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This is an advanced undergraduate course dealing with calculus in one complex variable with geometric emphasis. Since the course Analysis I (18.100B) is a prerequisite, topological notions like compactness, connectedness, and related properties of continuous functions are taken for granted. This course covers the algebra of complex numbers, the geometry of the complex plane, the spherical representation, the Analytic functions and the rational functions.


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

Module 01
lecture1 The algebra of complex numbers 00:05:00
lecture2 Exponential function and logarithm for a complex argument 00:10:00
lecture3 Analytic functions; rational functions 00:05:00
lecture4 Power series 00:05:00
lecture5 Exponentials and trigonometric functions 00:05:00
lecture6 Conformal maps; linear transformations 00:05:00
lecture7 Linear transformations (cont.) 00:10:00
lecture8 Line integrals 00:05:00
lecture9 Cauchy-Goursat theorem 00:05:00
lecture10 The special cauchy formula and applications 00:05:00
lecture11 Isolated singularities 00:05:00
lecture12 The local mapping; Schwarz’s lemma and non-Euclidean interpretation 00:10:00
Module 02
lecture13 The general Cauchy theorem 00:10:00
lecture14 The residue theorem and applications 00:10:00
lecture15 Contour integration and applications 00:10:00
lecture16 Harmonic functions 00:10:00
lecture17 Mittag-Leffer’s theorem 00:10:00
lecture18 Infinite products 00:10:00
lecture19 Normal families 00:05:00
lecture20 The Riemann mapping theorem 00:05:00
lecture21_22 The prime number theorem 00:20:00
lecture23 The extension of the zeta function to C, the functional equation 00:05:00
Submit Your Assignment 00:00:00
Certification 00:00:00

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