# Math 301

## Applied Complex Analysis

**Instructor:** Omer Angel

**email:** angel@math.ubc.ca (please specify "MATH 100" in the subject).

**Location:** Tu,Th 11:00-12:00 at LSK 460.

**Office hours:** Math Annex 1210, Monday after class, Friday 9:00-9:50
or by appointment.

### News

**Midterm information:** Midterm 1 will cover singularities and residue
theory, Cauchy's residue theory and it's application for computing
integrals over the reals, multi-valued functions, branch points and
branches, and integrals involving multi-valued functions. The relevant
sections are 6.1 to 6.6, and 3.3 for some multi-valued
functions. Sample midterm
hints actual Midterm solutions

Midterm 2 will cover conformal maps: sections 7.1,7.2,7.3,7.4. Older material may be needed, but will not be central. Sample midterm hints actual Midterm solutions

Additional notes on Branch points and branch cuts.

due date | problems | template | solutions |
---|---|---|---|

Not due | Homework 0 | template | PDF LaTeX |

Jan. 15 | Homework 1 | template | PDF LaTeX |

Jan. 22 | Homework 2 | template | PDF LaTeX |

Jan. 29 | Homework 3 | template | PDF LaTeX |

Feb. 5 | Homework 4 | template | PDF LaTeX |

Not due | Homework 5 | template | PDF LaTeX |

Feb. 26 | Homework 6 | template | PDF LaTeX |

Mar. 5 | Homework 7 | template | PDF LaTeX |

Mar. 14 | Homework 8 | template | PDF LaTeX |

Not due | Homework 9 | template | PDF LaTeX |

Mar. 26 | Homework 10 | template | PDF LaTeX |

Apr. 2 | Homework 11 | template | PDF LaTeX |

not due | Homework 12 | template | PDF LaTeX |

Additional example for section 6.2: Integration of forms involving trigonometric functions.

### Course Outline

- Complex integration - 1 week
- Multivalued functions, branch points and branch cuts - 1.5 weeks
- Integrals involving multivalued functions - 1.5 weeks
- Conformal mappings and applications - 3 weeks
- Poles and zeros of complex functions - 1 week
- Laplace transform - 2 weeks
- Fourier analysis - 2 weeks

### Textbook

*Fundamentals of Complex Analysis*by Saff and Snider (Third Edition). We may cover some material not in the textbook.

### Evaluation:

The final mark will be based on homework (15%), two mid-terms (35%) and the final exam (50%).**Homework:** Weekly assignments will be given. These are due at the
beginning of class on the due date, normally each Wed. Answers will be
posted online on the due date, and late assignments will not be
accepted. The single lowest assignment will be ignored. All submitted
assignments **must be typeset** (see
some suggestions
and tips). Due dates for assignments: Jan. 15,22,29; Feb. 5,26;
Mar. 5,12,26; Apr. 2.

** Mid-terms:** Mid-terms will take place during the regularly scheduled
class on ** Wednesday, February 12** and ** March 19**.

Midterm 1 will cover singularities and residue theory, Cauchy's residue theory and it's application for computing integrals over the reals, multi-valued functions, branch points and branches, and integrals involving multi-valued functions. The relevant sections are 6.1 to 6.6, and 3.3 for some multi-valued functions. Sample midterm

**Final Examination:** will take place on April 30, at 12:00 (the
last possible date).

**Missed mid-terms and assignments** will normally receive a zero grade.
Exceptions may be granted in two cases: prior consent of the
instructor or a medical emergency. In the latter case, the instructor
must be notified as soon as possible (preferably before the test), and
presented with a doctor's note immediately upon the student's return to
UBC. When an exception is granted for a missed test, there is no make-up
test, and the final exam mark will be used.