Isaac Newton¹ (1642--1727)

• Textbook:
• Required: Walter A. Strauss, Partial Differential Equations: An Introduction, John Wiley & Sons (1992), ISBN# 0-471-54868-5.
• Link to the author's errata list.
• Rutgers University Academic Integrity Policy
• Inst.: Bertram Walsh, Hill 728, ([1-]732-) [44]5-3733; e-mail bwalsh@math.rutgers.edu.
• For office hours, see the instructor's home page.

• Course Materials: (except for the syllabus, almost all linked names will be .pdf files)
  


• Syllabus
  


• Problem Sheets:
• Problem Sheet 1.
• Problem Sheet 2 due 11/01/2001.
• Problem Sheet 3 due 11/29/2001 (note new date).
• Problem Sheet 4 due at end of classes.
• New (12/11): Problem Sheet 5 (the fifth and final) due at end of classes.


• Supplementary Notes (many from Spring 2001--see the footlines):²
• Notes on Leibniz's formula (see also Strauss's A.3) and the little problem at the end of the first lecture last spring.
• Notes on discretizing pdes (featuring both the heat and wave equations, in space dimension 1 only).
• The details of deriving the plane Laplacian in polar coördinates (see also Strauss, pp. 150-151).
• Notes on the maximum principle for the heat and Laplace equations (originally from 2/6/2001).
• A new (9/25/01) version of notes on the Cauchy (Poisson) kernel for the Laplace equation in the upper half plane (and related matters).
• Notes on Sturm-Liouville orthogonality.  These have now been reëdited for Fall 2001.
• Notes on an example.
• Notes cleaning up the transport-equation derivation of 9/6/01.
• Notes on an algorithmic approach to classifying second-order linear p. d. operators with constant coefficients.
• Notes giving a proof of the Riemann-Lebesgue Lemma.
• Notes on the convergence of Fourier Series, in (presumably) final form.
• Notes, Part I, on the Laplace equation, including some connections with functions of a complex variable. These contain some material not (yet) dealt with in class; you may want to confine your attentions to §§5 through 8.
• Part II of the notes on the Laplace equation. These include corrections for the original pp. 15-16, whose hypotheses for the Schwarz reflection principle made it too good to be true.
• Part III, the final installment, of the notes on the Laplace equation (which seems to get less and less connected with complex-variable stuff).
• Ch. 1: §1.1: 2, 3, 5, 7, 9, 10.  §1.2: 1, 3, 5, 6, 8. §1.3: 2, 3, 5, 9.  §1.4: 1, 2, 3, 5.  §1.5: 1, 2, 4.  §1.6: 1(a,b), 3, 5, 6.
• Ch. 2: §2.1: 5, 6, 8, 9. §2.2: 1, 2, 5, 6. §2.3: 1, 2, 3, 6, 8. §2.4: 1, 4, 6, 9, 15, 16, 18, 19. §2.5: 1, 2*.
• Ch. 4: §4.1: 1, 2, 4, 5. §4.2: 1, 2, 3. §4.3: 1, 2, 3, 4, 5, 6, 7 (with a [quasi-]physical explanation), 9, 11, 17.
• Ch. 5: §5.1: 1, 2, 3 (use a machine!), 4, 5, 9, 10, 11. §5.2: 3, 4, 5, 6, 9, 13, 14, 15, 16. §5.3: 3, 4, 6, 8, 10, 11, 13, 15. §5.4: 1, 2, 6, 8, 9, 10, 11, 16, 18, 19, 20. §5.5: 2, 3, 4, 5, 6, 11, 12. §5.6: 1, 2, 3, 6, 7, 13.
• Ch. 6: §6.1: 2 (NB: substitute u = v/r, that is, v = ru [book has a typo]), 4, 5, 6, 10, 11, 12. §6.2: 2, 3. §6.3: 1, 2, 3 (typo in the trig identity). §6.4: 1, 2, 3, 6, 11, 12(b) (prove the uniqueness--you don't need the Hopf maximum principle).

The notes and solutions posted here are class materials. Class members at Rutgers University may copy them for their personal use. Copyright rests in Roger D. Nussbaum(³) and Bertram Walsh(²,³). Duplication of these materials for commercial purposes is expressly prohibited.

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