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Browse materialsMIT 18.04 · Fall 1999

Complex Variables with Applications

Subjects: Algebra · Calculus · Mathematics

Art: Johannes Kepler, Konjukce Saturnu a Jupiteru Originál, 1596 · Public domain

Instructor: Prof. R. Rosales
Term: Fall 1999
Level: Undergraduate
What's inside: 1 reading · 23 other files · 32 web pages
Materials open: MIT OCW

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18.04 · Spring 2018 · Study here
18.04 · Fall 1999 · Study here (this version)

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About this course

Source: MIT OpenCourseWare 18.04 Complex Variables with Applications, Fall 1999, Prof. R. Rosales — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

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Assignments

18 problem sets

Exams

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MATLAB® TutorialPDF Download

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1 file

CourseMatLabscripts.pdfPDF Download

54 images

MIT OpenCourseWare, Prof. R. Rosales, 18.04 Complex Variables with Applications, Fall 1999.

License: CC BY-NC-SA 4.0 · Edition: Fall 1999 · Open the original course on OCW ↗

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Complex Variables with Applications

Before you start

What's here, and what isn't

Not included here

Materials by section

Assignments

Exams

Tools

Other materials from this course

Lecture 1: 1

Lecture 2: 1.2 Polar Form. Complex Exponential. DeMoivre’s Theorem

Lecture 3: 1.3 Newton’s Method. Fractals

Lecture 4: 2-3

Lecture 5: 2.2 Cauchy-Riemann Eqns. Harmonic Functions

Lecture 6: 2.3 Exponential and Trig. Functions. Logarithmic Function

Lecture 7: 2.4 Branch Cuts. Applications

Lecture 8: 2.5 Complex Powers and Inverse Trig. Functions

Lecture 9: 4-5

Lecture 10: 3.2 Path Independence

Lecture 11: 3.3 Cauchy’s Theorem

Lecture 12: 3.4 Cauchy’s Integral Formula

Lecture 13: 3.5 Liuville’s Theorem. Mean Value and Max. Modulus

Lecture 14: 3.6 Dirichlet Problem

Lecture 15: EXAM #1: covering 1, 2 and about 1/2 of 3.

Lecture 16: 6

Lecture 17: 4.2 Laurent Series

Lecture 18: 4.3 Zeros. Singularities. Point at Infinity

Lecture 19: 7-8

Lecture 20: 5.2 Real Integrals. Conversion to Complex Contours

Lecture 21: 5.3 Trig. Integrals. Jordan’s Lemma

Lecture 22: 5.4 Indented Contours. Principal Value

Lecture 23: 5.5 Integrals Involving Multi-valued Functions

Lecture 24: 5.6 Argument Principle and Rouche’s Theorem

Lecture 25: EXAM #2: covering second half of 3, 4 and 5.

Lecture 26: 9-10

Lecture 27: 6.2 Oscillating Systems. Periodic Functions

Lecture 28: 6.3 Applications of Fourier Series

Lecture 29: 6.4 Fourier Transform and Applications

Lecture 30: 6.5 Laplace Transform and Inversion Formula

Lecture 31: 11-12

Lecture 32: 7.2 Inversion Mapping. Bilinear Mappings

Lecture 33: 7.3 Examples and Applications

Lecture 34: 7.4 More Examples (if time permits)

Lecture 35: EXAM #3: covering 6 and 7.