Fall 2026, Math 316 - Applied Ordinary Differential Equations - All sections
- Instructors: Michael Heitzman, Anna Nelson, Bill Spotz, Tada Takahashi
- Coordinator: Anna Nelson, annanelson@unm.edu, SMLC 226
- Teaching Assistants: Graduate student teaching assistants (Tanner and Jose) are available for tutoring and support at the Math Tutoring Center/Calc Table (SMLC 130, Gathering Place) at the following times:
- Jose: Thursday, 1:00-2:30pm
- Tanner: Monday, Wednesday, 10:00-11:30am
Course Topics & Description: Math 316 is an introductory course on ordinary differential equations. Topics include elementary theory of ordinary differential equations, analytical methods for solving linear first- and second-order equations, numerical methods, phase-plane analysis of nonlinear problems, and introduction to Laplace transform methods. Differential equations model many natural phenomena as well as applications in engineering and the physical sciences. The goals of this course are to
- Give students the tools and skills needed for upcoming classes in engineering and the natural sciences.
- Build your deductive reasoning and presentation skills. As a scientist or engineer you will have to explain your results to others. One focus in this class is on the presentation of your results, which must always be clear so that others who do not know the result can follow your work.
- Build your sense of how differential equations are used to model applications.
Prerequisite: Math 1522 (Calculus II) Corequisite: Calculus III — Math 2350 or Math 2351
Prerequisites & Review: We will use the differentiation and integration methods you learned in Math 1512 and Math 1522. A sample of review problems is posted on Canvas and here so you can review before the semester starts and be well prepared. (For solutions, see Solutions pdf. The goal of mathematics courses at UNM is to build your skills and strengthen them as you go semester after semester. Review is needed, but don’t worry if you do not feel 100% confident to start with. We will review as we go and gain skill and confidence throughout. If you have not taken a mathematics course in the last 3 semesters, we recommend that you do not take Calculus III and Math 316 concurrently. Math 316 is offered every summer at UNM which gives you an opportunity to take it at that point. Please meet with your instructor if you wish to talk about which is the appropriate course for you.
Textbook: J. David Logan, A first course in differential equations, 3rd edition (available here)
Canvas: Canvas will be used for posting course announcements, homework assignments, grades, files and any relevant supplementary material, which can be accessed from the Canvas website. Class notes will also be posted on Canvas. Students should check the Canvas page regularly for course information, announcements, and resources. Email notifications and correspondence will be sent to the student’s UNM email address; this email account must be checked regularly.
Grading: Your course grade will be determined from weekly homework, 4 mid-semester exams, and a final exam. Attendance and participation in all aspects of the course is required. Therefore, you need at least 50% in your total Homework score to pass the class. Note that inconsistent attendance and homework can lead to instructor-drop (see Attendance). See below for Grade Mode Change and Academic Dishonesty. Your final course grade will be determined by
| Assessment | Grade percentage |
|---|---|
| Weekly homework | 14% |
| Instructor discretion | 4% |
| 4 mid-semester exams | 60% |
| Cumulative final exam | 22% |
The lowest two homework scores will be dropped when calculating your course grade. Participation in all aspects of the course is required. Therefore, you cannot pass the class unless you score at least 50% of your total Homework grade. In addition, your instructor may choose to take attendance and grade participation. Participation may be in the form of reading material for the course, completing worksheets in class, etc.
Your current percentage grade will always be visible in your Canvas page. A comprehensive 90%, 80%, or 70% grade will guarantee a passing grade of A,B or C, respectively, in the course. However, a grade below 70% does not mean you will fail the class. While your instructor will give general feedback on grades in class, you should make sure to contact your instructor directly anytime you want to know more closely what your standing in the course is. In particular, you need to contact your instructor before deciding to drop the course.
If you decide to withdraw from the course you need to do so before the last day of classes. We do not assign a grade of W after the last Friday of classes.
Attendance Policy: Attendance at UNM is mandatory and engagement in the class (regular homework completion, questions/comments inside and outside class, and in office hours) is necessary to succeed in this course. If you need to miss class, please let your instructor know. Any unexplained and continued absences and lack of homework may lead to being withdrawn from the course. Please make sure to stay in touch with your instructor in case of special circumstances that temporarily prevent you from participating as needed. If you have 4 or more total in unexplained class absences and unsubmitted homeworks, the instructor may drop you from the class without further notice.
Homework: Weekly homework sets, posted on this website, are due on the given due date by 11:59pm, to be submitted through Canvas (pdf files only please, no jpg or png images). You need to work on these problems on a daily basis. Please note that UNM requires a minimum of two hours work outside of class for each credit hour, and this is a 3-credit course. Plan on working 2 hours per lecture. The homework is set up to make it clear which problems to work on after each lecture. Weekly homework sets are due on the posted due date, by 11:59pm, to be submitted through Canvas. You will need a scanning app for your mobile device to scan your solutions as a pdf file. Homework solutions are posted on Thursday mornings.
One of the main goals of the course is to develop your mathematical writing skills, clearly showing all steps taken using correct algebra and notation. Therefore, your homework will be graded on the clarity and correctness of your mathematical presentation. Please take care to submit neat, legible solutions, with problems listed in order. Solutions that are hard to find or read will receive zero credit. Same standards will be applied to exams.
You are encouraged and welcome to work together on the homework. However, the writeup you hand in must be your own work, in your own words. After you have had all your questions answered, you need to be able to do all problems on your own.
Referral to other sources outside of the material given in class (such as searching the web for answers) is not conducive to learning and does not lead to understanding. To understand the material you must work through it. You learn mathematics, just as you do the violin, or soccer, by practice, practice, practice. And just like playing the scales or doing the dribbling skills, it’s not necessarily always fun, but necessary. You will hit roadblocks, that is part of the process. But when you do come to your results after possibly a few detours, then you have really understood. So, please know that struggling is ok. But do not bang your head in frustration! It is perfectly ok to try, think about something for a bit, and then get more insight by asking questions.
Resources: There are several resources to help you succeed in this class. Please consider your instructor and your TA your primary resource. Visit them during drop-in hours, at the Tutoring Center (Calc Table), and during office hours. Ask questions inside and outside of class, let us know what difficulties you are having. We want to hear from you and we want to help you succeed. Below is a list of resources.
MATLAB: To download MATLAB, go to https://it.unm.edu/download. MATLAB can also be accessed on the computers in the computer pods. Some useful links for using MATLAB are: Mathworks MATLAB Onramp, Owen’s MATLAB Tutorial, MATLAB Basics: A Tutorial, Fundamentals of MATLAB by Michael Tanguay.
Important dates for this class:
| Date | Importance |
|---|---|
| Monday August 17 | First day of classes |
| Friday August 28 | Last day to add sections/change grade mode in LoboWeb |
| Friday September 4 | Last day to drop without grade of “W” |
| Friday September 11 | First in-class exam |
| Friday October 2 | Second in-class exam |
| Thurs.-Fri. October 8-9 | Fall break, no classes |
| Friday October 23 | Third in-class exam |
| Friday November 6 | Last day to drop on LoboWeb |
| Friday November 13 | Fourth in-class exam |
| Thurs.-Fri. November 26-27 | Thanksgiving Break, no classes |
| Mon.-Fri. December 7-11 | Finals week |
Weekly schedule
| Week | Topics covered during class | Book sections | HW to be turned in |
|---|---|---|---|
| 1. Aug. 17, 19, 21 | Ch 1. First order ODEs 1. First order equations, (1.1,1.2). 2. Show given function solves DE, direction fields, solution curves. 3. Separation of variables (1.3.1) | 1.1, 1.2, 1.3.1 | Instructions for all HW HW 1, due Tues Aug. 25 for days 1,2,3 |
| 2. Aug. 24, 26, 28 | 4. Linear equations: integrating factor (1.4.1) 5. Applications (1.3.2, 1.3.3, 1.4.2) 6. Autonomous Eqns: phase line, equilibria, stability (1.5.1) | 1.3.2, 1.3.3, 1.4.1, 1.4.2, 1.4.3, 1.5.1 | HW 2, due Tues Sept. 1 for days 4, 5,6 |
| 3. Aug. 32, Sept. 2, 4 | 7. Population models 8. Existence and uniqueness, examples Ch 2. Second order linear ODEs, homogeneous 9. Springs (unforced), damped, undamped (2.1) | 1.5.1, 1.5.3, 2.1 | HW 3, due Tues Sept 8 for days 7,8,9 |
| 4. Sept. 7, 9, 11 | No class, Labor Day 10. Review for exam 11. Exam 1 (HW 1-3) | Review 1 | No HW! |
| 5. Sept. 14, 16, 18 | 12. Characteristic eq: real distinct roots (2.2.1) 13. Characteristic eq: repeated roots (2.2.2) 14. Characteristic eq: complex roots (2.2.3) | 2.2.1-2.2.3 | HW 4, due Tues Sept. 22 for days 12, 13, 14 |
| 6. Sept. 21, 23, 25 | 15. Springs, unforced (2.2.4) Ch 2. Second order linear ODEs, nonhomogeneous 16. Method of undetermined coefficients (2.3.1) 17. Springs, forced, beats, and resonance (2.3.2) | 2.2.4, 2.3.1, 2.3.2 | HW 5, due Tues Sept 29 for days 15, 16, 17 |
| 7. Sept. 28, 30, Oct. 1 | Ch 3. Laplace Transforms 18. Definition, linearity, transforms of basic functions (3.1) 19. Review 20. Exam 2 (HW 4-5) | 3.1, Review 2 | HW 6 due Tues Oct. 6 for day 18 |
| 8. Oct. 5, 7, 9 | 21. Solving IVPs using tables, partial fractions (3.2) 22. The shift formula (3.1, 3.2) No class, Fall break | 3.1, 3.2 | HW 7, due Tues Oct. 13 for days 21, 22 |
| 9. Oct. 12, 14, 16 | 23. Step functions, piece-wise functions (3.2, 3.3) 24. Piece-wise forcing, convolution (3.3, 3.4) 25. Impulsive forces (3.4) | 3.2, 3.3., 3.4 | HW 8, due Tues Oct. 20 for day 23, 24, 25 |
| 10. Oct. 19, 21, 23 | Ch 4. Linear Systems x’=Ax 26. Solving Ax=b, matrices, inverses, determinants (4.1) 27. Review 28. Exam 3 (HW 6-8) | 4.1, Review 3 | HW 9, due Tues Oct. 27 for day 26 |
| 11. Oct. 26, 28, 30 | 29. Systems x’=Ax, vector valued fcns, graphs, derivatives (4.2) 30. Solving x’=Ax, eigenvalues, eigenvectors (4.3) 31. Real distinct eigenvalues: saddle, phase portrait (4.4.1) | 4.2.1, 4.2.2, 4.3, 4.4.1 | HW 10, due Tues Nov. 3 for days 29, 30, 31 |
| 12. Nov. 2, 4, 6 | 32. Real distinct eigenvalues: nodes, zero eigenvalue (4.4.1) 33. Complex eigenvalues: spirals, centers (4.4.2) 34. Repeated eigenvalues: stars, degenerate (4.4.3) | 4.4.1, 4.4.2, 4.4.3 | HW 11, due Tues Nov. 10 for days 32, 33, 34 |
| 13. Nov. 9, 11, 13 | Ch 5. Nonlinear systems 35. Second order as system, equilibria, linearization (5.1) 36. Review 37. Exam 4 (HW 9-11) | 5.1, Review 4 | HW 12, due Tues Nov. 17 for day 35 |
| 14. Nov. 16, 18, 20 | 38. Simple example, competing species (5.1) 39. Lotka-Volterra Model (predator-prey) (5.3.1) 40. Nonlinear mechanics, pendulum (5.2) | 5.1, 5.2, 5.3 | HW 13, due Tues Nov. 24 for days 38, 39, 40 |
| 15. Nov. 23, 25, 27 | 41. Catch-up/optional topic 42. Catch-up/optional topic No class, Thanksgiving break | optional: 5.2, 5.3, 5.5 | |
| 16. Nov. 30, Dec. 2, 4 | 43. Review for final 44. Review for final 45. Review for final | Final Review |
Work outside class/Credit hour statement: This is a three credit-hour course and class meets for three 50-minute sessions of direct instruction for fifteen weeks during the Fall 2026 semester. Please note that UNM requires a minimum of two hours work outside of class for each credit hour. Only with daily work and good use of your resources will you profit the most and succeed in this class. Please plan for a minimum of six hours of out-of-class work (or homework, study, assignment completion, and class preparation) each week. The homework is set up to make it clear which problems to work on after each lecture.
List of resources: There are several resources to help you succeed in this class. Please consider your instructor your primary resource. Visit them during drop-in hours help hours, ask questions inside and outside of class, let us know what difficulties you are having. We want to hear from you and we want to help you succeed. The TAs at the Math Tutoring Table are another resource for you. A list of all resources:
- Instructor’s drop-in hours, availability in and outside of class
- Teaching Assistants: TAs will be available for help at the Tutoring Center (schedule will be posted in Canvas)
- CAPS: Center for Academic Program Support. Located on the 3rd floor of Zimmerman Library, (505) 277-7205
- ESS Center: Engineering Student Success Center, (505) 277-4354
- Student Health and Counseling (SHAC) at (505) 277-3136.
- LoboRESPECT Advocacy Center (505) 277-2911 can offer help with contacting faculty and managing challenges that impact your UNM experience.
Most importantly: Ask questions!! In class, in recitations, at CAPS, to your instructor, to each other. You learn the most when you figure out what questions you have, formulate them, and find the answers to them. This is not the same as asking “how do you do this problem?” A better question would be “I tried this and got stuck, I don’t see alternatives, can you help?” or, in class, “I don’t see how that follows, can you explain?”
Exam dates: All exam dates are given in the syllabus at the beginning of the semester. Exams cannot be rescheduled except in documented emergencies. If you need to reschedule because of a documented emergency (eg, surgery), please let your instructor know as soon as you find out. If you miss an exam due to sickness, contact your instructor immediately. Do not schedule a personal trip during exams as you will not be given a makeup. Non-NCAA sporting events are also not university authorized emergencies. The final exam will be scheduled at the date determined by the university and when the date is determined, it will be posted on this syllabus.
Grade change mode and withdrawals: Deadlines to make changes to your registration status are published by the Office of the Registrar in the schedule of classes: http://registrar.unm.edu. To change grade mode or to withdraw after the deadlines posted therein, you need to (1) talk to your instructor to fully understand your standing in the class, and (2) meet with your advisor and discuss the best path for you to proceed, as well as all consequences for your studies. Please ask your advisor to email your instructor, with copy to you, of the final decision. For grade mode changes you may also be required to have your instructor sign a grade mode change form: http://www.unm.edu/~unmreg/images/Forms/EnrlAuth-GradeMode.pdf , and your instructor will accommodate the change. Please note that you cannot request a withdrawal from the course after 5 pm on the Friday before final exams week.
Academic dishonesty: Academic dishonesty will be reported to the Dean of Students. This includes copying answers from other sources to complete your homework, using external sources (other than pencil and paper) to complete exams, and copying or looking at another student’s exam or quiz while it is given. Cheating and plagiarism (academic dishonesty) are often driven by lack of time, desperation, or lack of knowledge about how to identify a source. Communicate with the instructor and ask for help, even at the last minute, rather than risking your academic career by committing academic dishonesty. Academic dishonesty involves claiming that work created by another source is your own original work. It is a Student Code of Conduct violation that can lead to a disciplinary procedure. When you use a resource in work submitted for this class, document how you used it and distinguish clearly between your original work and the material taken from the resource.
Accommodation statement: UNM is committed to providing equitable access to learning opportunities for students with documented disabilities. As your instructor, it is my objective to facilitate an inclusive classroom setting, in which students have full access and opportunity to participate. To engage in a confidential conversation about the process for requesting reasonable accommodations for this class and/or program, please contact the Accessibility Resource Center at arcsrvs@unm.edu or by phone at 505-277-3506.
Discrimination (UAP 2720 and 2740): Our classroom and university should foster mutual respect, kindness, and support. If you have concerns about discrimination, harassment, or violence, please seek support and report incidents. Find confidential services at LoboRESPECT Advocacy Center, the Women’s Resource Center, and the Arcoíris Center. UNM prohibits discrimination on the basis of sex (including gender, sex stereotyping, gender expression, and gender identity). All instructors are “responsible employees” who must communicate reports of sexual harassment, sexual misconduct and sexual violence to Compliance, Ethics and Equal Opportunity. For more information, please see UAP 2720 and UAP 2740.