Joseph M. Mahaffy SDSU
Math 531: Partial Differential Equations Spring 2023
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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 mySDSU ID number for a password. (Logins are case sensitive!) For example, suppose your name is Henri Poincare with mySDSU 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 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).
Take Home Exam 2: There is a Take-Home Exam available, which will be due Thur, Apr 20 at 10 PM. There is additional information to help with the Take-Home Exam, particularly for MatLab programming for Fourier series where the integrations are done inside the program (Fourier-Bessel example, bessel_fourier2.m).
HW Assignment #8: Work the Problems: 7.7.1, 7.7.2a, 7.9.1c, 7.9.2b. These problem are due Sat Apr 15 at 4 AM. There are solutions to HW 6.

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 Sun Apr 23 at 4 AM. There are solutions to HW 7 and solutions to HW 8.

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 (nonhomo), and 8.2.2b, 8.2.5, 8.3.1a, 8.4.2, 9.2.1(c,d). These problem are due Mon. May 1 at 4 AM. There are solutions to HW 9.

Week 14-15: 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 a MatLab code to create a Fourier Transform graph for just the boundary function of Semi-Infinite Strip example test_eg.m.) We may introduce the Method of Characteristics and examine Age-Structured Models. Lecture notes are available for Method of Characteristics (4-Panel).
HW Assignment #11: WeBWorK Problems (ftrans), and 10.3.1, 10.3.5, 10.4.1, 10.4.3, and Computer Problem. These problem are due Mon., May 8 at 4 AM. There are solutions to HW 10.
Take Home Final: There is a Take-Home Final available, which will be due Thur, May 11 at Noon.

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

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Notes about Exams

Take Home Exam 1: There is a Take-Home Exam available, which is due Wed, Mar 8, noon. That is the date of your first In-class Exam. You are allowed a 3x5 notecard (both sides) for the exam and a scientific calculator. There can be NO cellphone visible during the exam.

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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. Students can find Notes for Reviewing ODEs through this link.
Lecture Activity 1: There is a set of Problems based on the lecture notes for ODEs, which are written problems due Thu, Feb. 2 at 4 AM in Gradescope.
HW Assignment #1: Work the WeBWorK Problems (ode), which are due Thu, Feb. 2 at 4 AM. In addition, there is a set of Problems HW#1 from the text 1.2.9, 1.4.12. These written problems are due Thu, Feb. 2 at 4 AM in Gradescope.

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, heat_surf.m) are available.
Lecture Activity 2: There is a set of Problems based on the lecture notes for the Heat Equation, which are written problems due Thur, Feb. 9 at 4 AM in Gradescope. There are solutions to Lecture Activity 1.
HW Assignment #2: Work the WeBWorK Problems (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 Thur, Feb. 9 at 4 AM in Gradescope. 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 1. These problem are due Thur, Feb. 16 at 4 AM. There are solutions to Lecture Activity 2

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).
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 Sat Feb 25 at 4 AM.
Solutions are available for HW2 and Computer Problem 1.

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. Hint: The PDF file provided here gives information on what details are expected for solutions in the HWs and Exams.
HW Assignment #5: Work the WeBWorK Problems (string), 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 Mon Mar 13 at 4 AM.
Take Home Exam 1: There is a Take-Home Exam available, which will be due Wed, Mar 8, noon. That will be the date of your first In-class Exam. You are allowed a 3x5 notecard (both sides) and a scientific calculator for the exam.
Solutions are available for HW3 (MatLab cylindrical plot code WW6_plot.m), HW4, and Computer Problem 2.

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)).
HW Assignment #6: Work the WeBWorK Problems (Rayleigh), 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 Sat Mar 25 at 4 AM.
Solutions are available for Exam 1 and Take Home Exam 1.

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 (HighPDE), 7.3.1 (d), 7.3.2a, 7.3.4a, 7.3.5, 7.5.1a, 7.5.2a.
These problem are due Sat Apr 8 at 4 AM.



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