This page is located at https://www.math.ubc.ca/~rfroese/math301/ and will be updated regularly throughout the term.

Note: The focus has now shifted to the canvas page canvas page. Information about tests and exams on this page is out of date.

The second midterm is at https://www.math.ubc.ca:~rfroese/math301/2020WT2midterm2.pdf

- Instructor: Richard Froese
- Email: rfroese@math.ubc.ca
- Office: Math Annex 1106
- Hours: By appointment. I might set fixed hours later in the term.
- Office Phone: 822-3042

Topics. Timings are approximate.

- Complex integration: review and more applications of residue calculus - 1.5 weeks
- Multivalued functions, branch points and branch cuts - 1.5 weeks
- Integrals involving multivalued functions: e.g. - 1.5 weeks
- Conformal mappings and applications: Laplace's equation, ideal fluid flow in 2d - 2.5 weeks
- Poles and zeros of complex functions: Rouche's theorem. - 1 week
- Fourier analysis: Green's functions, delta function - 2 weeks
- Laplace transform: ODE's, delay equations, stability. - 2 weeks

Text

*Fundamentals of Complex Analysis*by Saff and Snider (Third Edition).

You may also consult

*Handwritten notes by Michael Ward (see below)**Complex Variables, Introduction and Applications*by Ablowitz and Fokas*A First Course in Complex Analysis*(Free online textbook) by Beck, Marchesi, Pixton and Sabalka.

We may cover some material not in the textbook.

MWF 11:00-12:00 in MATX 1100

There will be weekly homework assignments. The assignments and due dates will be posted on this page and also on the canvas page for this course. Late homework will not be accepted. Even if you miss the deadline, its a good idea to do the problems, since this is the best way to prepare for the tests and exam. You are welcome to discuss the homework problems with your friends, but are expected to hand in your own work.

There will be two midterm tests in class on *Friday, February 7* and *Friday March 20* as well as a final exam during the April exam period. You will not be permitted to bring calculators or formula sheets to the tests and exam.

The following weightings will be used in computing your final grade:

Homework (lowest two scores dropped): | 10% |

Midterms: | 2 x 20% |

Exam: | 50% |

I will replace your lowest midterm grade with the final exam grade, if this improves your final grade. So if you are sick for one of the midterms, no doctor's note is needed.

Please upload your homework as a pdf file on the canvas page for this course.

Homework 1 | 5.6: 1adeg, 5abcd, 12, 13, 14, 15; 6.1: 1bdf, 3ceg, 5, 7 | Due: Monday Jan 13 |
hmk01.solutions.pdf |

Homework 2 | 6.2: 2, 9, 10 (in 10 evaluate for all ); 6.3: 3, 10, 11 | Due: Monday Jan 20 |
hmk02.solutions.pdf |

Homework 3 | 6.4: 8, 9, 10; 6.5: 6, 9, 12 | Due: Monday Jan 27 |
hmk6.4.pdf, saffsnider6.5_69.pdf, saffsnider6.5_12.pdf |

Homework 4 | 6.6: 3, 5, 8, 10, 12 | Due:Monday Feb 3 |
sec6.6.solns.pdf <- some more details added |

Homework 5 | 6.7 (p.~364) 6, 7, 8, 9, 10, 11. | Due:Monday Feb 24 |
ss6.7.pdf |

Homework 6 | hmk6.problems.pdf | Due:Monday Mar 2 |
conformal.extras.solutions.5.pdf conformal.extras.solutions.1.scan.pdf conformal.extra.solutions.pdf ss7.2.pdf |

Homework 7 | 7.3: 2, 3, 6, 9, 11; 7.4: 4, 8, 9 | Due: Wednesday March 11 |
ss7.3 ss7.4 |

Homework 8 | 7.6: 1, 3, 4, 6, 8, 9 | Due: not due to help you prepare for the midterm |
ss7.6 |

Homework 9 | . | Due: |
. |

Homework 10 | . | Due: |
. |

Date | Reading | Topics |
---|---|---|

Mon Jan 6 | 5.6, 5.7 | Introduction, Classification of singularities, determining the type of singularity from the local behaviour |

Wed Jan 8 | 6.1, 6.2 | Review of residue calculus, computing the residue |

Fri Jan 10 | . | Computing the residue ctd. Review of Cauchy residue formula. residue at infinity, examples |

Mon Jan 13 | 6.3, 6.4 | Examples |

Wed Jan 15 | . | SNOW |

Fri Jan 17 | 6.5 | Indented contours |

Mon Jan 20 | Rosales notes | Multivalued functions, branch points, branch cuts |

Wed Jan 22 | . | more branch cuts |

Fri Jan 24 | 6.6 | finding the branch points for eg |

Mon Jan 27 | . | Range of angles method, cancellation of cuts. |

Wed Jan 29 | . | Dogbone contour example (completed), integrals using pie contours. |

Fri Jan 31 | Some practice problems for the test: hmk4.problems.pdf You don't need to hand these in! Here are solutions hmk4.solutions.pdf | . |

Mon Feb 3 | . | argument principal and winding number |

Wed Feb 5 | . | Rouche theorem, examples, fundamental theorem of algebra, (for the test: integralexample.pdf) |

Fri Feb 7 | . | TEST 1 |

Mon Feb 10 | . | open mapping theorem, proof using Rouche and consequences |

Wed Feb 12 | 6.7 | Nyquist criterion for counting zeros un in half plane. |

Fri Feb 14 | . | . |

Mon Feb 24 | . | conformal maps: mapping properties of |

Wed Feb 26 | . | conformal maps:upper half plane with piecwise constant boundary values |

Fri Feb 28 | . | conformal maps: Joukowski map handwritten notes |

Mon Mar 2 | . | conformal maps: examples using |

Wed Mar 4 | . | FLT |

Fri Mar 6 | . | FLT |

Mon Mar 9 | . | FLT |

Wed Mar 11 | . | FLT:symmetric points tablet notes notes |

Fri Mar 13 | . | Fluid Flow tablet notesnotes |

Mon Mar 16 | . | . |

Wed Mar 18 | . | . |

Fri Mar 20 | . | TEST 2 |

Mon Mar 23 | . | . |

Wed Mar 25 | . | . |

Fri Mar 27 | . | . |

Mon Mar 30 | . | . |

Wed Apr 1 | . | . |

Fri Apr 3 | . | . |

Mon Apr 6 | . | . |

Wed Apr 8 | . | . |

Here are a collection of handwritten notes by Michael Ward that you might find useful.

- m301.01.integ.pdf
- m301.02.sum.pdf
- m305_multi.pdf
- m305_branch.pdf
- m301.04.imval.pdf
- m301.05.res.pdf
- m301.06.map1.pdf
- m301.07.map2.pdf
- m301.08.conf.pdf
- m301.09.symm.pdf
- m301.10.fluid.pdf
- m301.11.four.pdf
- m301.12.lapl1.pdf
- m301.13.nyquist.pdf
- m301.14.lapl2.pdf

Scans of the first homework problems (oops, last page ) from text.

This file contains some basic examples of the residue calculus.

Here is the Math 300 exam from last term. It might help you review even if you were not in that class.

Here are some basic estimates that we use repeatedly.

Here are some notes on evaluating infinite sums using residues.

Here are some notes by Rosales on branch points and cuts.

Notes for the lecture on symmetric points.

Fourier and Laplace transform table.

Old midterms 1: 2011WT2midterm1.pdf, 2011WT2midterm1.solutions.pdf, 2012WT2midterm1.pdf, 2012WT2midterm1.solutions.pdf, 2016WT2midterm1.pdf, 2016WT2midterm1.solutions.pdf, 2018WT2midterm1.solutions.pdf

This yearâ€™s midterm 1: 2019WT2midterm1.pdf

Old midterms 2: 2011WT2midterm2.pdf, 2011WT2midterm2.solutions.pdf, 2012WT2midterm2.pdf 2012WT2midterm2.solution.pdf 2016WT2midterm2.pdf 2017WT2midterm2.pdf

Old exams:
2011WT2final.pdf
2011WT2final.solutions.pdf
2012WT2final.pdf
Math_301*April_2005*(Section_201).pdf
Math_301*April_2007*(Section_201).pdf
Math_301_April_2008.pdf
Math_301_April_2009.pdf
Math_301_April_2010.pdf