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This is an advanced undergraduate course dealing with calculus in one complex variable with geometric emphasis.
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English
English [CC]
FREE
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Description
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 content
- 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
Instructor
Massachusetts Institute of Technology
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1916
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