HW Assignment for Math 531

This page will give a complete listing of the reading and homework assignments that you are required to do. In addition, Exam and Final dates will be listed.There will be both written and electronic Homework with the latter done in WeBWorK. Information on logging into WeBWorK is given by this hyperlink. For WeBWorK students will login using their last name with a capital first letter and their Red ID number for a password. (Logins are case sensitive!) For example, suppose your name is Henri Poincare with Red ID number 314159265. Then you login with:

Username: Poincare
Password: 314159265

There is a Lab Manual (MATLAB and Maple) version, which will continue to be updated over the semester with detailed information for using MatLab and Maple on your assignments. There is a discount available to purchase Maple, Maple Adoption Discount.

Week 10-11: We complete Chapter 7 with higher dimensional PDEs, Bessel's Differential Equation, spherical problems and Legendre polynomials, then begin Chapter 8 on Nonhomogeneous problems. Lecture notes are available for Nonhomogeneous Problems (4-Panel).
HW Assignment #9: Work the Problems: 7.10.1e, 7.10.2c, 7.10.8, 7.10.9a. These problem are due Tue. Apr. 21.

Week 12-14:We finish Chapter 8 on Nonhomogeneous problems and begin Chapter 10 on Fourier Transforms. Lecture notes are available for Fourier Transforms (4-Panel) and Fourier Transforms B (4-Panel). There are Maple programs using the Fourier transform, fourier_heat.mws (PDF). Also, some MatLab code for Fourier transforms, heatFT3D.m, heatFTarbf.m.
HW Assignment #10: WeBWorK Problems, and 8.2.2b, 8.2.5, 8.3.1a, 8.4.2, 8.4.3, 9.2.1(c,d). These problem are due Sunday, May 3.

Week 13-15: We finish Chapter 10 on Fourier Transforms. Lecture notes are available for Fourier Transforms C (4-Panel). There are MatLab programs for this section, pde_eg1.m, laplace_eg.m. There is an optional section on the Method of Characteristics and examine Age-Structured Models, which will probably not get covered this year because of Covid-19. Lecture notes are available for Method of Characteristics (4-Panel). (If time becomes available, then I'll create a video for this, as it is closest to my research.)
HW Assignment #11: 10.3.1, 10.3.5, 10.3.6, 10.4.1, 10.4.3, Computer Problem. These problem are due Monday, May 11.
Take Home Final: There is a Take-Home Final available, which will be due Wed., May 13 by 5 PM.

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Lists of Lecture Videos and Lecture Quizzes
Most videos are on unsubscribed YouTube Channels

• Higher Dimensional PDEs -- https://youtu.be/3VirtXGLT68
  Lecture Worksheet 1 -- Solutions
• Vibrating Circular Membrane -- https://youtu.be/nYSmeg4UFLs
  Lecture Worksheet 2 -- Solutions
• Laplace's Equation on a Cylinder -- https://youtu.be/udPlRj-zyIA
  Lecture Worksheet 3 -- Solutions
• Wave Equation on a Sphere -- https://youtu.be/XexKBp_rFrc
  Lecture Worksheet 4
• Laplace's Equation on a Sphere -- https://youtu.be/cDQB4raulU4
  Lecture Worksheet 5
• Nonhomogeneous PDE E.F. Expansion -- https://youtu.be/ufvFGCJC860
  Lecture Worksheet 6
• Nonhomogeneous PDE Green's Formula and Green's Function -- https://youtu.be/cPT9UFVFul8
  Lecture Worksheet 7
• Fourier Transforms -- Introduction -- https://youtu.be/sTf_k40LO2s
  Lecture Worksheet 8
• Fourier Transforms -- B Heat Equation -- https://youtu.be/RapqPgBtUgE
  Lecture Worksheet 9
• Fourier Transforms -- C Sine and Cosine Transforms -- https://youtu.be/lHxOolMlyE0
  Lecture Worksheet 10

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Notes about Exams

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Old Assignments

Week 1: Read Chapters 1 and 2 from the text. Lecture notes are available for Introduction (4-Panel), Ordinary Differential Equations (4-Panel), and Heat Equation - Derivation (4-Panel). The first chapter introduces Partial Differential Equations and shows the derivation of the Heat Equation. The second chapter shows separation of variables and begins the process of solving the Heat Equation.
HW Assignment #1: Work the WeBWorK Problems (ode), which are due Mon, Feb. 3 at 4 AM. In addition, there is a set of Problems HW#1 and ones from the text 1.2.9, 1.4.12. These written problems are due Wed, Feb. 5.

Week 2: Read Chapters 2 and 3 from the text. Lecture notes are available for Heat Equation - 3D (4-Panel) and Separation of Variables (4-Panel). We continue techniques of separation of variables and introduce Fourier series. Computer code for Maple (heat1d (PDF)) and MatLab (heatjm.m) are available.
HW Assignment #2: Work the WeBWorK Problems (set1 HW1) and the ones from the text 1.5.22, 2.2.4, 2.3.1(b,c,f), 2.3.8. These problem are due Mon, Feb. 10.
Solutions are available for HW1.

Week 3: Read Chapters 2 and 3 from the text. Lecture notes are available for Separation of Variables B (4-Panel) and Fourier Series (4-Panel). MatLab code for Fourier series (fourier_1.m).
HW Assignment #3: Work the WeBWorK Problems (sepvar) and the ones from the text 2.4.1(a,c), 2.4.2, 2.5.1(d,g), 2.5.2, 2.5.6(b), 2.5.8(b), 2.5.10, 2.5.15(b), Computer Problem. These problem are due Wed, Feb. 19.

Week 4: Read Chapter 3 from the text. We continue Fourier series. MatLab code for Fourier series (gibb_c.m, gibb_d.m). Maple code for Fourier series (sawtooth.mw (PDF)). Read Chapter 4 from the text on the Vibrating String (4-Panel).
Solutions are available for HW2 .
HW Assignment #4: Work the WeBWorK Problems (fourier), text 3.3.1(c), 3.3.14, 3.4.6, 3.4.11, Computer Problem 2. These problem are due Wed, Feb. 26.

Week 5: Read Chapter 4 (through 4.4) the Vibrating String (4-Panel) and Chapter 5 Sturm-Liouville Problems (4-Panel) and Sturm-Liouville Problems B (4-Panel) from the text.
HW Assignment #5: Work the WeBWorK Problems, text 4.4.1, 4.4.9, 4.4.10, 5.3.2, 5.3.3, 5.3.9, 5.4.5.
These problem are due Wed, Mar. 4.

Week 6: Read Chapter 5 Sturm-Liouville Problems (4-Panel), Sturm-Liouville Problems B (4-Panel), and Sturm-Liouville Problems C (4-Panel) from the text. MatLab code for BC of Third Kind (fourier_rob.m, heatjm_rob.m) and Maple code (robin_ev.mw (PDF)).
Solutions are available for HW3 (also the Computer Prob 1),   HW4 (also the Computer Prob 2), and HW5
HW Assignment #6: Work the WeBWorK Problems, 5.5.1(c,d), 5.5.5, 5.5.8, 5.5.11, 5.8.5 (for b numerically find first 5 e.v.s with h = -1 and L = 1), 5.8.8 (for c numerically find first 5 e.v.s), 5.8.11.
These problem are due Mar 19 at 4 AM.
Take Home Exam 1: There is a Take-Home Exam available, which will be due Tues., Mar. 24, noon.

Week 7: We begin Chapter 7 with higher dimensional PDEs, Bessel's Differential Equation, spherical problems and Legendre polynomials. Lecture notes are available for Higher Dimensional PDEs (4-Panel) and Vibrating Circular Membrane (4-Panel). For those who want more details, there is a link to good notes on the Method of Frobenius (CalTech) or Method of Frobenius (4-Panel) (Math 537) needed for solving Bessel's equation.
HW Assignment #7: Work the WeBWorK Problems, 7.3.1 (d), 7.3.2a, 7.3.4a, 7.3.5, 7.5.1a, 7.5.2a.
These problem are due Tuesday, Apr. 7.

Week 8-9: We continue Chapter 7 with higher dimensional PDEs, Bessel's Differential Equation, spherical problems and Legendre polynomials. Lecture notes are available for Vibrating Circular Membrane (4-Panel) and Laplace's on Cylinder (4-Panel).
HW Assignment #8: Work the Problems: 7.7.1, 7.7.2a, 7.9.1c, 7.9.2b. These problem are due Fri. Apr. 17.
Take Home Exam 2: There is a Take-Home Exam available, which will be due Thur., Apr. 23.
Solutions are available for Take-Home Exam 1. As some of the results from the Take-Home Exam 1 are useful for Take Home Exam 2, answers will posted for some of the problems.