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The aim of this course is to explore topics such as complex algebra and functions, analyticity, contour integration. In addition to that, some more topics will be discussed in this course like Cauchy’s theorem, singularities, Taylor and Laurent series, residues, evaluation of integrals. At the end of the course multivalued functions, potential theory in two dimensions, Fourier analysis and Laplace transforms will be covered too.


This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.


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Course Credit: MIT

Course Curriculum

lecture1 Simple Mappings az+b, z2, √z 00:10:00
lecture2 Complex Exponential 00:10:00
lecture3 Complex Trigonometric and Hyperbolic Functions 00:02:00
lecture4 Contour Integrals 00:05:00
lecture5 Bounds,Liouville’s Theorem,Maximum Modulus Principle 00:05:00
lecture6 Radius of Convergence of Taylor Series 00:10:00
lecture7 Real Integrals From,Conversion to cx Contours 00:05:00
lecture8 Invariance of Laplace’s Equation 00:05:00
lecture9 BilinearMobius Transformations 00:02:00
lecture10 Applications I 00:02:00
lecture11 Applications II 00:03:00
lecture12 Complex Fourier Series 00:20:00
lecture13 Oscillating Systems,Periodic Functions 00:10:00
lecture14 Questions of Convergence,Scanning Function,Gibbs Phenomenon 00:10:00
lecture15 Special Topic The Magic of FFTs I 00:25:00
lecture16 Special Topic The Magic of FFTs II 00:15:00
Submit Your Assignment 00:00:00
Certification 00:00:00

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