The imaginary number is a fine and wonderful recourse of the divine spirit,
almost an amphibian between being and not being.
Gottfried Whilhem Leibniz  The shortest path between two truths in the real domain passes
through the complex domain.
 Jacques Hadamard 
The complexity of the complex variable course is
more imaginary than real.  An encouraging observation 
"The number you have dialed is imaginary.
Please rotate your phone 90 degrees and try again."
 A math joke 
Instructor:
Andrej V. Cherkaev,
professor

Exam  firstst midterm  second midterm  Final 
Sections  1  29  30  64  1  92 
Calculator: A calculator is not required for the course, although it may be useful for some homework problems. Calculators will be forbidden in exams.
Final exam: Half of the final will be devoted to material covered after the second midquarter exam. The rest will be comprehensive. Students must take the final to pass the course.
Grades: The final grade will be based on the following score: Two midquarter exams (50%) + homework(10%) + final score (40%).
ADA: The Americans with Disabilities Act requires that reasonable accommodations be provided for students with physical, sensory, cognitive, systemic, learning and psychiatric disabilities. Please contact me at the beginning of the quarter to discuss any such accommodations for the course.
Section  Topic  Page [Problems] 
1 2  Complex Numbers  5 [2, 4, 5, 9, 12] 
3 5  Geometric Prop.  11 [3, 10, 14], 17 [1, 4, 5, 8, 13] 
6 8  Roots  22 [1, 4, 6, 7, 8], 25 [15] 
914  Mappings  32 [3, 4, 5, 7] 
1518  Derivatives  42 [2, 4, 9], 47 [1, 3, 8], 54 [1, 2d, 7] 
1922  CR Eqns.  62 [1, 6, 7b, 10, 12] 
2325  Exponentials  68 [3, 6, 8, 10], 71 [2, 7, 9], 74 [2, 5] 
2629  Logs  79 [3, 6, 14], 84 [2, 6, 9, 10, 11] 
3033  Integrals  92 [3, 4, 11], 102 [1, 5, 7, 11, 13, 15] 
3435  Contour Integrals  119 [2, 3, 7] 
3638  Cauchy Goursat  128 [1, 3, 5] 
3940  Liouville's Th.  136 [1, 2, 3, 4, 5, 6] 
4345  Algebra & Series  156 [4, 6, 8] 
4651  Laurent Series  172 [1, 3, 10, 15] 
5355  Residues  188 [1, 2, 4, 7] 
5658  Poles  197 [1, 2, 3, 4, 10] 
6061  Evaluation of integrals  208 [1, 2, 3, 4, 6, 9], 214 [1, 2, 6, 13)] 
6264  Improper Integrals  218 [1, 3, 6], 226 
6667  Other applications  [1, 2, 3, 7], 242 [1, 6] 
6872  Linear fractions  250 [2, 8, 11, 17], 258 [2, 5, 6, 13] 
7981  Expsinlogroot  266 [4, 5, 6, 9], 275 [3, 4, 8] 
8283  Harmonic Mapping  289 [1, 4, 6], 297 [1, 3, 9] 
8485  Steady Temp.  307 [1, 2, 5, 8] 
8687  Electrost. potential  312 [2, 3, 7, 10] 
8892  Stream Function  322 [3, 4, 5, 7, 11] 
Quadratic, cubic and quartic equations; introduction of complex numbers
Irrotational flows by conformal mappings
Interactive page, a lot of pictures.
Lectures on
Advanced Topics in Theory of Functions of a Complex Variable by
Norm Bleistein
COMPLEX ANALYSIS: Mathematica 4.0 Notebooks by
John H. Mathews, and Russell W. Howell. Lecture notes and Mathematicabased
examples, including Julia & Mandelbrot sets, conformal mappings, etc.
68 lessons by Dr. John H. Mathews.
A part of the book, Complex Analysis for
Mathematics & Engineering, 4th Ed, 2001, by John H. Mathews and
Russell W. Howell
Please let me know if you find
interesting web sites related to the course
Thank you.