MATH-2200-ES31

Welcome to the permanent home page for Section ES31 of MATH-2200 (Differential Equations) at Southeast Community College in the Spring term of 2023. I am Toby Bartels, the instructor.

• Official syllabus (DjVu).
• Course policies (DjVu).
• Class hours: Tuesdays and Thursdays from 4:00 PM to 5:20 in ESQ 100C.
• Final exam: May 2 Tuesday from 4:00 PM to 5:40 in ESQ 100C (or by appointment).

Contact information

Feel free to send a message at any time, even nights and weekends (although I'll be slower to respond then).

The official textbook for the course is the 11th Edition of A First Course in Differential Equations with Modeling Applications by Dennis Zill published by Cengage. You automatically get an online version of this textbook through Canvas, although you can use a print version instead if you like.

Basics

1. Introduction:
• Reading from the textbook for January 12 Thursday: Chapter 1 through Section 1.1 (pages 2–12).
• Exercises from the textbook due on January 17 Tuesday: 1.1.1–8, 1.1.9, 1.1.11, 1.1.13, 1.1.15, 1.1.17, 1.1.21, 1.1.23, 1.1.24, 1.1.29, 1.1.41.
2. Initial examples:
• Reading from the textbook for January 17 Tuesday:
• Section 1.2 (pages 15–19);
• Section 1.3 (pages 22–29).
• Exercises from the textbook due on January 19 Thursday: 1.2.1, 1.2.3, 1.2.5, 1.2.7, 1.2.8, 1.2.11, 1.2.12, 1.2.17, 1.2.19, 1.2.21, 1.2.23, 1.3.1, 1.3.2, 1.3.5, 1.3.9, 1.3.10, 1.3.13, 1.3.17.
3. Solution curves:
• Reading from the textbook for January 19 Thursday:
• Chapter 2 through Section 2.1 (pages 36–43);
• Section 2.2 (pages 47–52).
• Exercises from the textbook due on January 24 Tuesday: 2.1.2, 2.1.15.a, 2.1.19, 2.1.20, 2.1.21, 2.1.22, 2.1.23, 2.1.24, 2.1.25, 2.1.26, 2.2.1, 2.2.3, 2.2.5, 2.2.7, 2.2.9, 2.2.23, 2.2.24, 2.2.25, 2.2.29, 2.2.31, 2.2.32, 2.2.33, 2.2.39, 2.2.41, 2.2.45.
4. First-order linear equations:
• Reading from the textbook for January 24 Tuesday: Section 2.3 (pages 55–62).
• Exercises from the textbook due on January 26 Thursday: 2.3.1, 2.3.3, 2.3.5, 2.3.7, 2.3.9, 2.3.11, 2.3.13, 2.3.17, 2.3.24, 2.3.25, 2.3.27, 2.3.37, 2.3.38.
5. Numerical solutions:
• Reading from the textbook for January 26 Thursday: Section 2.6 (pages 76–80).
• Exercises from the textbook due on January 31 Tuesday: 2.6.1, 2.6.3, 2.6.5, 2.6.6.
6. Models:
• Reading from the textbook for January 31 Tuesday:
• Chapter 3 through Section 3.1 (pages 80–91);
• Section 3.2 (pages 96–101).
• Exercises from the textbook due on February 2 Thursday: 3.1.1, 3.1.4, 3.1.5, 3.1.13, 3.1.15, 3.1.19, 3.1.21, 3.1.23, 3.1.27, 3.1.35, 3.1.38, 3.2.1, 3.2.3, 3.2.5.
Quiz 1, covering the material in Problem Sets 1–6, is on February 14 Tuesday.

Linear equations

1. Higher-order equations:
• Reading from the textbook for February 2 Thursday: Chapter 4 through Section 4.1 (pages 118–130).
• Exercises from the textbook due on February 7 Tuesday: 4.1.1, 4.1.2, 4.1.3, 4.1.9, 4.1.10, 4.1.15, 4.1.16, 4.1.17, 4.1.19, 4.1.21, 4.1.23, 4.1.24, 4.1.25, 4.1.26, 4.1.27, 4.1.31, 4.1.32, 4.1.33.
2. Reduction of order:
• Reading from the textbook for February 7 Tuesday: Section 4.2 (pages 132–134).
• Exercises from the textbook due on February 9 Thursday: 4.2.1, 4.2.3, 4.2.5, 4.2.9, 4.2.11, 4.2.14, 4.2.16, 4.2.21, 4.2.22.
3. Homogeneous equations:
• Reading from the textbook for February 16 Thursday: Section 4.3 (pages 135–140).
• Exercises from the textbook due on February 21 Tuesday: 4.3.1, 4.3.2, 4.3.3, 4.3.4, 4.3.5, 4.3.6, 4.3.13, 4.3.15, 4.3.16, 4.3.17, 4.3.18, 4.3.25, 4.3.26, 4.3.29, 4.3.31, 4.3.34, 4.3.37, 4.3.38.
4. Undetermined coefficients:
• Reading from the textbook for February 21 Tuesday: Section 4.5 (pages 152–158).
• Exercises from the textbook due on February 23 Thursday: 4.5.1, 4.5.3, 4.5.5, 4.5.6, 4.5.7, 4.5.11, 4.5.12, 4.5.13, 4.5.15, 4.5.16, 4.5.17, 4.5.18, 4.5.19, 4.5.20, 4.5.21, 4.5.30, 4.5.31, 4.5.32, 4.5.33, 4.5.39, 4.5.43, 4.5.47, 4.5.55, 4.5.64, 4.5.68.
5. Variation of parameters:
• Reading from the textbook for February 23 Thursday: Section 4.6 (pages 159–165).
• Exercises from the textbook due on February 28 Tuesday: 4.6.1, 4.6.2, 4.6.3, 4.6.6, 4.6.7, 4.6.11, 4.6.13, 4.6.15, 4.6.17.
6. Cauchy–Euler equations:
• Reading from the textbook for February 28 Tuesday: Section 4.7 (pages 166–171).
• Exercises from the textbook due on March 2 Thursday: 4.7.1, 4.7.3, 4.7.5, 4.7.7, 4.7.9, 4.7.11, 4.7.19, 4.7.23, 4.7.25, 4.7.27.
7. Applications of linear equations:
• Reading from the textbook for March 2 Thursday: Chapter 5 through Section 5.1 (pages 196–209).
• Exercises from the textbook due on March 7 Tuesday: 5.1.1, 5.1.3, 5.1.8, 5.1.13, 5.1.25, 5.1.26, 5.1.29, 5.1.33, 5.1.34, 5.1.35.
8. Linear systems of equations:
• Reading from the textbook for March 7 Tuesday: Section 4.9 (pages 183–187).
• Exercises from the textbook due on March 9 Thursday: 4.9.1, 4.9.3, 4.9.5, 4.9.7, 4.9.9, 4.9.21, 4.9.23.
Quiz 2, covering the material in Problem Sets 7–14, is on March 23 Thursday.

Laplace transforms

1. The Laplace transform:
• Reading from the textbook for March 9 Thursday: Chapter 7 through Section 7.1 (pages 278–284).
• Exercises from the textbook due on March 21 Tuesday: 7.1.11, 7.1.13, 7.1.15, 7.1.17, 7.1.19, 7.1.21, 7.1.23, 7.1.25, 7.1.27, 7.1.29, 7.1.31, 7.1.33, 7.1.43, 7.1.44.
2. Using the Laplace transform:
• Reading from the textbook for March 28 Tuesday: Section 7.2 (pages 286–293).
• Exercises from the textbook due on March 30 Thursday: 7.2.1, 7.2.2, 7.2.3, 7.2.4, 7.2.5, 7.2.7, 7.2.9, 7.2.11, 7.2.13, 7.2.15, 7.2.16, 7.2.19, 7.2.20, 7.2.23, 7.2.35, 7.2.36, 7.2.37, 7.2.38, 7.2.39.
3. Translations:
• Reading from the textbook for March 30 Thursday: Section 7.3 (pages 294–302).
• Exercises from the textbook due on April 4 Tuesday: 7.3.1, 7.3.2, 7.3.3, 7.3.4, 7.3.5, 7.3.6, 7.3.7, 7.3.8, 7.3.11, 7.3.13, 7.3.14, 7.3.15, 7.3.17, 7.3.21, 7.3.23, 7.3.25, 7.3.27.
4. Convolution:
• Reading from the textbook for April 4 Tuesday: Section 7.4 before the optional postscript about Green's functions in Subsection 7.4.2 (pages 306–312).
• Exercises from the textbook due on April 6 Thursday: 7.4.1, 7.4.3, 7.4.5, 7.4.8, 7.4.11, 7.4.13, 7.4.14, 7.4.19, 7.4.20, 7.4.21, 7.4.23, 7.4.25, 7.4.27, 7.4.28, 7.4.29, 7.4.30.
5. Integral equations:
• Reading from the textbook for April 6 Thursday: The remaining subsections of Section 7.4 (pages 313–315).
• Exercises from the textbook due on April 11 Tuesday: 7.4.41, 7.4.43, 7.4.45, 7.4.47, 7.4.49.
6. Delta functions:
• Reading from the textbook for April 11 Tuesday: Section 7.5 (pages 318–321).
• Exercises from the textbook due on April 13 Thursday: 7.5.1, 7.5.3, 7.5.5, 7.5.15, 7.5.16.
7. Systems of initial-value problems:
• Reading from the textbook for April 13 Thursday: Section 7.6 (pages 322–325).
• Exercises from the textbook due on April 18 Tuesday: 7.6.1, 7.6.3, 7.6.5, 7.6.7, 7.6.9.
Quiz 3, covering the material in Problem Sets 15–21, is on April 20 Thursday.

Quizzes

1. Basics:
• Review date: February 9 Thursday.
• Date taken: February 14 Tuesday.
• Corresponding problems sets: 1–6.
• Help allowed: Your notes, calculator.
• NOT allowed: Textbook, my notes, other people, websites, etc.
2. Linear equations:
• Review date: March 21 Tuesday.
• Date taken: March 23 Thursday.
• Corresponding problems sets: 7–14.
• Help allowed: Your notes, calculator.
• NOT allowed: Textbook, my notes, other people, websites, etc.
3. Laplace transforms:
• Review date: April 18 Tuesday.
• Date taken: April 20 Thursday.
• Corresponding problems sets: 15–21.
• Help allowed: Your notes, calculator, Appendix C on pages APP-29–31 of the textbook.
• NOT allowed: The rest of the textbook, my notes, other people, websites, etc.

Final exam

There is a comprehensive final exam on May 2 Tuesday, in our normal classroom at the normal time but lasting until 5:40 PM. (You can also arrange to take it at a different time May 1–5.) To speed up grading at the end of the term, the exam is multiple choice, with no partial credit.

For the exam, you may use one sheet of notes that you wrote yourself. However, you may not use your book or anything else not written by you. You certainly should not talk to other people! Calculators are allowed, although you shouldn't really need one, but not communication devices (like cell phones).

The exam consists of questions similar in style and content to those in the practice final exam (TBA).

This web page and the files linked from it (except for the official syllabus) were written by Toby Bartels, last edited on 2023 January 16. Toby reserves no legal rights to them.

The permanent URI of this web page is `http://tobybartels.name/MATH-2200/2023SP/`.