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
|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|
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