- Instructor: Dr. David Groisser. All first-person pronouns (I, me, my, etc.) refer to Dr. Groisser.
- Prerequisite
- Syllabus (course content)
- Communicating with Dr. Groisser outside class
- Graded components of course
- Homework
- Attendance policy
- Student Honor Code
- My grading system for this course
- Workload
- Scheduling appointments with Dr. Groisser outside office-hours
- In-class recording by students
- Accommodations for students with disabilities
- Teaching-evaluations
- UF Health and Wellness Resources
- Goals of course
- Other items that are required for a General Education "syllabus"
Prerequisite: MAC 2312 or equivalent. You will need a good working knowledge of Calculus 1 and 2 (as well as precalculus algebra and trigonometry). In particular, you will be expected to know integration techniques; the chain rule; partial fractions; and the algebra, calculus, and general properties of sines, cosines, and exponentials. If you are weak in any of these areas, or it's been a while since you took calculus, you will need to spend extra time reviewing or relearning that material. Mistakes in prerequisite material will be graded harshly on exams.
Prior knowledge of partial derivatives (usually covered in Calculus 3) is not a prerequisite but is helpful.Syllabus (course content): This course is an introduction to ordinary differential equations (ODEs). ODEs enable a mathematical description of the laws of simple physics and virtually every science. We will cover chapters 1, 2, 4, 6, and 7 of the textbook, with some omissions, and some material may be presented differently (and in a different order) from the way it's presented in the book. The content we cover will be similar to that of the non-honors sections, but with some enhancements and some omissions.
"Honors at the collegiate level is a challenge, not a reward." (https://www.honors.ufl.edu/about/ ) Concepts, definitions, and some theorems will be important in this honors section, in addition to techniques for solving ODEs. Topics will include:
- concept of "ordinary differential equation" and meaning of "solution";
- statement and understanding of the fundamental existence/uniqueness theorem for solutions to initial-value problems;
- methods for solving first-order differential equations (including linear, separable, and exact equations);
- some of the general theory of linear differential equations;
- methods for solving constant-coefficient linear ODEs of order greater than 1, with an emphasis on the second-order case;
- One or both of the following, as time permits:
- methods for solving some type(s) of linear ODEs with non-constant coefficients);
- method of Laplace transforms.
Note: Starting with Fall 2024, UF shortened the fall and spring semesters from 15 weeks to 14. The difference is significant. It simply is not possible to cover the same amount of material in 14/15 of the time. Although I have removed some formerly covered topics from the syllabus, I cannot be certain that there will be time for both of the above topics, or for solving order-greater-than-two constant-coefficient ODEs.Nagel, Saff, and Snider, Fundamentals of Differential Equations and Boundary Value Problems, 7th edition,
The second book consists of the first ten chapters of the first book. For these ten chapters, the two books are identical, page by page. Thus for this course, it does not matter which of the two books you use. (However, in case you think you might take UF's second course on differential equations, MAP4305, at some point: the longer textbook is used also in for material beyond what's in the shorter book.) There will also be some required readings from notes by Dr. Groisser. These notes will be linked to the Miscellaneous Handouts page.
OR
Nagel, Saff, and Snider, Fundamentals of Differential Equations, 9th edition.Tentative, approximate weekly schedule of lectures: Click here.
Communicating with Dr. Groisser outside class
For anything that needs a response, the primary way to communicate with me outside class is to see me in office hours. The circumstances under which you may communicate with me by email are limited; see "Emailing me" below.
- Office Hours:
Tentatively, Monday 9th period (4:05–4:55), Wednesday 5th period (11:45–12:35), and Friday 4th period (10:40 – 11:30). Please arrive early in the period or let me know to expect you later; otherwise I may not stay in my office for the whole period.
My office is Little Hall 308.
If you have COVID-19, the flu, or similarly contagious disease, or think you might, please do not come to my office.
See also the statement concerning office hours in the attendance policy.
If you have the flu or similar contagious disease, or think you might, please do not come to my office. If you need to speak with me at such a time, we can set up a virtual meeting.
If you have conflicts with all these hours, please let me know early in the semester (even if you don't need to meet with me soon); I may change one of the time-slots. Students who can't make any of my scheduled office hours may see me by appointment on most weekdays (but never on a Thursday). See Scheduling appointments with Dr. Groisser outside office-hours, later in this document. But I don't want to find myself making appointments every week; I'd rather change my regularly scheduled hour(s)—hence the importance of letting me know early in the semester whether you can't make any of the hours I've listed above.
- Emailing me.
I receive a ton of email, and replying is very time-consuming, so please be aware of the following:
- THE EXISTENCE OF EMAIL DOES NOT EXTEND MY OFFICE HOURS.
For student emails that deserve individual replies, in general I reply only during my next office hour or as soon thereafter as I can. Students who email me a question on a day I have an office hour, and don't explain why they're emailing me instead of attending my office hour, usually will not receive a response.- EMAIL IS NOT A SUBSTITUTE FOR SEEING ME IN OFFICE HOURS.
- I don't answer email that lacks an informative subject line and the sender's full name. Students should also state which of my classes they're in (but this may be done early in the body of the email rather than the subject line).
- I will not answer math questions by email. An interactive conversation is needed.
- There are many non-math questions that I won't answer by email either. In particular, I usually won't respond to email that asks questions that have already been answered in items you should have read (for example: this syllabus, the class home page, homework page(s), solutions handouts, emails I've sent to the class, and announcements I've posted in Canvas), or that were answered in a lecture or discussion that the student elected to miss for unapproved reasons, or that should be (or should have been) asked in office hours.
- I don't provide individualized grade information by email.
- I won't open attachments (or follow links) that look suspicious to me. I generally delete, without fully reading, any email that contains these.
- My email address is located here.
You are not expected to remember, at all times, each and every rule I'm putting into this syllabus (whether in the "Communications" category or any other). What you are expected to remember is that those rules are posted here—and that you should check this page and the class home page before asking me a question that I may already have answered on these pages.
Some examples of email-content that would be okay to send me are:
- "The link for [this item] on [this page] seems to be broken [or: takes me to the wrong page]."
- "I think there's a typo in the homework assignment. You listed exercise 1.2/3g, but exercise 1.2/3 doesn't have a part (g). Would you please clarify what you intended to assign?"
For clarifications to homework assignments, I'll usually take action ASAP after seeing your message. But once I'm done with my fix, I may only send the entire class message about the update (or post one), rather than replying to the individual student(s) who notified me of the problem.- "I'm planning on coming to your office hour tomorrow, but I can't get there till 30 minutes after it starts. I just wanted to let you know to expect me late."
- "I won't be in class on such-and-such date, for such-and-such reason."
- "I'm applying for a summer program [or scholarship, graduate school, etc.]. Would you be willing to write a letter of recommendation for me? The deadline is [month/day]."
Communications from me. You are required to read fully, and reasonably promptly, any communications from me. These communications include, but may not be limited to, emails (either to the class listserv or to you personally) and announcements on Canvas.
(However, your grade could be reduced by a penalty for unexcused absence(s).)
- Assuming there is enough time for three midterms this semester, your final grade will be determined by:
- Three midterms (50-minute exams), each counting for 20% of final grade.
- A cumulative final exam (two hours), counting for 40% of final grade.
- If there is only enough time for two midterms, then the worse of your two midterms (on a percentage basis) will count for 20% of your final grade, the better of your midterms will count for 35%, and the final exam will count for 45%.
I would prefer to have three midterms, but the shortened semester will make it difficult to fit in that many. (And even in the last pre-shortened semester, Spring 2024, I was only able to fit in two midterms.) To fit in a third midterm, I will either have to further reduce course-content, reduce classroom interactivity (my least-desired solution), or reduce or the number of class periods used for exams. Committing to one of these solutions (or a combination), or to the number of midterms, before I know what pace I can keep up with this semester's students, would not be in your best interests. Every class is different.
After Drop/Add, I may poll the class to see whether out-of-class, evening midterms are possible, in order not to lose a lecture for each exam. To have any chance of that possibility working, I will need full cooperation from the class; having even a single student not respond promptly to a poll—without my having to send out multiple messages— could eliminate the possibility for the whole class.
Whether there are three midterms or two, I reserve the right to adjust the above percentages (20-20-20-40 or 20-35-45) in individual cases, to a student's benefit, if I feel that circumstances warrant. I will not answer any questions about hypothetical situations in which I might do this.
On any exam, unless I say otherwise, you are responsible for knowing any material I cover in class, any subject covered in homework, and all the material in the textbook sections we've covered.
Exam dates
- Final Exam: I expect that the final exam will be given Wednesday April 30, starting at 3:00 p.m., in our usual classroom.
(As of 1/1/2025, one.uf and the UF Schedule of Courses are listing our final-exam slot as Saturday, Apr. 26, 7:30-9:30 a.m., but this is inconsistent with UF's rules for final-exam scheduling, which are posted here. The April 26, 7:30 a.m. time-slot is for an assembly exam for non-honors MAP2302, a large lecture course. We are a stand-alone section, with our own exams, and therefore should have what's called a time-of-class final exam [i.e. its time-slot should be the one for MWF 8th-period classes that do not have assembly exams]. The Registrar lists a room for our exam [our usual classroom], which is done in advance only for time-of-class exams. The Registrar's Office has been making the same exam-slot mis-assignment for last two+ years, and has fixed it after I've brought to their attention each semester. For the current semester, I attempted to notify the Registrar of this problem on Dec. 10, but have received no reply. I will try again in early January, and will let you know when I get a definitive answer.)
- Midterm exams: Because of the uncertainty in how many there will be, I will not be able to estimate dates before seeing what pace we are keeping up. Every MWF from Feb. 7 to Apr. 23 is a potential day for an in-class midterm. Expect a grade of 0 on an exam that you miss because you chose to be out of town on the date that an exam ends up being given. This includes the day before spring break (and the day after as well)! (See "Attendance Policy" and "What if you miss an exam?" below.)
If you will be participating in excusable-absence activities (weddings, UF-sanctioned extracurricular activities, etc.) that will cause you to miss class on any days that are not UF holidays, let me know the date(s) by Friday, Jan. 24, so that I can attempt to avoid scheduling a midterm on such dates.
Homework will be assigned daily and is due by the next class, but will not be collected. It is critical that you keep up with the homework daily. Far too much homework will be assigned for you to catch up after a several-day lapse, even if your past experience makes you think that you'll be able to do this. I cannot stress this strongly enough. Students who do not keep up with the homework frequently receive D's or worse (or drop the class to avoid receiving such a grade).
The assignments will be posted on the homework webpage. Assignments that are posted prior to class are estimates; they will often be modified within a few hours after class, according to how far we got that day. You are responsible for checking this page frequently (early enough for you to complete each assignment by its due-date), since in addition to updated assignments, other important information such as exam-dates will be confirmed on that page. Of course, changes of exam-dates will also be announced in class well in advance. However, if you are unaware of an exam-date (or change to it) because you were absent for the in-class announcement and you didn't check the homework page for several days, and this causes you to miss an exam or do poorly on it, that poor grade (0 if you miss the exam) will still be averaged into your final grade according to the percentages stated earlier.
On most days I will not answer homework questions in class; you should see me in office hours for questions about homework (or the material we're covering). Time permitting, the class day before an exam may be used for Q&A, during which homework questions will be fine.
I advise against using solutions-manuals. To learn mathematics, you need to see a small number of problems worked out by someone else, just to see the principles illustrated; you need to do a large number of problems by yourself. The problems I assign are selected to be doable based on what should be your accumulated store of knowledge and skills from your previous math classes, plus the material covered in class (or the textbook, or the assigned readings from my notes) up to that point. In the long run, you will learn more by struggling with a problem unsuccessfully for two hours, than by giving up after a few minutes and looking at someone else's solution. Also, the solutions in solutions-manuals are sometimes misleading, inefficient, or outright wrong.
I do not use any online homework system. I have not seen any that I could trust not to count some right answers as wrong, or some wrong answers as right.
Classroom decorum:
- As UF has advised, students with a contagious illness (or reasonable suspicion of one) should not come to class.
- Healthy students are expected to attend every lecture and discussion, barring excusable reasons such as family emergencies, weddings, funerals, UF-sanctioned extracurricular activities, and religious holidays (see below). Potentially excusable absences that you know about in advance will not be treated as excused unless you inform me of them in advance.
I expect students to arrive on time and to pay attention for all 50 minutes of the period. In most classrooms, arriving late is disruptive (as is leaving early). If a non-optional time commitment (e.g. a class the previous period in a distant location) will force you to be late on a regular basis, let me know at the start of the semester.
- The day before a holiday is not a holiday. Neither is the day after. These facts are not new, but have become even more important now that UF has shortened the fall and spring semesters by a week. Having a large number of absentees disadvantages not only the absentees, but their classmates; a half-empty class deadens the learning atmosphere. Every class day matters, and with the extra week off we've been given in January, nobody should feel any need for extra holidays not on the UF schedule. A grade penalty of up to 5% may be imposed for an unexcused absence on the Friday before Spring Break or the Monday. If you are absent on those days for an excusable reason, I will expect documentation from you promptly. (Note that "My ride is leaving at x o'clock" and "My parents already bought my plane ticket before the semester started" are not reasons of excusable type. If that's a problem for you, there are many non-honors sections of MAP2302—including an online section—one or more of which may have an instructor willing to accommodate your holiday plans.)
- Religious Holidays. The following is part of the University of Florida Policy on Religious Holidays. "Students, upon prior notification of their instructors, shall be excused from class or other scheduled academic activity to observe a religious holy day of their faith."
- Students who choose (for reasons not of excusable type) not to attend class regularly are forfeiting the right to my help in office hours, including explanations of their mistakes on homework and exams. These students should also not expect replies to their emails, even for questions like "Is there an exam tomorrow?" or "Have you decided when the next exam will be?" Also be aware that the University of Florida Attendance Policies contain the following paragraph:
The university recognizes the right of the individual professor to make attendance mandatory. After due warning, professors may prohibit further attendance and subsequently assign a failing grade for excessive absences.
I am giving you now your due warning that I may prohibit further attendance and subsequently assign a failing grade for excessive absences. I reserve the right to impose a less extreme penalty instead.
- If you are absent from lecture or discussion, for any reason, you should obtain written notes from a classmate. (Students are not permitted to share their own recordings of lectures with each other, if they make any such recordings. See In-class recording by students below.)
- If you miss class the day I return an exam or homework, you'll have to pick up your exam or homework from my office. I expect you to do this within a week (unless you are ill or quarantining); I will not hold onto your exam indefinitely. The same is true of any handouts that you missed receiving in class.
- Reading the newspaper, reading messages on your phone, looking at your computer, talking, texting, etc., are rude and disruptive. No electronic devices are to be used in class without explicit permission from me. If you generally take notes by writing in a tablet, see me to get permission. I may ask at any time to see what notes you've taken.
- Please avoid disruptive or distracting noises, such as the tapping of pencils or feet, or the zipping or unzipping of backpacks several minutes before the end of class.
If you miss an exam for an excusable reason, and supply me with satisfactory documentation promptly, I will work out with you some way that is as fair as is feasible for you to make up the missing grade-component. Except in very large classes (which I don't teach) with cookie-cutter exams (which I don't give), there is no such thing as an equitable make-up exam. Thus, the way I have you make up the missing grade-component may or may not be via an exam. If you miss an exam for a reason that I do not consider valid (consistent with UF policy on which absences should be excused), or do not supply me with satisfactory documentation within two days, you should expect to receive a zero for that exam. If extenuating circumstances cause a reasonable delay in your providing me with satisfactory documentation, I may treat your exam-absence as valid and documented. (However, I will be the sole judge of what is "satisfactory", "extenuating", and "reasonable".)
If you are too ill to take an exam, please notify me by email before the exam starts (if possible). In general, you will need to see a doctor or nurse that day to obtain illness-documentation that I'll accept.
UF students are bound by The Honor Pledge, which states:
We, the members of the University of Florida community, pledge to hold ourselves and our peers to the highest standards of honor and integrity by abiding by the Honor Code. On all work submitted for credit by students at the University of Florida, the following pledge is either required or implied: "On my honor, I have neither given nor received unauthorized aid in doing this assignment."
The Honor Code (which can be found here) specifies a number of behaviors that are in violation of this code, and the possible sanctions. Furthermore, students are obligated to report to appropriate personnel any condition that facilitates academic misconduct. If you have any questions or concerns about student conduct, please consult your instructor.
My grading system for this course
- After each homework or exam, I decide grade cutoffs for that item according to the philosophy "A = excellent, B = good, C = satisfactory, D = unsatisfactory but passing". In setting these cutoffs, I do not have a predetermined grade curve or predetermined percentages for letter grades.
- At the end of the semester, I compute a numerical "raw score" for each student, on a 1000 point scale, using the weighting scheme stated earlier: 20% (200 points) for each midterm and 40% (400 points) for the final exam.
On the exams themselves, you'll see point-totals different from the ones above. These are rescaled appropriately in the raw-score computation. For example, if point-values for the problems on the first midterm add up to 138, your exam score will be multiplied by 200/138 in the above computation.
- By applying the same weighting scheme to the cutoffs for exams and homework, I construct raw-score grade cutoffs for each of the grades A, B, C, D. The cutoffs I use for A- and B+ are the trisection points of the interval from the B cutoff to the A cutoff; the cutoffs for the B-, C+, C-, and D+ grades are computed analogously.
The grades that UF currently allows instructors to assign are A, A–, B+, B, B–, C+, C, C–, D+, D, D–, and E. (For grade-point equivalencies of these grades, see this catalog page.) All of these are grades are possible in this class, except the D–.
In my philosophy (and that of my own college professors) of what a minus-grade means, a B–, for example, is not the lower end of the B range; it is somewhat below the bottom of the B range, and means that your work falls a little short of "good". (Said another way: another professor whose regards your work as "a little short of 'good' ", but who regards B– as meaning "the low end of the 'good' range", would not assign you a B– ; he/she would assign you a C+.) This philosophy is consistent with the degree-requirements for most majors at UF: courses count towards your major only if you get a "flat" C or higher, because a C– means that your performance was less than satisfactory—not that it was barely satisfactory—and therefore that you did not satisfactorily complete the course. This philosophy is also consistent with UF's S-U grade option.
For similar reasons, I have never given the D– grade. "D" means "unsatisfactory but passing". My D cutoff is the rock bottom of what I consider to be the "passing" range, so anything below that is a failing grade, which at UF is the E grade. (Note: Because a C is usually needed for a course to count towards requirements for majors, minors, etc., an unfortunate number of faculty, advisors, and students have come to refer to every grade less than C as "failing". This is not the correct meaning of "failing grade", nor has it ever been; again see this catalog page.)
Since I don't determine the exam-grade cutoffs ahead of time, I can't tell you in advance exactly how many points you'll need to get a particular grade for the course. My Honors MAP2302 grade-scale pages for Fall 2024, Spring 2024, and Spring 2023 may give you a rough idea of what to expect. In addition to grade-scales, these pages include a "Distribution of final grades for course" grid at the bottom. You can find more examples of my past grade-scales (not all of which were for honors sections) by navigating from the "Past Classes" link on my home webpage. However, there is no guarantee that this semester's grade-cutoffs will be close to those of any particular past class of mine; they could be higher or lower. Also note that there's been a lot of variation in the distribution of course grades from semester to semester. (There has been a great deal of variability in the strength of my students in the nearly 40 times I have taught MAP 2302. Most of my past sections were non-honors sections—taught before those were converted to large-lecture format—and were been graded somewhat less rigorously than my honors sections. But even among the honors sections, there has been great variability in the strength of the students.)
On average, in order to receive an average grade, students should expect to spend eight to ten hours per week studying and doing homework for this class. This time-estimate is an average, not a maximum—some students will require more time, some less; some weeks the workload will be heavier, some lighter. Some circumstances that may increase your workload are:
- You did not study a similar amount in your previous calculus or precalculus classes.
- You have not retained the knowledge and skills that are the purpose of the prerequisites for this course.
- You cannot do algebra quickly and accurately without a calculator (this may be the case if you did not do a large number of exercises in your calculus or precalculus classes, or if you have relied heavily on calculators in the past).
- You want to get an A.
Scheduling appointments with Dr. Groisser outside office-hours
Before asking to make an appointment outside of my scheduled office hours, please make sure you have first checked when all my office hours are. Even though my office hours are really easy to find (in this syllabus and on my home webpage), more than half my conversations with students who think they can't make my scheduled office hours go something like this: Student: "There's something I wanted to ask you about, but I have a class that meets MWF period X" [where period X is the time of, say, my Wednesday office hour that semester].
Me: "What about my Monday period Y or Friday period Z office hour?"
Student: "Oh, I didn't realize you had a period Y or period Z office hour. Yes, I could make your Monday period Y [or Friday period Z] hour."
Scheduling an appointment usually requires some back-and-forth questions about possible and/or convenient times. Usually, coming up to me at the end of class is the most efficient way to handle this; email is inefficient for this. But in case you do try to handle this by email, here are some do's and don'ts for what to send me: "I'd like to meet with you, but I have a conflict with each of the days/times of your three regular office hours." [So far, so good. Student has indicated awareness that I have office hours at three different days and times, and has not (yet) asked any questions.]
- [DON'T WRITE THIS:] "Are you available any other times this week?"
This is the wrong question to ask by email, even if directly followed by a second question like, "If so, what times could you meet?" The times that are convenient for me might not work for you. In that case, if I answer with only my preferred times, we'll need at least one extra round of (avoidable!) back-and-forth emails. To give any answer that could avoid several rounds of back-and-forth email (other than "Speak to me after class"), I have to spend time a lot of time thinking about my answer. Also, I either have to spend time writing some sort of preference-order list, or wind up with you choosing a time that's really not convenient for me but that I listed in case your schedule conflicts with all the other times I'm listing.
- [DO WRITE SOMETHING LIKE THIS:] "Here is the full schedule of times I can't meet during the week" [followed by a listing of all classes, work conflicts, etc.], or "Here is a list of all the times I could possibly meet during the week" [followed by an appropriate list]." It's okay if, in addition, you state your preferences among the times that are possible for you. What's not okay is stating only your preferred times and asking me to choose from among them.
In-class recording by students
Students are allowed to record video or audio of class lectures. However, the purposes for which these recordings may be used are strictly controlled. The only allowable purposes are (1) for personal educational use, (2) in connection with a complaint to the university, or (3) as evidence in, or in preparation for, a criminal or civil proceeding. All other purposes are prohibited. Specifically, students may not publish recorded lectures without the written consent of the instructor.
A class lecture does not include private conversations between students, or between a student and the instructor, that happen to take place during a class session. Recording of these conversations is prohibited.
Publication without permission of the instructor is prohibited. To "publish" means to share, transmit, circulate, distribute, or provide access to a recording, regardless of format or medium, to another person (or persons), including but not limited to another student. Additionally, a recording, or transcript of a recording, is considered published if it is posted on or uploaded to, in whole or in part, any media platform, including but not limited to social media, book, magazine, newspaper, leaflet, or third party note/tutoring services. A student who publishes a recording without written consent may be subject to a civil cause of action instituted by a person injured by the publication and/or discipline under UF Regulation 4.040 Student Honor Code and Student Conduct Code.
Accommodations for students with disabilities. If you wish to request accommodation for a disability you must first register with the Disability Resource Center. It is always important that you share your accommodation letter with your instructor, and discuss your accommodations, as early as possible in the semester. "Discuss" does not mean merely "notify"; it means more than just having the DRC email me your accommodation letter. Initiating a discussion of an accommodation is the responsibility of the student.
Teaching-evaluations. Students are expected to provide professional and respectful feedback on the quality of instruction in this course by completing course evaluations online via GatorEvals. Guidance on how to give feedback in a professional and respectful manner is available at gatorevals.aa.ufl.edu/students/. Students will be notified when the evaluation period opens, and can complete evaluations through the email they receive from GatorEvals or via ufl.bluera.com/ufl/. Summaries of course-evaluation results are available to students at gatorevals.aa.ufl.edu/public-results/ .
UF Health and Wellness Resources:
- U Matter, We Care initiative. If you or someone you know is in distress, please contact umatter@ufl.edu, 352-392-1575, or visit umatter.ufl.edu/ to refer or report a concern, and a team member will reach out to the distressed student.
- Contact information for the Counseling and Wellness Center. Visit counseling.ufl.edu/ or call 352-392-1575 for information on crisis services as well as non-crisis services.
- Student Health Care Center. Call 352-392-1161 for 24/7 information to help you find the care you need, or visit shcc.ufl.edu/.
- University Police Department. Visit police.ufl.edu/ or call 352-392-1111 (or 9-1-1 for emergencies).
- UF Health Shands Emergency Room / Trauma Center. For immediate medical care call 352-733-0111 or go to the emergency room at 1515 SW Archer Road, Gainesville, FL 32608; ufhealth.org/emergency-room-trauma-center.
For the student to know:
- the meanings and definitions of basic terminology of (ordinary) differential equations (DEs), including: (ordinary) differential equation; initial condition(s); initial value problem (IVP); solution of a DE; solution of an initial-value problem; existence of and uniqueness of (maximal) solutions of an IVP; order of a DE.
- mild conditions that guarantee the existence of a unique maximal solution of an IVP.
For the student to be able to:
- determine whether a given DE is
- linear and homogeneous;
- linear and non-homogeneous;
- separable;
- exact;
- equivalent (on some region) to one of the above;
- not equivalent (on any region) to any of the above.
- produce, for each of the DE-types 1–6 above, an example and a non-example of a DE of that type.
- find the set of all solutions of a first-order DE (or IVP) of any of the types 1–3 above, assuming that functions appearing in the DE satisfy certain mild conditions.
- solve (completely) any homogeneous second-order linear DE with constant coefficients, and any homogeneous second-order Cauchy-Euler DE.
- solve, completely, any higher-order constant-coefficient, homogeneous, linear DE, given a factorization of the characteristic polynomial.
- know when the Method of Undetermined Coefficients (MUC) is applicable, and to be able to apply it to find at least one solution of any linear constant-coefficient non-homogeneous DE of "MUC type".
- know when the method of Variation of Parameters ed is applicable, and to be able to apply it to find at least one solution of any linear constant-coefficient non-homogeneous DE not of "MUC type".
- know, and be able to establish, the relation between the general solution of a linear non-homogenoues DE and the general solution of the associated homogeneous DE.
- apply the preceding relation and write down the general solution of a of a linear non-homogenoues DE for which the student should be able to find a particular solution of the non-homogeneous DE as well as the general solution of the associated homogeneous DE.
- solve suitable linear initial-value problems via the method of Laplace Transforms.
- recognize whether a given DE can be solved via methods studied in this course; when it is, to recognize which method(s) is/are usable; and when more than one method is usable, to recognize which method, if any, is likely to be easier to use than the other usable methods.
Other items that are required for a General Education "syllabus"
Link to statement of General Education Objectives in mathematics and other subject areas.
Student Learning Outcomes (SLOs) The list of SLOs is identical to the list of course goals, earlier in this document. These SLOs are assessed through the three midterms and the final exam. Knowledge of definitions and existence/uniqueness conditions, as well as first-order methods, are assessed primarily in the first midterm and final exam. SLOs concerning second- and higher-order equations are assessed primarliy in the second and third midterms and the final exam. SLO concerning Laplace Transform is assessed primarily in the third midterm and final exam. SLO concerning series solutions is assessed in the final exam. Criterion for Gen Ed credit. A minimum grade of C is required for general education credit.