Math 3160 - 1 Applied Complex Variables January 9, 2015
Credit Hours: Two
Meeting Time: T, Th 12:25 - 1:45 PM in AEB 320
Homepage: http://www.math.utah.edu/~treiberg/M3161.html
Instructor: Prof. A. Treibergs, JWB 224, 581 - 8350.
Office Hours: MWF 10:45 AM - 11:45 PM (tent.) & by appt.
E-mail: treiberg@math.utah.edu
Prerequisites: "C" or better in MATH 2250 OR (MATH 2270 AND MATH 2280).
Text: Brown and Churchill, Complex variables and applications,
9th edition, McGraw-Hill, New York, 2013
(ISBN-13: 978-0073383170 )
Course Description:
Analytic functions, complex integration, Cauchy integral
theorem, Taylor and Laurent series, residues and contour integrals,
conformal mappings with applications to electrostatics, heat, and
fluid flow.
Chapter 1 - The Complex Numbers (3 Lectures)
Chapter 2 - Analytic Functions (4 Lectures)
Chapter 3 - Elementary Functions (2 Lectures)
Chapter 4 - Integrals (5 Lectures)
Chapter 5 - Series (3 Lectures)
Chapter 6 - Residues and Poles (3 Lectures)
Chapter 7 - Applications of Residues (2 Lectures)
Chapter 8 - Mapping by Elementary Functions (3 Lectures)
Expected Learning Outcomes:
Upon successful completion of Math 3160 - Applied Complex
Variables, students will be able to: compute algebraic expressions and
elementary functions in complex variables; relate complex-derivatives,
the Cauchy Riemann equations and harmonic functions; perform contour
integrals and use Cauchy's theorems; manipulate series and understand
Taylor's and Laurent's Theorems; calculate and apply residues to
integrals; employ mapping properties of elementary functions to solve
boundary value problems for harmonic functions. In addition to topical
content, students will also gain experience and further mastery of
complete problem solving fluency. Students will be able to read and
interpret problem objectives, be able to select and execute appropriate
methods to achieve objectives, and finally, be able to interpret and
communicate results.
Teaching and Learning Methods:
Material will be presented in lectures and read from the test and other
sources. Students will solidify their learning by solving problems
assigned weekly. Significant time will be devoted to working homework
problems in class group work. Students should read the section in the text
before each class.
Evaluation Methods and Grading
Homework: To be assigned weekly.
Homework will be due Fridays and will be collected in
class Thursdays. Papers turned into the graders ???
mailbox in the math mail room (JWB 228) by ??? PM Fridays
before he leaves will be regarded as being turned in on
time. Homework that is late but not more than one week
late will receive half credit. Homework that is more
than one week late will receive no credit at all.
Exams: Exams will be closed book except that you will be allowed
to bring a "cheat sheet," an 8.5" x 11" piece of paper
with notes on both sides. Your text, notes, homework
papers, calculators laptops, tablets, phones, text
messaging devices, and other books will not be allowed.
Midterms: There will be two in-class one-hour midterm exams
on Thursdays Feb. 12 and Mar. 26.
Final Exam: Fri., May 1, 10:30 AM - 12:30 PM. Half of the final
will be devoted to material covered after the second
midterm exam. The other half will be comprehensive.
Students must take the final to pass the course.
Course grade: Two midterms 40% + HW 30% + final 30%.
Grades will be assigned "on the curve."
Withdrawals: Last day to register is Jan. 19. Last day to drop class
is Jan 19. Until Mar. 6 you can withdraw from class with
no approval at all. After that date you must petition
your dean's office to be allowed to withdraw.
ADA: The University of Utah seeks to provide equal access to
its programs, services and activities for people with
disabilities. If you will need accommodations in this
class, reasonable prior notice needs to be given the
Center for Disability Services, 162 Olpin Union Building,
581-5020 (V/TDD). CDS will work with you and the
instructor to make arrangements for accommodations. All
information in this course can be made available in
alternate format with prior notification to the Center for
Disability Services
(www.hr.utah.edu/oeo/ada/guide/faculty/)
Faculty and Student Responsibilities:
All students are expected to maintain professional behavior
in the classroom setting, according to the Student Code,
spelled out in the Student handbook. Students have specific
rights in the classroom as detailed in Article III of the
Code. The Code also specifies proscribed conduct (Article
XI) that involves cheating on tests, plagiarism and/or
collusion, as well as fraud, theft, etc. Students should
read the Code carefully and know they are responsible for
the content. According to the Faculty Rules and
Regulations, it is faculty responsibility to enforce
responsible classroom behaviors, beginning with verbal
warnings and progressing to dismissal from class and a
failing grade. Students have the right to appeal such
action to the Student Behavior Committee. Faculty must
strive in the classroom to maintain a climate conductive to
thinking and learning (PPM 6-316). Students have a right to
support and assistance from the University in maintaining a
climate conducive to thinking and learning (PPM 6-400).
Note: The syllabus is not a binding legal contract. It may be
modified by the instructor when the student is given
reasonable notice of the modification.