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.
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 |
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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 |
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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 |
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6 | 2.2 | Power series expansions | 1--19, 22, 23, 25--27 | Tutorial-5 |
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Quiz 3:Drawn from assignments for Week 4; during Tutorials |
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7 | 2.3 | Cauchy's theorem and Cauchy's formula | 1—20, 21(a)–(e) | Tutorial-6 |
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2.3.1 | The Cauchy-Goursat Theorem (optional) | |||
8 | 2.4 | Applications of Cauchy's formula | 1—24 | Tutorial-7 |
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* | Quiz 4:Drawn from assignments for Weeks 6 and 7; during Tutorials |
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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 |
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11 | 3.1 | Zeros of analytic function | 1–9, 12–19 | Tutorial-10 |
3.2 | Maximum modulus and mean value | 1–12 | ||
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12 | 3.3 | Linear fractional transformations | 1—8 | Tutorial-11 |
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3.4 |
Conformal mappings (if time permits) |
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Quiz 7:Drawn from assignments for Weeks 10--11; during Tutorials |
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13 | * | Review | Tutorial-12 (TBA) | |
* | Review | |||
Final Exam |