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. |

## Calendar

## Course Info

##### Learning Resource Types

*grading*Exams with Solutions

*assignment_turned_in*Problem Sets with Solutions