**Time and Place:** MWF 11:30-12:20 in MSCS 514

**Professor:** Igor E. Pritsker

**Office:** MSCS 519C

**Office Hours:** MW 10:45 - 11:30 a.m. F 10:30-11:30 a.m.

**Office Phone:** 744-8220

**E-mail:** igor@math.okstate.edu

**Web:** http://www.math.okstate.edu/~igor/math4283/math4283_fall2017.html

**Textbook:** Fundamentals of Complex Analysis with Applications to Engineering and Science, by E. B. Saff and A. D. Snider, 3rd ed.

Complex analysis is a classical and beautiful part of mathematics with numerous applications in mechanics, thermodynamics, electrostatics, fluid mechanics and many other sciences. The course and our textbook are tailored for mathematics, science and engineering students who completed the calculus sequence.

** Grading:** There will be three semester tests and the Final Exam. The break up of your course grade is as follows:

Tests 1-3 | 60% (20% each) | |

Homework | 10% | |

Final Exam | 30% |

A | 90-100 | |

B | 80-89 | |

C | 70-79 | |

D | 60-69 | |

F | 59 and lower |

** Attendance is mandatory** in this class.

** Homework** will be assigned daily (see the detailed schedule below), and will be collected periodically. It is required that you complete all homework.

** Extra Credit:** I plan to give a number of extra credit problems. They will be optional, of course.

** Make-up Exams** are given only in cases of serious illness or extreme emergency that prevents you from taking a test at the specified time. You have to contact me before the test and communicate all circumstances.

**
University Syllabus Attachment:**
Contains drop deadlines and procedures, as well as many other important dates and university policies.

Chapter 1 | Chapter 2 | Test 1 | Chapter 3 | Chapter 4 | Test 2 | Chapter 5 | Chapter 6 | Test 3 | Chapter 7 | Final Exam |

**Schwarz-Christoffel toolbox for MATLAB**

**Note:** The homework problems below are assumed to be odd numbered, unless
it is indicated otherwise.

Week | Date | Sec | Page | Topic | Homework |
---|---|---|---|---|---|

1 | M, Aug 21 | 1.1-2 | 1, 7 | Algebra and Representation of Complex Numbers | 3-15, 19-23 (p. 5); 1-13 (p. 12) |

W, Aug 23 | 1.3 | 14 | Vectors and Polar Forms | 3-11, 17 | |

F, Aug 25 | 1.4 | 26 | The Complex Exponential | 1-13 | |

2 | M, Aug 28 | 1.5 | 33 | Powers and Roots | 1-13 |

W, Aug 30 | 1.6 | 39 | Planar Sets | 1-15 | |

F, Sep 1 | 2.1-2 | 53, 58 | Functions of a Complex Variable, Limits and Continuity | 1-7 (p. 56); 1-5, 9-11 (p. 63) | |

3 | M, Sep 4 | Labor Day | |||

W, Sep 6 | 2.3 | 65 | Analyticity | 3-11 | |

F, Sep 8 | 2.4 | 73 | The Cauchy-Riemann Equations | 1-11 | |

4 | M, Sep 11 | 2.5 | 79 | Harmonic Functions | 1-11 |

W, Sep 13 | 2.6 | 87 | Steady State Temperature as a Harmonic Function | 1, 3 | |

F, Sep 15 | Test 1 (1.1-1.6, 2.1-2.5) |
||||

5 | M, Sep 18 | 3.1 | 99 | Polynomials and Rational Functions | 1-7, 11, 13 |

W, Sep 20 | 3.2 | 110 | The Exponential, Trigonometric, and Hyperbolic Functions | 1-9, 15, 17 | |

F, Sep 22 | 3.3 | 118 | The Logarithmic Function | 1-5, 9-15 | |

6 | M, Sep 25 | 3.4 | 125 | Washers, Wedges, and Walls | 1, 2, 3, 4, 5 |

W, Sep 27 | 3.5 | 131 | Complex Powers and Inverse Trigonometric Functions | 1-11 | |

F, Sep 29 | 4.1 | 149 | Contours | 1-11 | |

7 | M, Oct 2 | 4.2 | 161 | Contour Integrals | 1-11 |

W, Oct 4 | 4.3 | 173 | Independence of Path | 1-7 | |

F, Oct 6 | 4.4 | 180 | Cauchy's Integral Theorem | 1-5, 9-13 | |

8 | M, Oct 9 | 4.4-5 | 180, 204 | Cauchy's Integral Theorem and Formula | 15-17 (p. 202), 1-5 (p. 212) |

W, Oct 11 | 4.5 | 204 | Cauchy's Integral Formula | 7-13 | |

F, Oct 13 | 4.6 | 214 | Bounds for Analytic Functions | 1-7, 11 | |

9 | M, Oct 16 | 4.7 | 221 | Applications to Harmonic Functions | 1-5, 11 |

W, Oct 18 | Test 2 (3.1-3.5, 4.1-4.7) |
||||

F, Oct 20 | Fall Break | ||||

10 | M, Oct 23 | 5.1 | 235 | Sequences and Series | 1-11 |

W, Oct 25 | 5.2 | 242 | Taylor Series | 1-7, 13 | |

F, Oct 27 | 5.3 | 252 | Power Series | 1-7, 11 | |

11 | M, Oct 30 | 5.5 | 269 | Laurent Series | 1-9 |

W, Nov 1 | 5.6 | 277 | Zeros and Singularities | 1-5 | |

F, Nov 3 | 5.6 | 277 | Zeros and Singularities | 7-11 | |

12 | M, Nov 6 | 6.1 | 307 | The Residue Theorem | 1-7 |

W, Nov 8 | 6.2 | 314 | Trigonometric Integrals | 1-9 | |

F, Nov 10 | 6.3 | 318 | Improper Integrals | 1-7 | |

13 | M, Nov 13 | 6.7 | 355 | The Argument Principle and Rouche's Theorem | 1-5 |

W, Nov 15 | 6.7 | 355 | The Argument Principle and Rouche's Theorem | 7, 9, 13 | |

F, Nov 17 | Test 3 (5.1-5.3, 5.5, 5.6, 6.1-6.3, 6.7) |
||||

14 | M, Nov 20 | 7.1 | 369 | Invariance of Laplace's Equation | 1, 3, 7 |

W, Nov 22 | Thanksgiving Holidays | ||||

F, Nov 24 | Thanksgiving Holidays | ||||

15 | M, Nov 27 | 7.2 | 377 | Geometric Considerations | 1-7, 11 |

W, Nov 29 | 7.3 | 383 | Moebius Transformations | 1-7, 11 | |

F, Dec 1 | 7.4 | 395 | Moebius Transformations, Continued | 1-9, 15, 17 | |

16 | M, Dec 4 | 7.5 | 407 | The Schwarz-Christoffel Transformation | 1-5 |

W, Dec 6 | 7.6 | 419 | Applications to Electrostatics, Heat Flow, and Fluid Mechanics | 1-5 | |

F, Dec 8 | 7.7 | 432 | Further Applications of Conformal Mapping | ??? | |

17 | F, Dec 15 | Final Exam
(MSCS 514, 10-11:50 a.m.) |