# 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 2022. I am Toby Bartels, the instructor.

## 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 11 Thursday: Chapter 1 through Section 1.1 (pages 2–12).
• Exercises from the textbook due on January 18 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 18 Tuesday:
• Section 1.2 (pages 15–19);
• Section 1.3 (pages 22–29).
• Exercises from the textbook due on January 20 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 20 Thursday:
• Chapter 2 through Section 2.1 (pages 36–43);
• Section 2.2 (pages 47–52).
• Exercises from the textbook due on January 25 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 25 Tuesday: Section 2.3 (pages 55–62).
• Exercises from the textbook due on January 27 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 27 Thursday: Section 2.6 (pages 76–80).
• Exercises from the textbook due on February 1 Tuesday: 2.6.1, 2.6.3, 2.6.5, 2.6.6.
6. Models:
• Reading from the textbook for February 1 Tuesday:
• Chapter 3 through Section 3.1 (pages 80–91);
• Section 3.2 (pages 96–101).
• Exercises from the textbook due on February 3 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 15 Tuesday.

### Linear equations

1. Higher-order equations:
• Reading from the textbook for February 3 Thursday: Chapter 4 through Section 4.1 (pages 118–130).
• Exercises from the textbook due on February 8 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 8 Tuesday: Section 4.2 (pages 132–134).
• Exercises from the textbook due on February 10 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 17 Thursday: Section 4.3 (pages 135–140).
• Exercises from the textbook due on February 22 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 22 Tuesday: Section 4.5 (pages 152–158).
• Exercises from the textbook due on February 24 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 24 Thursday: Section 4.6 (pages 159–165).
• Exercises from the textbook due on March 1 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 March 1 Tuesday: Section 4.7 (pages 166–171).
• Exercises from the textbook due on March 3 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 3 Thursday: Chapter 5 through Section 5.1 (pages 196–209)
• Exercises from the textbook due on March 8 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 8 Tuesday: Section 4.9 (pages 183–187).
• Exercises from the textbook due on March 10 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 24 Thursday.

### Laplace transforms

1. The Laplace transform:
• Reading from the textbook for March 10 Thursday: Chapter 7 through Section 7.1 (pages 278–284)
• Exercises from the textbook due on March 22 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 29 Tuesday: Section 7.2 (pages 286–293).
• Exercises from the textbook due on March 31 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 31 Thursday: Section 7.3 (pages 294–302).
• Exercises from the textbook due on April 5 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 5 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 7 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 7 Thursday: The remaining subsections of Section 7.4 (pages 313–315).
• Exercises from the textbook due on April 12 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 12 Tuesday: Section 7.5 (pages 318–321).
• Exercises from the textbook due on April 14 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 14 Thursday: Section 7.6 (pages 322–325).
• Exercises from the textbook due on April 19 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 21 Thursday.

## Quizzes

1. Basics:
• Review date: February 10 Thursday.
• Date taken: February 15 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 22 Tuesday.
• Date taken: March 24 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 19 Tuesday.
• Date taken: April 21 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 3 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 from April 29 to May 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 (DjVu).

This web page and the files linked from it (except for the official syllabus) were written by Toby Bartels, last edited on 2022 May 2. Toby reserves no legal rights to them.

The permanent URI of this web page is `https://tobybartels.name/MATH-2200/2022SP/`.