MATH 463: Complex Variables for Scientists and Engineers

Spring 2011

Instructor: Dionisios Margetis

LECTURES: Tuesdays and Thursdays, 9:30am-10:45am; Rm MTH0307

Instructor's office hours: Tuesdays 10:50am-12:15pm (after class); or by appointment

Teaching Assistant/Grader: Mr. Bradford A. Sanders (brad@math.umd.edu); see info below

FINAL EXAM: Friday May 13, 8:00am-10:00am

Textbook:

Fundamentals of Complex Analysis with Applications to Engineering and Science ;
authors: E. B. Saff and A. D. Snider; publisher: Prentice Hall, 2002

Short Syllabus and Detailed Course Policies (PDF)

For detailed syllabus see the Mathematics Department webpage

Teaching Assistant (TA)/Grader Information

HOMEWORKS:


  • Homework 1 , due Thurs. Feb. 17


  • Homework 2 , due Thurs. March 3


  • Homework 3 , due Thurs. March 17


  • Homework 4 , due Tuesday April 5


  • Homework 5 , due Thursday April 21


  • Homework 6 , due Thursday May 5


    • EXAMS:

  • QUIZ 1, Thurs. Feb. 10

  • EXAM 1 , Tues. March 8

  • QUIZ 2 , Tues. March 15

  • EXAM 2 , Thurs. April 7

  • EXAM 3 , Tues. May 3

    • LECTURES:

  • Lecture 1, Tues. Jan. 25:
    Secs. 1.1-1.4 from text: Algebra of complex numbers
  • Lecture 2, Tues. Feb. 1:
    Sec. 1.5 from text: n-th root of complex number
  • (Extra) Lecture 3, Tues. Feb. 1, 5pm-6:15pm:
    Secs. 1.6, 2.1-2.3: Open sets; functions of complex variables; analyticity
  • Lecture 4, Thurs. Feb. 3:
    Sec. 2.4: Cauchy-Riemann equations
  • Lecture 5, Tues. Feb. 8:
    Sec. 2.5: Harmonic functions; Review problems
  • Lecture 6, Thurs. Feb. 10:
    Secs. 3.1-3.3: Elementary functions of complex variable
    QUIZ 1
  • Lecture 7, Tues. Feb. 15:
    Secs. 3.3, 3.5: Elementary functions (cont.): Logarithm and complex power
  • Lecture 8, Thurs. Feb. 17:
    Branch cuts and branch points
    Secs. 4.1, 4.2: Introduction to Complex integrals
  • Lecture 9, Tues. Feb. 22:
    Secs. 4.2, 4.3 : Independence of paths
  • Lecture 10, Thurs. Feb. 24:
    Secs. 4.4, 4.5 : Cauchy Integral Theorem & Formula
  • Lecture 11, Tues. March 1:
    Secs. 4.5 : Cauchy Integral Formula and Consequences
  • Lecture 12, Thurs. March 3:
    Review Problems (including bounds of analytic functions)
  • Lecture 13, Tues. March 8 :
    Sec. 4.6 : Mean value property; maximum principle
    EXAM 1 (60min)
  • Lecture 14, Thurs. March 10 :
    Sec. 5.1 : Convergence of series
  • Lecture 15, Tues. March 15 :
    Secs. 5.2, 5.3 : Taylor series; power series
    QUIZ 2
  • Lecture 16, Thurs. March 17 :
    Sec. 5.5 : Laurent series