Math 353 ~ Complex Calculus   (SPRING 2017)

Schedule:

Wednesdays       12:40-14:30, room: M-102
Fridays             12:40-14:30, room: M-13

Instructor: Fırat Arıkan,    Office: M-130,    Email: farikan(at)metu.edu.tr,   

Office hours: Tuesday 11:40-12:30 & Thursday 09:40-10:30 (or by appointment)

Announcements:  All course announcements will be posted here!

*** Click Here to see Final Exam RESULTS ***

*** Click Here to see Final Exam SOLUTIONS ***

*** Click Here to see Midterm-II SOLUTIONS ***

*** Click Here to see Midterm-II RESULTS ***

* Exercise SET-5 is announced below !!!

*** Click Here to see Midterm-I SOLUTIONS ***

*** Click Here to see Midterm-I RESULTS ***

* Exercise SET-3, Set-4 are announced below !!!

* Exercise SET-2 is announced below !!!

* Exercise SET-1 is announced below !!!

Exams and Grading:
 
There will be two Midterm Exams (35 points each) and a Final Exam (50 points)

IMPORTANT: %70 Attendance is mandatory for this course !!! (Otherwise you will get NA grade)

Midterm 1: Time:   April 7, 2017 (Friday), STARTING AT: 12:40, ROOM:  M-13  (in class exam)
                 Topics included:  up to (and including) mapping by elementary functions
 
Midterm 2: Time:    May 12, 2017 (Friday), STARTING AT: 12:40, ROOM :  M-13  (in class exam)
                    Topics included:  up to (and including) Power Series
 
Final Exam: Time:   June 06, 2017 (Tuesday), STARTING AT: 17:00, ROOM: M-102
                      Topics included: Everything seen during the semester.

Content: Algebra of complex numbers. Polar representation. Analyticity. Cauchy-Riemann equations. Power series. Elementary functions. Mapping by elementary functions. Linear fractional transformations. Line integral. Cauchy-Theorem. Cauchy integral formula. Taylor`s Series. Laurent series. Residues. Residue theorem. Improper integrals.

Prerequisite: MATH 252

Suggested textbooks:  J.W.Brown & R.V.Churchill, ''Complex Variables and Applications'' (7th. Edition)
                                      S.D.Fisher, ''Complex Variables''
                                     

Course Outline:

(2 Weeks)  Algebra of complex numbers. Polar and spherical representations.

(3 Weeks)   Functions of a complex variable. Limits. Continuity. Analyticity. Cauchy-Riemann equations.

(3 Weeks)   Elementary functions. Mapping by elementary functions. Line (contour) integral.

(3 Weeks)   Cauchy's Theorem. Cauchy integral formula. Power series. Taylor's Series.

(3 Weeks)   Laurent series. Residues, residue theorem. Linear fractional transformations. Improper integrals.

Suggested Problems: Problem numbers in each set below refer to exercises in the 7th. edition of the book  ''Complex Variables and Applications'' by J.W.Brown & R.V.Churchill.

Set-1: All questions of all sections in Charter 1.

Set-2: All questions of Sections: 11, 13, 17 (except 12, 13), 19 (ecxept 9), 22

Set-3: Sec 24 (Q: 1,2,7), Sec 25 (Q: 1,2,3), all questions of Sections 28, 30, 32, 33, 34, 35

Set-4: All questions of Sections: 37, 38 (except 6), 40, 41 (ecxept 7), 43

Set-5: Sec 48 (All ecxept 4, 6), Sec 50 (6, 8), Sec 52 (All), Sec 54 (1,2,3,6,7,9,13), Sec 56 (1,3,4,5,7,8), Sec 60 (1,2,3)