Mathematical Methods for the Physical Sciences
Academic Calendar and Homework Assignments

WeekLecture No.DateChapter/ExamHomework
11Tue, Jan 22Introduction. Course logistics. Benefits and challenges of CAS. Low entropy expressions. Differential operator. Translation (shift) operator.
 2Thu, Jan 24Euler-MacLaurin summation formula. Logarithmic derivatives. A very short introduction to Mathematica: Exp[x], Series[....{x,0,6}].
23Tue, Jan 29Euler-MacLaurin summation formula, II. Properties of the differential operator.
 4Thu, Jan 31Ordinary differential equations I.
35Tue, Feb 5Ordinary differential equations II. A very short introduction to sympy.
HW1 due
 4Thu, Jan 31Ordinary differential equations III.
47Tue, Feb 12Complex numbers and complex variables: coordinate and polar form; Euler’s formula; trigonometric identities; complex roots.
 8Thu, Feb 14Ch. 2B, Analytic functions; Cauchy-Riemann equations. Contour integrals in the complex plane. Gaussian integrals.
HW2 due
59Tue, Feb 19Cauchy integral theorem.
 10Thu, Feb 21Singular points; residues; evaluation of integrals I.
611Tue, Feb 26Evaluation of integrals II.
 Thu, Feb 28Midterm I
HW3 due
712Tue, Mar 5Midterm I review; Evaluation of integrals III.
 13Thu, Mar 7Laplace method for solving ODEs.
814Tue, Mar 12Laplace method for integrals; Gamma function, Γ(x). Stirling formula.
 15Thu, Mar 14Laplace method, II.
9 Tue, Mar 19Spring recess 
  Thu, Mar 21Spring recess 
1016Tue, Mar 26Method of stationary phase.
HW4 due
 17Thu, Mar 28First order PDE. Characteristics. Hydrodynamic description of traffic
1118Tue, Apr 2First order PDE, II. Eulerian and Lagrangian description of flows.
 19Thu, Apr 4First order PDE, III.
1220Tue, Apr 9Midterm II
HW5 due
 21Thu, Apr 11Midterm II review. Take-home project discussion.
1322Tue, Apr 16Fourier integrals. Dirac δ-finction.
 23Thu, Apr 18Properties of Dirac δ-finction. Partial differential equations (PDE) I: Laplace equation.
1424Tue, Apr 23PDE II: diffusion equation.
 25Thu, Apr 25Fourier series. PDE III
1526Tue, Apr 30PDE IV.
 27Thu, May 2Random walks, diffusion, and Levi flights.
HW6 due
16-Thu, May 9FINAL EXAM, 1pm–3pm, M407 

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