MATH 305:201. Applied Complex Analysis


  • All homework solutions are now available
  • Homework 11 and Solution 10 are available
  • This website is up to date as of March 24.
  • Homework 10 and solution 9 are now both available
  • The syllabus is updated to reflect the change in the grading scheme.
  • The course will run online starting on Monday, March 16.
    There will be videos made available (under Pages, available for one week each) on Canvas, organized by topic.
  • Questions should be posted as Discussions on Canvas, and I will answer them as promptly as possible. Making them visible to everyone avoids duplicates.
  • The full set of lecture notes is now available -- that is in case of a campus closure.
    They may be updated as the course continues, so download the latest version at regular intervals.
  • Typos in HW 8 are corrected and now in red
  • Solution 7 is available
  • Homework 8 is there!
  • The solution key of the midterm is available on Canavs
  • Homework 7 is available
  • There is no Homework due February 28.
  • The solution of Homework 6 is available on Canvas
  • Please see the syllabus for details about academic concessions in case of missed exams.
  • Practice midterms: here and here.
  • There is a double office hour on Friday, Feb 21, 2-4
  • Homework 6 is already online
  • Homework 5 is available, and so is Solution 4
  • Homework 4 and Solution 3 are online
  • The third homework and the solution to the second one are available
  • Homework 2 is available
  • Solution 1 is available on Canvas under the `File' tab
  • Lecture notes for week 1 are below.
  • The first homework sheet is available. Due January 17 at 11:59am. Please upload your solution as pdf file to Canvas
  • Welcome to Term 2!

Basic Information

Lecture notes

  • Handwritten lecture notes will be uploaded weekly. Part 1 and Part 2
  • The main textbook for this course is
    Fundamentals of Complex Analysis: with Applications to Engineering and Science
    by Saff and Snider

Homework Assignments

Sheet Number Due Date Solution
Homework 11 April 03 On Canvas
Homework 10 March 27 On Canvas
Homework 9 March 20 On Canvas
Homework 8 March 13 On Canvas
Homework 7 March 06 On Canvas
Homework 6 February 21 On Canvas
Homework 5 February 14 On Canvas
Homework 4 February 7 On Canvas
Homework 3 January 31 On Canvas
Homework 2 January 24 On Canvas
Homework 1 January 17 On Canvas

Weekly lecture summaries
Week 13 Review.
Week 12 The Fourier transform. Application to the heat equation on the line; Qualitative discussion. The convolution product and relation to the Fourier transform. The Poisson summation formula.
Week 11 Applications of the Argument Principle. Fourier series and application to the heat equation on a ring.
Week 10 Laurent series; Definitions, convergence in annuli and examples. Zeros, poles and essential singularities; The Argument Principle.
Week 9 More applications of the residue theorem. Series; Rational functions of trigonometric polynomials; Using branch cuts.
Week 8 Isolated singularities and the power series representation around poles. Meromorphic functions; Residues; The residue theorem; Computation of sums of series.
Week 7 The fundamental theorem of algebra. Power series. Analytic functions. Holomorphic functions are analytic and analytic functions are holomorphic. Zeros and poles.
Week 6 Cauchy's integral formula and first consequences. Holomorphic functions are infinitely differentiable; Cauchy estimates; The mean value property; The maximum modulus principle; Rouché's theorem.
Week 5 Contour integration. Examples and bounds; Consequences of the existence of an antiderivative; Cauchy's theorem and its proof; Consequences and examples.
Week 4 Trigonometric and hyperbolic functions, and equations involving them; Powers and roots. Dynamics of oscillating systems. Smooth paramatrised curves and contour integration; First examples.
Week 3 More on holomorphic functions and the Cauchy-Riemann eqations; Harmonic functions; The complex exponential and its properties; The logarithm: principal value and multivalued function, branch points and branch cuts.
Week 2 Complex functions. Functions as mapping of domains; Contunuity; Differentiability; Holomorphic functions; The Cauchy-Riemann equations; Examples.
Week 1 The complex numbers. Introduction and motivation; the complex plane; polar coordinates; modulus, conjugate and argument; the complex exponential; boundedness, connectedness, path connectedness.