Introduction covers complex numbers; complex functions; sequences and continuity; and differentiation of complex functions. Representation formulas covers integration of complex functions; Cauchy’s theorem and Cauchy’s integral formula; Taylor series; and Laurent series.
Calculus of residues covers residue calculus; winding number and the location of zeros of complex functions; analytic continuation; Euler’s gamma function and Riemann’s zeta function. Finally, Applications covers conformal mappings; fluid flows; complex analytic dynamics; Julia sets; and the Mandelbrot set. You need a sound knowledge of differentiation and integration of real functions for this Complex Analysis module at The Open University UK.
What you will study
There is no real number whose square is –1, but mathematicians long ago invented a system of numbers, called complex numbers, in which the square root of –1 does exist. These complex numbers can be thought of as points in a plane, in which the arithmetic of complex numbers can be pictured. When the ideas of calculus are applied to functions of a complex variable a powerful and elegant theory emerges, known as complex analysis.
The module shows how complex analysis can be used to:
The module consists of thirteen units split between four books:
Book A: Complex numbers and functions
Book B: Integration of complex functions
Book C: Geometric methods in complex analysis
Book D: Applications of complex analysis
The texts have many worked examples, problems and exercises (all with full solutions), and there is a module handbook that includes reference material, the main results and an index.
You can apply until:
Always verify the dates on the programme website programme website .
You will learn
Successful study of this module should enhance your skills in understanding complex mathematical texts, working with abstract concepts, constructing solutions to problems logically and communicating mathematical ideas clearly.
This programme requires students to demonstrate proficiency in English.
This is an OU level 3 module. Level 3 modules build on study skills and subject knowledge acquired from studies at levels 1 and 2. They are intended only for students who have recent experience of higher education in a related subject, preferably with the OU.
You need proficiency in algebra, trigonometry and calculus, and the mathematical maturity gained from OU level 2 mathematics modules. To study this module you should have a grade 2 pass (minimum) in at least one of the following: Pure mathematics (M208), Mathematical methods, models and modelling (MST210), Mathematical methods (MST224), or the equivalent.
Check the programme website for information about funding options.
StudyPortals Tip: Students can search online for independent or external scholarships that can help fund their studies. Check the scholarships to see whether you are eligible to apply. Many scholarships are either merit-based or needs-based.
Together with the ISIC Association and British Council IELTS, StudyPortals offers you the chance to receive up to £10000 to expand your horizon and study abroad. We want to ultimately encourage you to study abroad in order to experience and explore new countries, cultures and languages.