M361 Syllabus

THEORY OF FUNCTIONS OF A COMPLEX VARIABLE

Prerequisite and degree relevance: The prerequisite is M427K or M427L with a grade of at least C-, or consent of the instructor.

Course description: M361 consists of a study of the properties of complex analytic functions. Students are mainly from physics and engineering, with some mathematics majors and joint majors. Representative topics are Cauchys integral theorem and formula, Laurent expansions, residue theory and the calculation of definite integrals, analytic continuation, and asymptotic expansions. Rigorous proofs are given for most results, with the intent to provide the student with a reliable grasp of the results and techniques.

Text: a reasonable text is Brown and Churchill, Complex variables and Applications, sixth edition.

Topics:

  • Complex Numbers
  • Analytic Functions
  • Elementary Functions
  • Integrals
  • Series
  • Residues and poles
  • Applications of Residues

Responsible party: John Dollard 2001