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| Week | Lecture No. | Date | Chapter/Exam | Homework |
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1 | 1 | Tue, Jan 22 | Introduction. Course logistics.
Benefits and challenges of CAS. Low entropy expressions.
Differential operator. Translation (shift) operator.
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| | 2 | Thu, Jan 24 | Euler-MacLaurin summation formula.
Logarithmic derivatives. A very short introduction to Mathematica:
Exp[x], Series[....{x,0,6}].
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2 | 3 | Tue, Jan 29 | Euler-MacLaurin summation
formula, II. Properties of the differential operator.
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| | 4 | Thu, Jan 31 | Ordinary differential
equations I.
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3 | 5 | Tue, Feb 5 | Ordinary differential
equations II. A very short introduction to sympy.
| HW1 due |
| | 4 | Thu, Jan 31 | Ordinary differential
equations III.
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4 | 7 | Tue, Feb 12 | Complex numbers and complex variables: coordinate and polar
form; Euler’s formula; trigonometric identities; complex
roots.
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| | 8 | Thu, Feb 14 | Ch. 2B, Analytic functions;
Cauchy-Riemann equations. Contour integrals in the complex
plane. Gaussian integrals.
| HW2 due |
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5 | 9 | Tue, Feb 19 | Cauchy integral theorem.
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| | 10 | Thu, Feb 21 | Singular points;
residues; evaluation of integrals I.
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6 | 11 | Tue, Feb 26 | Evaluation of
integrals II.
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| | – | Thu, Feb 28 | Midterm I
| HW3 due |
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7 | 12 | Tue, Mar 5 | Midterm I review;
Evaluation of integrals III.
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| | 13 | Thu, Mar 7 | Laplace method for
solving ODEs.
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8 | 14 | Tue, Mar 12 | Laplace method for
integrals; Gamma function, Γ(x). Stirling formula.
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| | 15 | Thu, Mar 14 | Laplace method, II.
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9 | | Tue, Mar 19 | Spring recess | |
| | | Thu, Mar 21 | Spring recess | |
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10 | 16 | Tue, Mar 26 | Method of stationary
phase.
| HW4 due |
| | 17 | Thu, Mar 28 | First order PDE. Characteristics.
Hydrodynamic description of traffic
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11 | 18 | Tue, Apr 2 | First order PDE, II.
Eulerian and Lagrangian description of flows.
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| | 19 | Thu, Apr 4 | First order PDE, III.
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12 | 20 | Tue, Apr 9 | Midterm II
| HW5 due |
| | 21 | Thu, Apr 11 | Midterm II review.
Take-home project discussion.
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13 | 22 | Tue, Apr 16 | Fourier integrals.
Dirac δ-finction.
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| | 23 | Thu, Apr 18 | Properties of Dirac
δ-finction. Partial differential equations
(PDE) I: Laplace equation.
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14 | 24 | Tue, Apr 23 | PDE II:
diffusion equation.
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| | 25 | Thu, Apr 25 | Fourier series.
PDE III
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15 | 26 | Tue, Apr 30 | PDE IV.
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| | 27 | Thu, May 2 | Random walks,
diffusion, and Levi flights.
| HW6 due |
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16 | - | Thu, May 9 | FINAL EXAM, 1pm–3pm, M407 | |
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