MATH 115A Introduction to Complex Analysis

General Information

• Time: Mon. Wed. & Thu. 9:00 AM - 09:50 AM

• Place: Gerstenzang 124

• Prerequisite: MATH 15 A or 22A, MATH 20A or 22B, and MATH 23B

• Textbook: J. Brown, R. Churchill, Complex Variables and Applications, 9th Ed. McGraw-Hill. ISBN:9780073383170.

• Course description

• Syllabus
  

Online classs

• Zoom address for online courses: https://brandeis.zoom.us/j/878295959

• The course will be completely online after Mar. 16th.
  
  

Instructor: Yoosik Kim

• Email: yoosik (at) brandeis (dot) edu

• Office hours (via Zoom): Wed. 10 AM - 12 PM or by appointment
  

Grader. Eric Hanson

• Email: ehanson4 (at) brandeis (dot) edu

• Office hours (via Zoom): Wed. 4 PM - 5 PM or by appointment

Grader: Ethan Huffmann

• Email: dhuffman (at) brandeis (dot) edu

• Office hours (via Zoom): Tue. 6 PM - 7 PM or by appointment

Lecture notes

• The 1st Week - Review of complex numbers

• The 2nd Week - Functions of a complex variable, limits

• The 3rd Week - Derivatives, Cauchy--Riemann equations

• The 4th Week - Analytic functions, harmonic functions, exp and log functions

• The 5th Week - Complex exponents and trig functions

• The 6th Week - Hyperbolic and inverse trig functions, contour integrals

• The 7th Week - Antiderivatives, Cauchy--Goursat theorem

• The 8th Week - Cauchy integral formula, Derivatives of analytic functions, Morera's theorem

• The 9th Week - Liouville's theorem, Maximum modulus principle, Taylor series

• The 11th Week - Laurent series, Residues

• The 12th Week - Poles and zeros, More residue calculations

• The 13th Week - Applications of residues, Jordan's lemma

• The 14th Week - Indented contours, Integrals involving trig functions, argument principle

• The 15th Week - Rouche's theorem, open mapping theorem, some additional topics
  
  
  

Exams

• The 1st midterm

  • Feb. 12th (Wed) during the class,

  • Chap. 1 - Chap. 3. The exponential functions,

  • Problems, Solutions.
    

• The 2nd midterm

  • Mar. 26th (Thu) - Mar. 28th (Sat) take-home and open book exam.

  • Chap. 3. The logarithmic functions - Chap. 4.

  • Problems, Solutions.
    

• The final cumulative exam

  • May 6th (Wed) - May 8th (Fri) take-home and open book exam.

  • Chap. 1 - Chap. 7.

  • Problems, Solutions.