This is the course page for James Pascaleff's MATH 285, sections E1 and F1.
James Pascaleff will have office hours Monday 12/15 11:00am-2:00pm.
| Midterm Exam 1 | Friday, September 19 |
| Midterm Exam 2 | Friday, October 17 |
| Midterm Exam 3 | Friday, November 14 |
| Final Exam | Wednesday, December 17, 1:30 pm-4:30 pm in 314 ALTGELD |
This course will cover parts of chapters 1, 2, 3, 9, and 10 in Edwards and Penney. This schedule will be updated daily as the semester progresses.
| Date | Topic | Lecture Notes | Ungraded Homework | Graded Homework |
| M Aug 25 | §1.1 Differential equations and mathematical models | Lecture 1 | §1.1: 3, 7, 15, 19, 25, 35, 47 | |
| W Aug 27 | §1.2 Integrals as general and particular solutions | Lecture 2 | §1.2: 4, 17, 21, 27, 29, 33 | |
| F Aug 29 | §1.3 Slope field and solution curves | Lecture 3 | §1.3: 1-10 (as you please), 21, 27, 28, 30 | |
| M Sep 1 | Labor Day holiday | |||
| W Sep 3 | §1.4 Separable equations and applications | Lecture 4 | §1.4: 3, 11, 17, 20, 27 | Graded Homework Set 1 assigned |
| F Sep 5 | §1.5 Linear first order equations | Lecture 5 | §1.5: 9, 13, 15, 29, 33 | |
| M Sep 8 | §1.6 Substitution methods and exact equations | Lecture 6 | §1.6: 7, 16, 21 (use u = y-2), 63, 65 | |
| W Sep 10 | §1.6 Exact equations cont'd | Lecture 7 | §1.6: 33, 37, 38 | Graded Homework Set 1 DUE in lecture |
| F Sep 12 | §2.1 Population models | Lecture 8 | §2.1: 2, 15, 17, 21 | |
| M Sep 15 | §3.1 Linear second order equations | Lecture 9 | §3.1: 3, 5, 7, 13, 15 | |
| W Sep 17 | §3.1 cont'd, 3.2 General solutions of linear equations | Lecture 10 | §3.1: 33, 35, 41, 46 | Graded Homework Set 2 assigned |
| F Sep 19 | Exam 1 | |||
| M Sep 22 | §3.2 cont'd | Lecture 11 | §3.1: 24, 25; §3.2: 3, 5, 7, 9, 13, 17 | |
| W Sep 24 | §3.2 cont'd | Lecture 12 | §3.2: 21, 22, 23, 24 | |
| F Sep 26 | §3.3 Homogeneous constant coefficient equations | Lecture 13 | §3.3: 1, 2, 3, 4, 6 | Graded Homework Set 2 DUE in lecture |
| M Sep 29 | §3.3 cont'd | Lecture 14 | §3.3: 7, 11, 15, 39 | |
| W Oct 1 | §3.3 cont'd | Lecture 15 | §3.3: 8, 14, 17, 22 | Graded Homework Set 3 assigned |
| F Oct 3 | §3.5 Mechanical vibrations | Lecture 16 | §3.4: 1, 13, 24, 27, 30 | |
| M Oct 6 | §3.5 Nonhomogeneous equations | Lecture 17 | §3.5: 2, 4, 6, 7, 31, 33 | |
| W Oct 8 | §3.5 Nonhomogeneous equations: resonant case | Lecture 18 | §3.5: 8, 9, 10, 14, 17, 29, 34 | Graded Homework Set 3 DUE in lecture |
| F Oct 10 | §3.6 Forced oscillations and resonance | Lecture 19 | §3.6: 1, 2, 3, 5, 6 | |
| M Oct 13 | §3.6 cont'd | Lecture 20 | §3.6: 7, 8, 9, 15 | |
| W Oct 15 | Review for Exam 2 | Graded Homework Set 4 assigned | ||
| F Oct 17 | Exam 2 | |||
| M Oct 20 | §9.1 Periodic functions and trigonometric series | Lecture 21 | §9.1: 27, 28, 29, 30 | |
| W Oct 22 | §9.1 cont'd | Lecture 22 | §9.1: 13, 15, 20, 25 | |
| F Oct 24 | §9.1 cont'd | Lecture 23 | Graded Homework Set 4 DUE in lecture | |
| M Oct 27 | §9.2 General Fourier series and convergence | Lecture 24 | §9.2: 6, 9, 11, 18, 20 | |
| W Oct 29 | §9.3 Convergence, integration, differentiation | Lecture 25 | §9.3: 17, 19, 20 | Graded Homework Set 5 assigned |
| F Oct 31 | §9.4 Sine and Cosine series, applications | Lecture 26 | §9.3: 7, 9; §9.4: 3 | |
| M Nov 3 | §9.4 Forced oscillation and Fourier series | Lecture 27 | §9.4: 4, 7, 8, 9 | |
| W Nov 5 | §3.8 Endpoint problems and eigenvalues | Lecture 28 | §3.8: 3 | Graded Homework Set 5 DUE in lecture |
| F Nov 7 | §3.8 cont'd | Lecture 29 | §3.8: 1, 2, 4, 5, 6 | |
| M Nov 10 | §9.5 Heat conduction and separation of variables | Lecture 30 | ||
| W Nov 12 | §9.5 cont'd | Lecture 31 | Graded Homework Set 6 assigned | |
| F Nov 14 | Exam 3 | |||
| M Nov 17 | §9.5 cont'd | Lecture 32 | §9.5: 1, 3, 4, 5 | |
| W Nov 19 | §9.5 Heat cont'd; §9.6 One-dimensional waves | Lecture 33 | §9.5: 2, 11, 17 | |
| F Nov 21 | §9.6 cont'd | Lecture 34 | Graded Homework Set 6 DUE in lecture | |
| M Nov 24 | Fall Break | |||
| W Nov 26 | Fall Break | |||
| F Nov 28 | Fall Break | |||
| M Dec 1 | §9.6 cont'd | Lecture 35 | §9.6: 1, 3, 5, 8, 13 | Graded Homework Set 7 assigned |
| W Dec 3 | §9.7 Steady-state temperature and Laplace's equation | Lecture 36 | ||
| F Dec 5 | §9.7 cont'd | Lecture 37 | §9.7: 4, 6, 7 | |
| M Dec 8 | Review | Graded Homework Set 7 DUE in lecture | ||
| W Dec 10 | Review | PDE review |
Total: 43 class periods of 50 minutes (approx 35.8 hours)
Ungraded homework problems are assigned for each lecture. These are intended to help you learn the material through practice. The problems are listed in the schedule of lectures. Separately, an number of graded homework sets will be assigned throughout the semester. These contribute to your grade and are intended to give you a chance to get feedback about your solutions.
| Assignment (PDF) | DUE DATE | Solutions |
| Graded Homework set 1 | Wednesday September 10 in lecture | Solutions 1 |
| Graded Homework set 2 | Friday September 26 in lecture | Solutions 2 |
| Graded Homework set 3 | Wednesday October 8 in lecture | Solutions 3 |
| Graded Homework set 4 | Friday October 24 in lecture | Solutions 4 |
| Graded Homework set 5 | Wednesday November 5 in lecture | Solutions 5 |
| Graded Homework set 6 | Friday November 21 in lecture | Solutions 6 |
| Graded Homework set 7 | Monday December 8 in lecture | Solutions 7 |
The three midterm exams will be given in class, at the usual time and location. All of the exams are cumulative. The final exam will be given at a special date, time, and place to be determined by the registrar.
| Lectures covered | Exam | Solutions | Histogram | ||
| Midterm Exam 1 | Friday, September 19 | 1-6 | 1A 1B | 1A 1B | E1/F1 Combined |
| Midterm Exam 2 | Friday, October 17 | 7-17 | 2A 2B 2C | 2A 2B 2C | E1/F1 Combined |
| Midterm Exam 3 | Friday, November 14 | 18-27 (excluding 23) | 3A 3B 3C | 3A 3B 3C | E1/F1 Combined |
That is, the Final Exam will be held on Wednesday, the seventeenth of December (in the two-thousand-fourteenth year of the common era) starting at one hour and thirty minutes post meridiem, being of three hours in duration, in the room numbered three hundred fourteen in Altgeld hall.
If you have a conflict with the final exam: Please let the instructor know by email as soon as possible (for example, open up your email program and send it right now). In your message, please include the nature of the conflict.
Unless otherwise specified, no books, notes, or calculators are permitted on the exams.
One of the midterm exam scores may be dropped and replaced with the final exam score, assuming that doing so would result in a higher grade (see the section on grading). Because of this, you may miss one midterm exam without necessarily incurring any penalty.
Students who require special accommodation for exams (e.g., for reasons of disability) should contact the instructor at the beginning of the semester to figure out those accommodations.
| Homework | 15% |
| Midterm Exams | 51% (3 at 17% each) |
| Final Exam | 34% |
The grade scale will be no harder than the following scale, but it may be made easier at the sole discretion of the instructor.
Where x is your percentage score:
| A | 93 ≤ x < ∞ |
| A- | 90 ≤ x < 93 |
| B+ | 87 ≤ x < 90 |
| B | 83 ≤ x < 87 |
| B- | 80 ≤ x < 83 |
| C+ | 77 ≤ x < 80 |
| C | 73 ≤ x < 77 |
| C- | 70 ≤ x < 73 |
| D+ | 67 ≤ x < 70 |
| D | 63 ≤ x < 67 |
| D- | 60 ≤ x < 63 |
| F | -∞ < x < 60 |
The University has established policies for dealing with issues of academic integrity (e.g. cheating). For a summary see http://www.las.illinois.edu/students/integrity/. With regard to the exams, we quote a paragraph from that document that is particularly relevant:
"Avoiding cheating and accusations of cheating: First and foremost, you should take all tests and quizzes without assistance of any kind unless such collaboration is required or otherwise allowed by the instructional faculty of the course. Additionally, you should make sure you understand what materials are allowed in exams and make sure you don’t bring things that aren’t allowed. You should also be prepared to show your student ID whenever you take an exam, and you should never pass anything to another student or touch your cell phone during an exam. In short, you should avoid any behavior that can be interpreted as cheating."
In this course, unless otherwise specified, you are not allowed to use anything other than a writing utensil on the exams.
For the graded written homework, it is permissible and even advisable to discuss the problems with your fellow students, but each individual student should write up their answers separately. Copying solutions directly from another student's paper or from an online or printed source is considered a violation of academic integrity.
The Student Code, Article 1, Part 4 contains a fuller description of the University policies.
Attendance to lectures is recommended, but does not directly influence the course grade.
For absences from required activities (exams and homework), legitimate excuses include illness, family emergency, religious holidays, and obligations to officially-recognized university groups, including sports teams. See the policy in the Student Code, Article 1, Part 5. This policy requires that "For excused absences, … [t]he student must make arrangements with the instructor to make up missed work expeditiously." So please let the instructor know as soon as possible if you will miss a test or homework assignment.
