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Created by:
Last updated:
December 24, 2022
Duration:
Unlimited Duration
FREE
This course includes:
Unlimited Duration
Badge on Completion
Certificate of completion
Unlimited Duration
Description
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 offers biweekly problem sets with solutions, two term tests and a final exam, all with solutions.
Course Curriculum
- The algebra of complex numbers Unlimited
- Exponential function and logarithm for a complex argument Unlimited
- Analytic functions Unlimited
- Power series Unlimited
- Exponentials and trigonometric functions Unlimited
- Conformal maps; Unlimited
- Linear transformations (cont.) Unlimited
- Line integrals Unlimited
- Cauchy-Goursat theorem Unlimited
- The special cauchy formula and applications Unlimited
- Isolated singularities Unlimited
- The local mapping Unlimited
- The general Cauchy theorem Unlimited
- The residue theorem and applications Unlimited
- Contour integration and applications Unlimited
- Harmonic functions Unlimited
- Mittag-Leffer’s theorem Unlimited
- Infinite products Unlimited
- Normal families Unlimited
- The Riemann mapping theorem Unlimited
- The prime number theorem Unlimited
- The extension of the zeta function to C, the functional equation Unlimited
About the instructor
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Massachusetts Institute of Technology
