-------------------------------------------------------------------------- Updated regularly; only authoritative version is current version! Homework assignments pertinent to each lecture will be posted shortly after the lecture is completed. Class meets TTh 8:00-9:15 in MH 111 Solutions for graded homework problems can be found at: http://ereserves.unm.edu/courseindex.asp (you will need a course password, which I will announce in class) -------------------------------------------------------------------------- Last update: Thu Nov 18 21:21:53 MST 2004 (note there were two errata in the exam2 specs, now fixed) --------------------------------------------------- Math. 312 - Homework Assignments and Exams Schedule --------------------------------------------------- Based on R. Haberman's text. ------------------ Syllabus ------------------ I. The method of separation of variables: Heat flow. II. Fourier Series and vibrations: strings, membranes, electromagnetic waves. III. Problems with symmetry: Sturm-Liouville theory and the special functions of mathematical physics. IV. Green's functions: sources for the Heat, Laplace and Wave equations. V. Introduction to characteristics: conservation laws and shock waves. -------------------------------------------------------------------------- 1( 8/24) 1.1-3 one-dimensional heat conduction 2( 8/26) 1.4, 2.1-2.3.4 Separation of variables Set 1 (due 9/2) 1.2.5, 1.3.2, 1.4.1(a,c,f), 1.4.3, 1.4.10, 2.3.2(b,d), 2.3.4(a) -------------------------------------------------------------------------- 3( 8/31) 2.3.5-2.4 Examples - heat conduction 4( 9/ 2) 2.5.4 Set 2 (due 9/ 9) 2.3.6, 2.3.8, 2.4.1(a,b,c), 2.4.2, 2.4.3 (for 2.4.3 you will need to modify the formulas given in class a bit since the domain of definition is -L <= x <= L; see Sec. 2.4.2) -------------------------------------------------------------------------- 5( 9/ 7) 2.5.1-2 Laplace's equation in a rectangle and disk 6( 9/ 9) 2.5.3-4 Laplace's equ. in polar coords; flow past a cylinder Set 3 (due 9/16) 2.5.1a, 2.5.3a, 2.5.6a, 2.5.8a, 2.5.19, 2.5.21 -------------------------------------------------------------------------- 7( 9/14) Flow past a cylinder 8( 9/16) 3.1-2 Fourier Series Set 4 (due 9/23) 2.5.24, 2.5.25, 3.2.1(a,d,g), 3.2.2(a,b,d,e,f) Last Day to Change Grade Option Friday, Sept 17, 2004 -------------------------------------------------------------------------- 9( 9/21) 3.3 Sine and Cosine series 3.4 Properties of Fourier Series; 10( 9/23) Differentiation of Fourier Series Set 5 (due 9/30) 3.3.2(a,d), 3.3.3a, 3.3.10, 3.3.13 3.4.6, 3.4.9, 3.4.12, 3.5.7 (NOTE: the material required for 3.4/5 will be covered on Tuesday, 9/28 -------------------------------------------------------------------------- 11( 9/28) 3.4 Example: diffusion equation with a source 3.5 Integration of Fourier series; Review -------------------------------------------------------------------------- 12( 9/30) 4.4 Vibrating String with fixed ends. Exam 1 next Thursday, October 7 (no homework due!) Last Day to Drop a Class W/O Grade Friday, Oct. 1, 2004 -------------------------------------------------------------------------- 13(10/ 5) 2.5.4 Qualitative properties of Laplace's equation 14(10/ 7) Exam Part I (Ch. 1,2,3) -------------------------------------------------------------------------- 15(10/12) 5.1-3 Sturm-Liouville theory and eigenvalue problems Set 6 (due 10/21) 4.4.(1,3), 5.3.3, 5.3.(5,6)(a,b,c) **(10/14-15) Fall Break -------------------------------------------------------------------------- 16(10/19) 5.4-5 Self-adjoint Operators 17(10/21) 5.6-8 Rayleigh quotient and approximation of eigenvalues Set 7 (due 10/28) 5.(3.7, 5.1g, 5A.5, 6.1c, 7.1) -------------------------------------------------------------------------- 18(10/26) Review; the minimum principle for eigenvalues. 19(10/28) 5.10 Approximation properties 7.1-4 Separating the time; heat conduction vs. wave propagation: the Helmholtz equation Set 8 (due 11/ 4) 5.(8.3, 8.10, 10.2(b)) -------------------------------------------------------------------------- 20(11/ 2) 7.1-4 Separating the time; heat conduction vs. wave propagation: the Helmholtz equation -------------------------------------------------------------------------- 21(11/ 4) 7.5-6 Green's formula and Rayleigh Quotient 7.7 Bessel functions and cylindrical symmetry Set 9 (due 11/11) 7.5.(6, 7, 8a), 7.7.(3a, 8, 10, 12(a,c)) Note: some material pertaining to the last three problems will be completed on Tuesday, 11/9. -------------------------------------------------------------------------- 23(11/ 9) 7.7 Bessel functions and cylindrical symmetry 22(11/11) 7.8,9 More on Bessel functions: series and recurrence relations Exam Part II (Ch. 4-5-7 including Bessel fncs) due in class, Tue. 11/16: work alone, open book/notes < PROBLEMS: 4.4.8, 5.6.1b, 5.8.6(add case d: let h=1, determine eigenvalues graphically, use a root finding numerical algorithm to find the lowest eigenvalue correct to 3 significant digits), 7.7.9c, 7.7.12b, 7.7.13 > -------------------------------------------------------------------------- 24(11/16) 7.9 Bessel functions, special cases 25(11/18) 7.10 Legendre polynomials and spherical symmetry -------------------------------------------------------------------------- 26(11/23) 7.10 Legendre polynomials, spherical harmonics Set 10 (due 12/2) 7.(8.(7,10), 9.(2a, 3c), 10.(3c, 9c, 10c)) and 1 problem given in class **(11/25-26) Thanksgiving Break -------------------------------------------------------------------------- 27(11/30) 8.1-4 Problems with sources: heat equation 28(12/ 2) "" wave equation -------------------------------------------------------------------------- 29(12/ 7) 8.5 Forced vibrations; resonance 30(12/ 9) 8.6 Poisson's equation Exam Part III (Ch. 7.10, 8.1-6, 9.1-3) (due in my office by 11:30, T 12/16) Problems: <<< 7.9.2d, 7.10.11, 8.2(1f, 2e -- counts as one problem), 8.3.6, 8.4.3, 8.5.3( work with sinwt instead of coswt; for part b instead of comparing with the previous problem, you must compare the solution for small beta with the solution for beta = 0), 8.6.7 >>> (Notice that I extended the due date to Thursday--by popular demand. If I am not in my office, please turn your papers in to the front desk and ask them to mark the time. I'll plan on picking them up by 12noon be sure your paper is in before that! No late papers will be accepted!) -------------------------------------------------------------------------- (Below is material from previous semesters just for comparison!) -------------------------------------------------------------------------- 9.1-3 Green's functions; Delta functions; sources Set 10 (due 12/ 9) 9.3(1, 5abc, 13ab, 15ab, 21, 25ab) < (1) 7.10.10c, (2) 8.3.1b, (3) 8.3.6, (4) 8.4.2, (5) 8.5.3, (6) 8.5.6, (7) 9.3.11ab-12b, (8) 9.3.23-24 > NOTE: 7.10.10c is the problem I intended to assign here, not 7.10.9c as was written down! Set 9 (due 12/2) 8.3(1c, 7), 8.4.1b, 8.6(3a, 5, 6, 9ab) 12.1-2 Characteristics 12.6 Shock Waves Exam Part III (Ch. 7.10, 8.1-6, 9.1-3) (due in my office by 10:30, T 12/14) --------------------------------------------------------------------------