## MAT334 Complex Variables

Explanation Fall 2018: Assigned Exercises (Home Assignments) mainly from
Stephen D. Fisher. Complex Variables 2nd Edition (Dover Books on Mathematics). ISBN-13: 978–0486406794,ISBN-10: 0486406792 and some extra problems, posted on this cite.

Home assignments will be neither submitted, nor graded but... there will be 7 quizzes of duration 15–20 min. from the assigned homework. Each consecutive quiz covers homework from the previous quiz up to and including the week preceding the week this quiz is administered.
You may discuss home assignments on forum.

• Click to see extra problems and lecture notes.
• Week 1 is incomplete (only Thu, Fri); Week 13 is also incomplete (only Mon—Wed and may be Thu for Thanksgiving Monday makeup.
• Only current week is finalized. Please check Saturday or Sunday for forthcoming week.

### Week 9: November 12—16, 2018

 Week Sections Topics Home Assignment Problems Notes 1–2 1.1 The complex numbers and the complex plane 1–6, 13, 15 No quiz weeks 1–3 1.1.1 A formal view of the complex numbers 3, 7–10 1.2 Some geometry 1–18, 20–22,24, 23–27 Tutorial-1 Week 2 1.3 Subsets of the plane 1–10, 15, 18, 19 3 1.4 Functions and limits 1–25, 30–41 Tutorial-2 1.5 Exponential and logarithmic functions 1–14, 16–18, 21, 22 1.5 Trigonometric and inverse trigonometric functions 4 1.5 Mappings with the exponential, logarithmic, and trigonometric functions 23—30 Tutorial-3 1.6 Line integrals, Green's theorem (real variables) LN-1.6-1 1.6 Line integrals, Green's theorem (complex variables) 1 – 10, 17 - 20;     LN-1.6-2 Quiz 1:Drawn from assignments for Week 1--2; during Tutorials 5 2.1 Analytic functions Cauchy-Riemann equations 1, 2, 4, 6, 7, 8, 12, 14, 16, 18, 20, 22, 24, 26 Tutorial-4 2.1 Harmonic functions, conjugate harmonic functions 2.1.1 Flows, fields, and analytic functions: optional) 2, 4, 6, 8: optional: post solutions on forum for karma--after I post problems Quiz 2:Drawn from assignments for Week 3; during Tutorials 6 2.2 Power series expansions 1--19, 22, 23, 25--27 Tutorial-5 * * Quiz 3:Drawn from assignments for Week 4; during Tutorials 7 2.3 Cauchy's theorem and Cauchy's formula 1—20, 21(a)–(e) Tutorial-6 * 2.3.1 The Cauchy-Goursat Theorem (optional) Test 1 Arrangement Scope 8 2.4 Applications of Cauchy's formula 1—24 Tutorial-7 * * Quiz 4:Drawn from assignments for Weeks 6 and 7; during Tutorials 9 2.5 Isolated singularities 1— 27 Tutorial-8 * Post on Forum solutions Bonus: 28—31 * Quiz 5:Drawn from assignments for Week 8; during Tutorials Reading Week 10 2.6 The residue theorem, evaluation of definite integrals 1— 23 Tutorial-9 * Post on Forum solutions Bonus: 24—26 * Post on Forum solutions Bonus: 27—34 Quiz 6:Drawn from assignments for Week 9; during Tutorials 11 3.1 Zeros of analytic function 1–9, 12–19 Tutorial-10 3.2 Maximum modulus and mean value 1–12 * Test 2 Arrangement Scope 12 3.3 Linear fractional transformations 1—8 Tutorial-11 * 3.4 Conformal mappings (if time permits) - Quiz 7:Drawn from assignments for Weeks 10--11; during Tutorials 13 * Review Tutorial-12 (TBA) * Review Final Exam