Functions of a Complex Variable | Mathematics | MIT OpenCourseWare

Course Info

Instructor

Prof. Sigurdur Helgason

Departments

Mathematics

As Taught In

Fall 2008

Level

Undergraduate

Topics

Mathematics

Learning Resource Types

Exam Solutions

Exams

Lecture Notes

Problem Set Solutions

Problem Sets

Download Course

Lecture Notes

Lecture 1: The algebra of Complex numbers

Lecture 2: Exponential function & Logarithm for a complex argument

Lecture 3: Analytic Functions; Rational Functions

Lecture 4: Power Series

Lecture 5: Exponentials and Trigonometric Functions

Lecture 6: Conformal Maps; Linear Transformations

Lecture 7: Linear Transformations

Lecture 8: Line Integrals

Lecture 9: Cauchy-Goursat Theorem

Lecture 10: The Special Cauchy’s Formula and Applications

Lecture 11: Isolated Singularities

Lecture 12: The Local Mapping. Schwarz’s Lemma and non-Euclidean interpretation

Lecture 13: The General Cauchy Theorem

Lecture 14: The Residue Theorem and Application

Lecture 15: Contour Integration and Applications

Lecture 16: Harmonic Functions

Lecture 17: Mittag-Leffer’s Theorem

Lecture 18: Infinite Products

Lecture 18: Infinite Products

Lecture 19: Normal Families

Lecture 20: The Riemann Mapping Theorem

Lecture 21 and 22: The Prime Number Theorem

Lecture 23: The Gamma Function and the Functional Equation for the Zeta Function

Course Info

Instructor

Prof. Sigurdur Helgason

Departments

Mathematics

As Taught In

Fall 2008

Level

Undergraduate

Topics

Mathematics

Learning Resource Types

Exam Solutions

Exams

Lecture Notes

Problem Set Solutions

Problem Sets

Download Course

MIT Open Learning

Over 2,500 courses & materials

Freely sharing knowledge with learners and educators around the world. Learn more

© 2001–2026 Massachusetts Institute of Technology

Accessibility

Creative Commons License

Terms and Conditions

Proud member of:

© 2001–2026 Massachusetts Institute of Technology