18.04 | Fall 1999 | Undergraduate

Complex Variables with Applications

Calendar

Week # Lec # Topics Key Dates
1 1 1.1 Complex Algebra. Complex Plane. Motivation and History  
  2 1.2 Polar Form. Complex Exponential. DeMoivre’s Theorem  
  3 1.3 Newton’s Method. Fractals  
2-3 4 2.1 Complex Functions. Analyticity  
  5 2.2 Cauchy-Riemann Eqns. Harmonic Functions  
  6 2.3 Exponential and Trig. Functions. Logarithmic Function  
  7 2.4 Branch Cuts. Applications  
  8 2.5 Complex Powers and Inverse Trig. Functions  
4-5 9 3.1 Contour Integrals  
  10 3.2 Path Independence  
  11 3.3 Cauchy’s Theorem  
  12 3.4 Cauchy’s Integral Formula  
  13 3.5 Liuville’s Theorem. Mean Value and Max. Modulus  
  14 3.6 Dirichlet Problem  
  15   EXAM #1: covering 1, 2 and about 1/2 of 3.
6 16 4.1 Taylor Series. Radius of Convergence  
  17 4.2 Laurent Series  
  18 4.3 Zeros. Singularities. Point at Infinity  
7-8 19 5.1 Residue Theorem. Integrals over the Unit Circle  
  20 5.2 Real Integrals. Conversion to Complex Contours  
  21 5.3 Trig. Integrals. Jordan’s Lemma  
  22 5.4 Indented Contours. Principal Value  
  23 5.5 Integrals Involving Multi-valued Functions  
  24 5.6 Argument Principle and Rouche’s Theorem  
  25   EXAM #2: covering second half of 3, 4 and 5.
9-10 26 6.1 Complex Fourier Series  
  27 6.2 Oscillating Systems. Periodic Functions  
  28 6.3 Applications of Fourier Series  
  29 6.4 Fourier Transform and Applications  
  30 6.5 Laplace Transform and Inversion Formula  
11-12 31 7.1 Invariance of Laplace’s Eqn. Conformality  
  32 7.2 Inversion Mapping. Bilinear Mappings  
  33 7.3 Examples and Applications  
  34 7.4 More Examples (if time permits)  
  35   EXAM #3: covering 6 and 7.

Course Info

Instructor
Departments
As Taught In
Fall 1999
Learning Resource Types
Exams with Solutions
Problem Sets with Solutions