Math 132: Complex Analysis for Applications
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| Date | Topic | Homework
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| 1/5 (Mon) | Section I.1: Complex numbers | I.1:
1(a)(b)(c)(f)(g),2,4,5,8,9,10 |
| 1/7 (Wed) | Section I.2: Polar representation |
I.2: 1(a)(b)(c)(d)(f)(h),5,6,7,8 |
| 1/9 (Fri) | Section I.3: Stereographic projection Section I.4: The square and the square root |
I.3: 1,2,4 I.4: 1(b)(d)(e)(f),2,3,4(a)(b) |
| 1/12 |
Sections I.5 and I.6:
Exponentials and logarithms |
I.5:
1(b)(c)(d)(f),2(a)(b)(c),3 I.6: 1,2(a)(b)(c)(e)(f),3,4 |
| 1/13 or 1/15 | Quiz 1 in discussion | |
| 1/14 |
Sections I.7 and I.8: Power functions and trigonometric functions | I.7: 1,2,5 I.8: 1,2,3 |
| 1/16 |
Section II.1: Review of analysis (limits and continuity) | II.1: 1(a)(b),2,11,15 |
| 1/19 | University Holiday (MLK Jr Day) | |
| 1/20 or 1/22 | Quiz 2 in discussion | |
| 1/21 | Section II.2: Differentiation | II.2: 1(a)(c)(g),5 Prove directly from the definition that f(z)=z^2 is analytic. Prove directly from the definition that f(z)=\overline{z} is not analytic. Here \overline{z} is the complex conjugate of z. |
| 1/23 | Sections II.3 and II.5: Cauchy-Riemann equations and harmonic functions | II.3: 1,2,3,5 II.5: 1(a)(b)(c),2 |
| 1/26 | Section II.6: Conformal mappings Section II.7: Fractional linear transformations, Day I |
II.6: 1,2,4 |
| 1/27 or 1/29 | Quiz 3 in discussion | |
| 1/28 |
Section II.7: Fractional linear transformations, Day II | II.7: 1(a)(b)(c),3,4 |
| 1/30 |
Section III.1: Line integrals and Green's theorem | III.1: 1,2,3,4 |
| 2/2 | Section III.2: Differentials and independence of path | III.2: 1,2,3 |
| 2/3 or 2/5 | Quiz 4 in discussion | |
| 2/4 |
Section IV.1: Complex line integrals |
IV.1: 1, 2(a)(b),4 |
| 2/6 |
Section IV.2: Fundamental
theorem of calculus for line integrals Section IV.3: Cauchy's theorem |
IV.2: 1(a)(b),2,3 IV.3: 4 |
| 2/9 | Midterm Exam | midterm
info sample midterm problems |
| 2/11 |
Section IV.4: Cauchy integral formula | IV.4: 1(a)(b)(c),2 |
| 2/13 |
Section IV.5: Liouville's theorem | IV.5: 1,2 |
| 2/16 | University Holiday (Presidents' Day) | |
| 2/17 or 2/19 | Quiz 5 in discussion | |
| 2/18 |
Section V.1: Infinite
series Section V.2: Convergence of functions |
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| 2/20 |
Section V.3: Power series |
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| 2/23 |
Section V.4: More power
series |
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| 2/24 or 2/26 | Quiz 6 in discussion | |
| 2/25 | Section VI.1: Laurent series |
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| 2/27 |
Section VI.2: Isolated singularities |
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| 3/2 |
Section VI.3: Partial fractions |
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| 3/3 or 3/5 | Quiz 7 in discussion | |
| 3/4 |
Section VII.1: Residues |
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| 3/6 |
Section VII.2: Some integrals |
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| 3/9 |
Section VII:3: More integrals |
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| 3/10 or 3/12 | Quiz 8 in discussion | |
| 3/11 |
Section VII.4: Even more integrals |
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| 3/13 |
Review |
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| 3/16 (Mon) | Final
Exam 8-11am Location TBA |
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