Academic Calendar and Homework Assignments

WeekLecture No.DateChapter/ExamHomework1 1 Tue, Jan 22 Introduction. Course logistics. Benefits and challenges of CAS. Low entropy expressions. Differential operator. Translation (shift) operator.

2 Thu, Jan 24 Euler-MacLaurin summation formula. Logarithmic derivatives. A very short introduction to Mathematica: Exp[x], Series[....{x,0,6}].

2 3 Tue, Jan 29 Euler-MacLaurin summation formula, II. Properties of the differential operator.

4 Thu, Jan 31 Ordinary differential equations I.

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.

4 7 Tue, Feb 12 Complex numbers and complex variables: coordinate and polar form; Euler’s formula; trigonometric identities; complex roots.

8 Thu, Feb 14 Ch. 2B, Analytic functions; Cauchy-Riemann equations. Contour integrals in the complex plane. Gaussian integrals.

HW2 due 5 9 Tue, Feb 19 Cauchy integral theorem.

10 Thu, Feb 21 Singular points; residues; evaluation of integrals I.

6 11 Tue, Feb 26 Evaluation of integrals II.

– Thu, Feb 28 Midterm I

HW3 due 7 12 Tue, Mar 5 Midterm I review; Evaluation of integrals III.

13 Thu, Mar 7 Laplace method for solving ODEs.

8 14 Tue, Mar 12 Laplace method for integrals; Gamma function, Γ( x). Stirling formula.

15 Thu, Mar 14 Laplace method, II.

9 Tue, Mar 19 Spring recessThu, Mar 21 Spring recess10 16 Tue, Mar 26 Method of stationary phase.

HW4 due 17 Thu, Mar 28 First order PDE. Characteristics. Hydrodynamic description of traffic

11 18 Tue, Apr 2 First order PDE, II. Eulerian and Lagrangian description of flows.

19 Thu, Apr 4 First order PDE, III.

12 20 Tue, Apr 9 Midterm II

HW5 due 21 Thu, Apr 11 Midterm II review. Take-home project discussion.

13 22 Tue, Apr 16 Fourier integrals. Dirac δ-finction.

23 Thu, Apr 18 Properties of Dirac δ-finction. Partial differential equations (PDE) I: Laplace equation.

14 24 Tue, Apr 23 PDE II: diffusion equation.

25 Thu, Apr 25 Fourier series. PDE III

15 26 Tue, Apr 30 PDE IV.

27 Thu, May 2 Random walks, diffusion, and Levi flights.

HW6 due 16 - Thu, May 9 FINAL EXAM, 1pm–3pm, M407

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