/undergrad/course_web_pagesSum01.htm

Office Hours: 9:30 - 10:45

COURSE DESCRIPTION:

This course is an introduction to complex variables accessible to juniors and seniors in engineering, physics and mathematics. The algebra of complex numbers, analytic functions, Cauchy Integral Formula, theory of residues and application to the evaluation of real integrals, conformal mapping and applications to physical problems.

TEXT:

Complex Variables and Applications, Sixth Edition, by Churchill and Brown, McGraw-Hill, 1996, ISBN: 0-07-912146-2 (MAC Set) or 0-07-912147-0 (IBM Set)

GRADING:

Based on total points as follows:
   Exams : 100 points each
   Homework percentage: 100 points Homework assignments
   Final exam: 100 points Homework to be handed in

Each exam will be curved immediately after it is graded. The homework will be curved 90, 80, 70, 60. The exam and homework curves will be added to produce a curve for the entire course.

FINAL EXAMINATION:

Friday, August 24, during the regular classtime.

ACADEMIC INTEGRITY:

Students are subject to the University's Code of Academic Integrity as approved by the Campus Senate.

HOMEWORK ASSIGNMENTS:

CHAPTER 1
page 5 Ex. 1, 3, 4(a,b), 12
page 11 Ex. 4, 9-11, 13, 14, 18 (Hint for Ex. 4: 2ab< or = a2+b2 if a and b are real)
page 17 Ex. 1-6
page 22 Ex. 1, 2, 6, 7
page 25 Ex. 1, 3-5

CHAPTER 2
page 31 Ex. 1-8
page 42 Ex. 4, 7, 9-11
page 47 Ex. 3, 4, 8, 9
page 54 Ex. 1-3, 4(b,c), 5, 6
page 62 Ex. 1-7, 10, 11, 14, 15
CHAPTER 3
page 67 Ex. 1, 3, 8(b), 10-13
page 71 Ex. 2, 16
page 74 Ex. 2(a), 8
page 79 Ex. 1, 3, 5, 9, 13
page 84 Ex. 1, 3

CHAPTER 4
page 92 Ex. 1-3, 8, 11
page 102 Ex. 1-7, 9, 10, 13
page 119 Ex. 1-7, 9
page 128 Ex. 1-5
page 136 Ex. 1, 2, 4-10

CHAPTER 5
page 142 Ex. 1, 2, 4
page 149 Ex. 1-3, 5, 8, 10(a,b), 11
page 156 Ex. 1-6, 8
page 172 Ex. 1-5, 7-10

CHAPTER 6
page 188 Ex. 1(a-c), 2(a,b,c), 3(b,c), 4-6
page 197 Ex. 2, 4

CHAPTER 7
page 208 Ex. 1-3
page 214 Ex. 2, 4
page 218 Ex. 4, 7
page 233 Ex. 6, 8-10

CHAPTER 8
page 250 Ex. 2
page 258 Ex. 1, 5, 6, 7(a), 9, 10

CHAPTER 9
page 289 Ex. 1-3, 5
page 297 Ex. 3-6
CHAPTER 10

page 307 Ex. 4

Homework to be handed in

              7/18/01           p. 11   Ex. 1(c);   p.22 Ex. 1(a), 6
                         7/19/01           p. 31   Ex. 2, 4, 5
                         7/20/01           p. 42   Ex. 9, 10
                         7/23/01           p. 54   Ex. 3(b), 4(c), 6
                         7/24/01           p. 62   Ex. 1(c), 7(a)
                         7/25/01           p. 68   Ex. 11; p. 71   Ex. 2
                         7/26/01           EXAM
                         7/27/01           p. 92   Ex. 2, 3
                         7/30/01           p. 102 Ex. 1(c), 3
                         7/31/01           p. 119 Ex. 2(b), 4(a), 7(a)
                         8/01/01           p. 119 Ex. 5(a,b); p. 128 Ex. 1(b), 3
                         8/02/01           p. 128 Ex. 4; p. 136 Ex. 1
                         8/03/01           p. 136 Ex. 2, 6
                         8/06/01           p. 142 Ex. 2, 4
                         8/07/01           p. 149 Ex. 3; p.156 Ex. 7
                         8/08/01           No problems due
                         8/09/01           p. 173 Ex. 5
                         8/10/01           EXAM
                         8/14/01           p. 188 Ex. 2(d)
                         8/15/01           p. 197 Ex. 4
                         8/16/01           p. 208 Ex. 2
                         8/17/01           p. 233 Ex. 8, 10
                         8/20/01           p. 250 Ex. 2; p. 258 Ex. 6, 7(a)
                         8/21/01           p. 289 Ex. 3; p. 297 Ex. 3
                         8/22/01           p. 307 Ex. 4
                         8/24/01           EXAM