MATH 305: Applied Complex Analysis


  • Two additional office hours on Monday, April 16 10-11 and Wednesday April 18, 13-14
  • All solutions online
  • Assignement 11 (due on Friday, April 6) and Solution 10 are available
  • It is almost the end of term! Please log in here to input your evaluations and comments
  • Assignement 10 and Solution 9 are available
  • The office hour on Tuesday, March 19 is cancelled due to departmental duties
  • The second midterm and its solution are online
  • Solution 8 and Assignment 9 posted
  • Sign mistake in HW 6, Problem 2(ii) corrected
  • Solution 7 available
  • Regular office hours moved to 9:00am - 10:00am
  • Additional office hour on Friday March 2nd, 1:45pm - 3:15pm
  • Assignment 8 posted, due on Monday!
  • Solution 6 and Assignment 7 posted
  • Solution 5 and Assignment 6 posted
  • The midterm and its solution are online
  • Assignment 5 is available
  • Solution 4 online
  • Solution 3 and Assignment 4 (due on Monday!) are available
  • Solution 2 and Assignment 3 are available
  • Assignments will be returned through the Math Learning Center (MLC), which is also an additional resource for learning support
  • Solution 1 and Assignment 2 are available
  • Assignment 1 is posted below
  • Have a good start in Term 2!

Basic Information

Homework Assignments

Sheet Number Due Date Solution
Assignment 11 April 6 Solution 11
Assignment 10 March 28 Solution 10
Assignment 9 March 21 Solution 9
Assignment 8 March 5 Solution 8
Assignment 7 February 28 Solution 7
Assignment 6 February 14 Solution 6
Assignment 5 February 7 Solution 5
Assignment 4 January 29 Solution 4
Assignment 3 January 24 Solution 3
Assignment 2 January 17 Solution 2
Assignment 1 January 10 Solution 1

Weekly lecture summaries
Week 13 The Fourier transform: some properties; Application to the solution of the heat equation; Review of the term's material.
Week 12 From Taylor series to Fourier series; The Fourier transform.
Week 11 Cauchy's integral formula in an annulus; Computing Laurent series: Examples; The Argument Principle; The winding number; Applications.
Week 10 Summary and further applications of the Residue Theorem; Short review of the midterm; Laurent series and the classification of singularities.
Week 9 The Residue Theorem; Computing residues; Examples; Summary; Application: evaluating convergent series.
Week 8 Application of the maximum modulus principle to count zeros; The fundamental theorem of algebra; Taylor series; Holomorphic functions are analytic; Zeros, poles and their multiplicities; The residue.
Week 7 Cauchy's integral formula (updated notes); Discussion and an example; Holomorphic functions are infinitely differentiable; The mean value theorem; The maximum modulus principle; The case of harmonic functions.
Week 6 Cauchy's theorem (Notes and a proof to be found here); Examples; Review of the midterm.
Week 5 Parametrized curves; Definition and examples; Integration of complex functions; Definition and examples; An upper bound; The case of functions with an antiderivative; Path independence.
Week 4 Trigonometric and hyperbolic functions; The multivalued logarithm; The principal branch of general powers; The multivalued square root; Outlook on Riemann surfaces; Dynamics of driven oscillating systems.
Week 3 The Cauchy-Riemann equations; Conjugate harmonic functions; Examples; The exponential and the logarithm.
Week 2 More on the complex exponential; Subsets: bounded, open connected; Complex functions; Examples; Continuity: Definition and examples; Differentiability; Holomorphic functions.
Week 1 Introduction; The set of complex numbers; The complex conjugate, inverses; The absolute value and the argument; The complex exponential; Trigonometric identities.