The exam will involve questions similar to the ones given in the homework assignments from §4.1–4.6, §5.1–5.6, and §6.1–6.7, which basically means that the study topics are

If you study the above subjects well, there is 99% chance you will succeed in the exam, and of course, 100% chance you will succeed in life.

Practice these problems. I will not post answers to these problems.

Please do not hesitate to drop by my office (Burnside 1123) during the exam period.

Date |
Topics |

Mo 9/10 | Complex numbers [§1.1-§1.3] |

We 9/12 | Fractional powers [§1.4]. Limits and continuity [§2.2]. |

Mo 9/17 | Complex derivative. Cauchy-Riemann equations [§2.3] |

We 9/19 | Analyticity [§2.4]. Exponential [§3.1] |

Mo 9/24 | Trigonometric and hyperbolic trigonometric functions [§3.2-3.3]. |

We 9/26 | Logarithm [§3.4-3.5] |

Mo 10/1 | Complex powers [§3.6]. Inverse trigonometric functions [§3.7]. Harmonic functions [§2.5] |

We 10/3 | Line integration [§4.1]. Complex line integration [§4.2] |

Mo 10/8 | Thanksgiving |

We 10/10 | Cauchy-Goursat theorem [§4.3]. Deformation of paths [§4.4] |

Mo 10/15 | Midterm |

We 10/17 | Fundamental theorem of calculus [§4.4]. Cauchy's formula [§4.5] |

Mo 10/22 | Mean value property. Maximum and minimum modulus principles [§4.6] |

We 10/24 | Liouville's theorem. Fundamental theorem of algebra [§4.6] |

Mo 10/29 | Series and sequences [§5.1-5.2]. Uniform convergence [§5.3] |

We 10/31 | Taylor series [§5.4] |

Mo 11/05 | Taylor series [§5.5]. |

We 11/07 | Laurent series [§5.6] |

Mo 11/12 | Isolation of zeroes [§5.7]. Residues [§6.1] |

We 11/14 | Isolated singularities [§6.2] |

Mo 11/19 | Residue calculus [§6.3]. Integration over a circle [§6.4] |

We 11/21 | Integrals over the real line [§6.5] |

Mo 11/26 | Jordan's lemma [§6.6] |

We 11/28 | Examples [§6.5-§6.6] |

Mo 12/03 | Indented contours [§6.7] |

We 12/05 | Branch cuts [§6.8]. Review of selected topics |

Mo 12/17 | Final exam |

§1.2: 14, 17

§1.3: 11

§1.4: 14, 27, 32

§1.5: 8

§2.1: 11, 17

§2.2: 8, 9, 15

§2.3: 7, 13

§2.4: 3, 4, 15

§3.1: 17, 22

§3.2: 14, 28

§3.3: 11, 15

§3.4: 21, 22, 25

§3.5: 2, 3

§3.6: 11, 15, 19, 20

§3.7: 4

§2.5: 9

§4.1: 5, 6

§4.2: 4, 6, 14

§4.3: 15, 17, 21

§4.4: 4, 16, 19

§4.5: 2, 3, 15

§4.6: 5, 12

§5.1: 5, 11, 14

§5.2: 5, 7, 10, 15

§5.3: 3, 5

§5.4: 8, 15, 20

§5.5: 1, 7, 10a, 19

§5.6: 14, 21, 26

§5.7: 7

§6.1: 3, 6, 7

§6.2: 5, 6, 9, 25

§6.3: 4, 5, 26, 31

§6.4: 3, 14

§6.5: 24, 25, 30

§6.6: 8, 9, 13

§6.7: 5, 8, 13

§6.8: 2, 14

Midterm: problems with solutions

**Lectures:** MW 14:35–15:55, Burnside 1B45

**Tutorials:** R 10:35–11:25 Trottier 2100,
R 11:35–12:25 Burnside 1B23

**Office hours:** W 13:30–14:30

**Instructor:** Dr. Gantumur Tsogtgerel

**Teaching assistants:** Ibrahim Al Balushi, Padina Suky, and Mashbat Suzuki

**Calendar description:**
Analytic functions, Cauchy-Riemann equations, simple mappings,
Cauchy's theorem, Cauchy's integral formula,
Taylor and Laurent expansions, residue calculus.
Properties of one and two-sided Fourier and Laplace transforms,
the complex inversion integral, relation between the Fourier and Laplace transforms,
application of transform techniques to the solution of differential equations.
The Z-transform and applications to difference equations.

**Textbook:** David A. Wunsch, *Complex Variables with Applications*, 3rd edition, Addison Wesley 2004

**Topics:** We will cover essentially all of Chapters 1-5, half of Chapter 6, and the beginning of Chapter 7.
These topics can be described as follows.

**Prerequisite:** MATH 264 (Advanced calculus)

**Restriction:** Open only to students in Faculty of Engineering

**Grading:** Homework 20% + max ( Midterm 30% + Final 50% , Midterm 10% + Final 70% )