View Specification DocumentMathematics 3U: Complex Methods MATHS3016
- Academic Session: 2026-27
- School: School of Mathematics and Statistics
- Credits: 10
- Level: Level 3 (SCQF level 9)
- Typically Offered: Semester 2
- Available to Visiting Students: No
- Collaborative Online International Learning: No
- Curriculum For Life: No
Short Description
The aim of this course is to introduce students to complex functions and their applications.
Timetable
Lectures at 1.00 pm on Fridays some Thursdays. Tutorials fortnightly, at a time to be arranged.
Requirements of Entry
Maths 2A and 2D at Grade D3 or above.
Please note: this is one of a package of 4 level-3 courses in Mathematics leading to a designated degree in Mathematics.
Full details of the requirements for a designated degree can be found in the University Calendar.
The requirements for the designated degree include a second-year curriculum that includes Mathematics 2A, 2B, 2D and another level 2 Mathematics course. An average grade of D3 over these 4 level-2 courses is required.
Excluded Courses
Methods of Complex Analysis (85JN)
Assessment
90% Examination, 10% Coursework.
Main Assessment In: April/May
Course Aims
The aim of this course is to introduce students to complex functions and their applications. It will focus on properties of analytic functions, contour integration and conformal maps.
Intended Learning Outcomes of Course
By the end of this course students will be able to:
■ state the Cauchy-Riemann equations; use the Cauchy-Riemann equations to determine whether a complex function is analytic on a specified domain; determine whether a function is harmonic and calculate a harmonic conjugate; define and compute with elementary (polynomial, rational, exponential, trigonometric) complex functions; define and compute complex logarithms and powers;
■ compute integrals of continuous functions along curves in the complex plane;
■ state Cauchy's theorem for a simple closed path, Taylor's theorem and Cauchy's integral formula for the n-th derivative;
■ determine the nature of singularities and compute the residues at poles of suitable meromorphic functions; state the residue theorem and use the residue theorem to evaluate real integrals using methods from the course;
■ define the notion of a conformal map; give examples of conformal maps between elementary simple domains; establish properties of bilinear maps; compute the image of a line or circle under a bilinear transformation.