This is the course page for James Pascaleff's MATH 285.
| Date | Lectures covered | |
| Module 1 Exam | Wednesday February 17 | Lectures 1-9 |
| Module 2 Exam | Friday March 18 | Lectures 10-21 |
| Module 3 Exam | Monday April 18 | Lectures 22-30 |
This course will cover parts of chapters 1, 2, 3, 9, and 10 in Edwards and Penney. The course naturally falls into four modules
| Module 1 | First-order ordinary differential equations | Lectures 1-9 |
| Module 2 | Second- and higher-order linear ODE | Lectures 10-21 |
| Module 3 | Fourier series and eigenvalue problems | Lectures 22-30 |
| Module 4 | Partial differential equations | Lectures 31-39 |
The daily schedule of lectures is below; it will be updated as the semester progresses.
| Date | Topic | Lecture Notes | Homework |
| W Jan 20 | 1. Introductory lecture (§1.1) | Lecture 1 | |
| F Jan 22 | 2. Directly integrable equations (§1.2) | Lecture 2 | |
| M Jan 25 | 3. Slope fields (§1.3) | Lecture 3 | |
| W Jan 27 | 4. Separable equations (§1.4) | Lecture 4 | HW 1 due |
| F Jan 29 | 5. First order linear equations (§1.5) | Lecture 5 | |
| M Feb 1 | 6. Popluation models (§2.1) | Lecture 6 | |
| W Feb 3 | 7. Equilibria and stability (§2.2) | Lecture 7 | HW 2 due |
| F Feb 5 | 8. Existence and uniqueness (Appendix) | Lecture 8 | |
| M Feb 8 | 9. Numerical methods (§2.4) | Lecture 9 | |
| W Feb 10 | 10. Intro to Second-order linear equations (§3.1) | Lecture 10 | HW 3 due |
| F Feb 12 | 11. General solutions of linear equations (§3.2) | Lecture 11 | |
| M Feb 15 | 12. Linear independence and general solutions (§3.2) | Lecture 12 | |
| W Feb 17 | Exam on Module 1 (Lectures 1-9) | ||
| F Feb 19 | 13. Nonhomogeneous linear equations (§3.2) | Lecture 13 | HW 4 due |
| M Feb 22 | 14. Constant coefficient linear homogeneous equations (§3.3) | Lecture 14 | |
| W Feb 24 | 15. Constant coefficient differential operators (§3.3) | Lecture 15 | |
| F Feb 26 | 16. Complex roots of the characteristic equation (§3.3) | Lecture 16 | HW 5 due |
| M Feb 29 | 17. Mechanical vibrations (§3.4) | Lecture 17 | |
| W Mar 2 | 18. Nonhomogeneous equations and undetermined coefficients (§3.5) | Lecture 18 | |
| F Mar 4 | 19. Nonhomogeneous equations: the resonant case (§3.5) | Lecture 19 | HW 6 due |
| M Mar 7 | 20. Forced oscillations and resonance (§3.6) | Lecture 20 | |
| W Mar 9 | 21. The damped, forced oscillator (§3.6) | Lecture 21 | |
| F Mar 11 | 22. Intro to Fourier series: orthogonality (§9.1) | Lecture 22 | HW 7 due |
| M Mar 14 | 23. Periodic functions and Fourier coefficients (§9.1) | Lecture 23 | |
| W Mar 16 | 24. Fourier series (§9.1) | Lecture 24: see Lecture 23 notes | |
| F Mar 18 | Exam on Module 2 (Lectures 10-21) | ||
| M Mar 21 | Spring vacation | ||
| W Mar 23 | Spring vacation | ||
| F Mar 25 | Spring vacation | ||
| M Mar 28 | 25. General Fourier series (§9.2) | Lecture 25 | HW 8 due |
| W Mar 30 | 26. Convergence, integration, differentiation of Fourier series (§9.3) | Lecture 26 | |
| F Apr 1 | 27. Sine and cosine series (§9.4) | Lecture 27 | |
| M Apr 4 | 28. Forced oscillation and Fourier series (§9.4) | Lecture 28 | HW 9 due |
| W Apr 6 | 29. Endpoint problems and eigenvalues (§3.8) | Lecture 29 | |
| F Apr 8 | 30. More examples of eigenvalue problems (§3.8) | Lecture 30 | |
| M Apr 11 | 31. Begin Heat equation (§9.5) | Lecture 31 | HW 10 due |
| W Apr 13 | 32. Heat equation and separation of variables I (§9.5) | Lecture 32 | |
| F Apr 15 | 33. Heat equation and separation of variables II (§9.5) | Lecture 33 | |
| M Apr 18 | Exam on Module 3 (Lectures 22-30) | ||
| W Apr 20 | 34. Wave equation I (§9.6) | Lecture 34 | HW 11 due |
| F Apr 22 | 35. Wave equation II (§9.6) | Lecture 35 | |
| M Apr 25 | 36. Laplace equation I (§9.7) | Lecture 36 | |
| W Apr 27 | 37. Laplace equation II (§9.7) | Lecture 37 | HW 12 due |
| F Apr 29 | 38. Sturm-Liouville theory I (§10.1) | Lecture 38 | |
| M May 2 | 39. Sturm-Liouville theory II (§10.1) | Lecture 39 | |
| W May 4 | Review session | HW 13 due | |
| T May 10 | Final Exam including Module 4 (Lectures 31-39) |
| Problems | Due date | Solutions | |
| HW 1 | §1.1: 3, 7, 19, 35, 43; §1.2: 17, 20, 27, 33; §1.3: 6, 21, 28 | Wednesday January 27 | HW 1 Solutions |
| HW 2 | §1.4: 4, 12, 20; §1.5: 9, 13, 15, 33; §2.1: 2, 15, 17 | Wednesday February 3 | HW 2 Solutions |
| HW 3 | §2.2: 3, 7, 9, 28; §Appendix (p. 714): 2, 4, 10; §2.4: 2, 6, 10 | Wednesday February 10 | HW 3 Solutions |
| HW 4 | §3.1: 3, 13, 24, 33, 35, 46; §3.2: 3, 5, 9 (use any method), 13 | Friday February 19 | HW 4 Solutions |
| HW 5 | §3.2: 22, 23, 24; §3.3: 3, 4, 6, 7, 11, 15, 39 | Friday February 26 | HW 5 Solutions |
| HW 6 | §3.3: 8, 14, 22; §3.4: 13, 24, 27, 30; §3.5: 4, 6, 31, 33 | Friday March 4 | HW 6 Solutions |
| HW 7 | §3.5: 10, 14, 17, 34; §3.6: 2, 5, 6, 7, 8, 15 | Friday March 11 | HW 7 Solutions |
| HW 8 | §9.1: 13, 15, 20, 25, 27, 28, 29, 30 | Monday March 28 | HW 8 Solutions |
| HW 9 | §9.2: 9, 11, 18; §9.3: 7, 9, 17, 19, 20; §9.4: 3 | Monday April 4 | HW 9 Solutions |
| HW 10 | §9.4: 4, 7, 8; §3.8: 1, 2, 4, 5, 6 | Monday April 11 | HW 10 Solutions |
| HW 11 | §9.5: 1, 3, 5, 10, 11, 17 | Wednesday April 20 | HW 11 Solutions |
| HW 12 | §9.6: 1, 3, 5, 8, 16 | Wednesday April 27 | HW 12 Solutions |
| HW 13 | §9.7: 1; §10.1: 3, 8 | Wednesday May 4 | HW 13 Solutions |
The two lowest homework scores are dropped when computing the final grade. No late homework will be accepted, and no make-up homework will be given. Because the two lowest scores are dropped, you can miss one or two assignments without penalty.
The three midterm exams will be given in class, at the usual time and location. The final exam will be given at a special date, time, and place to be determined by the registrar.
| Date | Lectures covered | Exam | Solutions | Histogram | |
| Module 1 Exam | Wednesday February 17 | Lectures 1-9 | 1A 1B 1C | 1A 1B 1C | G1 |
| Module 2 Exam | Friday March 18 | Lectures 10-21 | 2A 2B 2C | 2A 2B 2C | G1 |
| Module 3 Exam | Monday April 18 | Lectures 22-30 | 3A 3B 3C | 3A 3B 3C | G1 |
| Final Exam including Module 4 | Tuesday May 10, 8:00-11:00 am, 156 Henry | All lectures | Final, Extra Credit | G1 | |
That is, the Final Exam will be held on Tuesday, the tenth of May in the two-thousand-sixteenth year of the common era, starting at eight o'clock in the morning and being of three hours in duration, in the room numbered one hundred fifty six of the Henry Administration Building.
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. This policy is intended to cover cases of illness, required attendance of university sanctioned events, and other situations.
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.
You can view your scores for assignments in 285 online: Go to http://www.math.illinois.edu/Classes/ and in the left-hand column, click Score Reports. You will be prompted to enter your NetID and password in order to view your scores.
| Homework | 20% |
| Midterm Exams | 48% (3 at 16% each) |
| Final Exam | 32% |
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.
Remember that, according to the grading policy, two homework scores and possibly one midterm exam score will be dropped when determining the final grade. Therefore, you can miss one or two homework assignments and one midterm exam without necessarily incurring any penalty.
In the event that multiple excused abscences will require a student to miss more than one exam or two homeworks, the student should contact the instructor as soon as possible to make arrangments. 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."
