Complex Analysis 1
| Code | School | Level | Credits | Semesters |
| MATH2101 | Mathematical Sciences | 2 | 10 | Autumn UK |
- Code
- MATH2101
- School
- Mathematical Sciences
- Level
- 2
- Credits
- 10
- Semesters
- Autumn UK
Summary
This course introduces the theory and applications of functions of a complex variable, using an approach oriented towards methods and applications. The elegant theory of complex functions is developed and then used to evaluate certain real integrals. Topics covered include:
- An introduction to the topology of the (complex) plane.
- Application of the Cauchy-Riemann equations to identify analytic functions.
- Calculation of Taylor and Laurent series expansions of analytic functions.
- Calculation and application of contour integrals.
- Evaluation of real definite integrals using residues.
Target Students
Single Honours and Joint Honours students from the School of Mathematical Sciences, Mathematical Physics students, Natural Sciences students, Liberal Arts students.
Classes
- One 2-hour lecture
- One 1-hour lecture
Teaching will be through a variety of methods, with the delivery tailored to the material on a week-by-week basis.
Assessment
- 40% Coursework 1: Summative assessment based on tasks distributed through the semester.
- 60% Exam 1 (2-hour): 2 hour written examination – Autumn
Assessed by end of autumn semester
Educational Aims
The aim of this course is to introduce the theory of functions of a complex variable, a topic which is very important for applications as well as leading to more advanced study in later years.Learning Outcomes
Single Honours and Joint A student who completes this course successfully will be able to:
L1 – Reason logically and construct rigorous mathematical arguments related to basic plane topology and results in the theory of complex analysis.
L2 – Demonstrate an understanding of the concept of an analytic function, including identification of analytic functions using the Cauchy-Riemann equations when appropriate.
L3 – Calculate and manipulate Taylor and Laurent series expansions to a high degree of accuracy and demonstrate awareness of the domain of validity of such expansions.
L4 – Estimate the magnitude of contour integrals and directly compute the value of elementary examples.
L5 – Apply complex variable methods, including calculation of residues, to evaluate real definite integrals.
L6 – Present conclusions and solutions to problems verbally or in writing, using structured and mathematically rigorous arguments and contextually appropriate language.