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| Week | Lecture No. | Date | Chapter/Exam | Homework |
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1 | 1 | Tue, Jan 17 | Introduction. Course logistics.
Ch. 2A, Complex numbers and complex variables: coordinate and polar
form; Euler’s formula; trigonometric identities; complex
roots. Mathematica: Integrate[], N[], Sin[], Pi
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| | 2 | Thu, Jan 19 | Ch. 2B, Analytic functions;
Cauchy-Riemann equations.
OofMP: (1−є)n ≈ e−nє,
∫−11cos(x)100dx, Gaussian integrals.
Mathematica: Plot[]
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2 | 3 | Tue, Jan 24 | Ch. 2C, Contour integrals
in the complex plane. OofMP: Feynman’s “different box of tools”
– evaluation of integrals by differentiation with respect to a
parameter.
| HW1 due |
| | 4 | Thu, Jan 26 | Ch. 2C, Contour integrals
of analytic functions; Ex: ∫0∞cos(x2)dx ;
Cauchy integral formula.
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3 | 5 | Tue, Jan 31 | Ch. 2C, Taylor and Laurent series;
isolated singularities; Cauchy residue theorem.
| HW2 due |
| | 6 | Thu, Feb 2 | Ch. 2D, Calculating residues.
Evaluation of integrals I.
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4 | 7 | Tue, Feb 7 | Ch. 2D, Evaluation of integrals II.
| HW3 due |
| | 8 | Thu, Feb 9 | Ch. 2F, Guest lecture: Fourier
integrals
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5 | 9 | Tue, Feb 14 | Ch. 2D, Evaluation of integrals
III.
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| | | Thu, Feb 16 | Midterm I | |
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6 | 10 | Tue, Feb 21 | | |
| | 11 | Thu, Feb 23 | | |
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7 | 12 | Tue, Feb 28 | | HW5 due |
| | 13 | Thu, Mar 1 | | |
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8 | | Tue, Mar 6 | Spring recess | |
| | | Thu, Mar 8 | Spring recess | |
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9 | 14 | Tue, Mar 13 | | HW6 due |
| | 15 | Thu, Mar 15 | | |
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10 | 16 | Tue, Mar 20 | | HW7 due |
| | 17 | Thu, Mar 22 | | |
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11 | 18 | Tue, Mar 27 | | HW8 due |
| | | Thu, Mar 29 | Midterm II | |
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12 | 19 | Tue, Apr 3 | | |
| | 20 | Thu, Apr 5 | | |
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13 | 21 | Tue, Apr 10 | | HW9 due |
| | 22 | Thu, Apr 12 | | |
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14 | 23 | Tue, Apr 17 | | HW10 due |
| | 24 | Thu, Apr 19 | | |
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15 | 25 | Tue, Apr 24 | | HW12 due |
| | 26 | Thu, Apr 26 | | |
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16 | | TBA | FINAL EXAM | |
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