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 11-12:We finish Chapter 8 on Nonhomogeneous problems and may 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.
Solutions are available for HW4.
Old Solutions are available for HW6, HW7, HW8, and HW9. (Note that these problems may not exactly match the ones that you worked for you HWs. Appropriate solutions will be posted for current semester as they become available.)
HW Assignment #10: 8.2.2b, 8.2.5, 8.3.1a, 8.4.2, 8.4.3, 9.2.1(c,d).
These problem are due Monday, Apr. 24.

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. We introduce the Method of Characteristics and examine Age-Structured Models. Lecture notes are available for Method of Characteristics (4-Panel). There is a Take-Home Final, which is due on Thur. May 11, 3 PM.
Solutions are available for Take Home 1. (Note that these solutions are somewhat crude, as they were modified from previous questions asked in the past.)
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 1.

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Notes about Exams

For Take Home Exam 1, you must do all the work yourself without help from outside. Answers need to be clearly written and computer programs must be appended to your document.

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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: There is a set of problems HW#1 to work. Also work the WeBWorK Problems (ode) and the ones from the text 1.2.9, 1.4.12.
These problem are due Wed, Feb. 1.

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, 1.5.22, 2.2.4, 2.3.1(b,c,f), 2.3.8.
These problem are due Wed, Feb. 8.

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, 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. 15.

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)). We begin material on the Vibrating String (4-Panel).
HW Assignment #4: Work the WeBWorK Problems, 3.3.1(c), 3.3.14, 3.4.6, 3.4.11, Computer Problem 2. These problem are due Wed, Feb. 22.

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.
Solutions are available for HW1.
HW Assignment #5: Work the WeBWorK Problems, 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. 1.

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)). There is a Take-Home Exam, which is due on Fri. Mar 10, 4PM.
HW Assignment #6: Work the WeBWorK Problems, 5.5.1(c,d), 5.5.5, 5.5.8, 5.5.11, 5.6.1(a), 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 Wed, Mar. 15.

Week 7-8: 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 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 Wednesday, Mar. 22.

Week 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 Wednesday, Apr. 5.

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). There is a Take-Home Exam, which is due on Fri. Apr 21, 3:30PM.
Solutions are available for HW2 and HW3.
HW Assignment #9: Work the Problems: 7.10.1e, 7.10.2c, 7.10.8, 7.10.9a.
These problem are due Wednesday, Apr. 12.