MATH 286: Intro to Differential Eq Plus

Sections B1, F1

Fall 2018: August 27 - December 20


Description and Prerequisite

"Techniques and applications of ordinary differential equations, including Fourier series and boundary value problems, linear systems of differential equations, and an introduction to partial differential equations. Covers all the MATH 285 plus linear systems. Intended for engineering majors and other who require a working knowledge of differential equations.

Credit is not given for both MATH 286 and any of MATH 284, MATH 285, MATH 441. Prerequisite: MATH 241. This course satisfies the General Education Criteria in Fall 2018 for: Quantitative Reasoning II" (UIUC Course Catalog)

Instructor

Name: Jer-Chin (Luke) Chuang
Office: Illini Hall 24 (corner of S. Wright St. and E. John St., across from Altgeld Hall)
E-mail: jchuang [at] illinois [dot] edu please add [math286] in subject line when emailing me
Homepage: http://faculty.math.illinois.edu/~jchuang/ (Current course syllabi are linked at this webpage.)

Teaching Assistants

Names: Shufan Mao, Hanna Kim, Sophie Le, and Michael Toriyama
Tutoring Center: 441 Altgeld, at least one of the above TAs will be present during the following times

Class Location and Time

Section B1: MWRF 9-9:50 AM Location: 23 PSYCH BLD
Section F1: MWRF 2-2:50 PM Location: 100 GREG HALL

Textbook and Coverage

The text is Elementary Differential Equations with Boundary Value Problems, 10th edition by Boyce and DiPrima. We will cover most of chapters 1-4 and 7-11.

A tentative list of topics may be found here.

A link to a tentative weekly schedule.

Please enroll yourself in the online discussion for this course at Piazza. Search for "MATH286 BF"

Students are encouraged to use the computer algebra system Mathematica. UIUC students may access the program online for free, or download a copy for a fee.

Mathematica examples parallel to the course textbook as well as chapter review sheets may be found at the student companion site for the course textbook.

The free, downloadable Java applets dfield and pplane may also be helpful.

Course Objectives and Outcomes

Students will become familiar with the concepts of ordinary and partial differential equations (ODE/PDE) and their utility in modeling physical phenomena. They will explore (1) both the geometric and analytic perspective to solving ODEs, (2) the importance of linearity in simplifying the study of ODEs, and (3) the power tool of Fourier series in constructing solutions to certain PDEs. Time permitting, the numerous challenges attendant nonlinear ODE systems will be introduced.

At the conclusion of the course, students should be able to (1) solve certain basic classes of first-order ODEs, (2) solve first-order constant coefficient linear ODE systems, (3) understanding the pivotal simplying role of linearity for solving ODEs, and (4) solve certain classes of PDEs via Fourier series, and time permitting, (5) solve certain regular Sturm-Liouville problems

Because of their utility in modeling physical phenomena, ODEs and PDEs are used in numerous disciplines within the natural sciences and engineering. Their study draws from a multitude of mathematical perspectives, and the ease with which one may initiate their study belies the richness of its theory and interconnections, a consideration of which will significantly expand critical thinking and problem-solving skills. These will be fostered via regular homework assignments and semester exams that balance assessment of conceptual understanding and technical execution.

Assessments

Homework will be assigned weekly via WebAssign and due at 9am each Friday. For setup instructions see here. For support questions see their student support page.

There will be three 75-minute midterm exams from 7-8:15PM on the following Tuesdays in 1LMS (Loomis Laboratory of Physics) Room 141: 10/2, 10/30, 12/4

Student scores will be based on homework (altogether 10%), three midterms (altogether 60%) and a final exam (30%). All assessments are cumulative, closed book and closed notes. Partial credit may be awarded on a question-by-question basis.

Midterm and final exam scores are visible via Moodle using your NETID login.

Important: All grading inquiries must be made within 5 working days from the return of the assessment (or announcement of its availability for pick-up). No score changes will be made to the assessment thereafter.

You must bring your student ID card to each in-class assessment. I reserve the right to check I.D. cards before/during any semester or final exam. You are requested to turn off and store away all cellphones during midterms and final exams.

I construe your volitional enrollment at UIUC as tacit affirmation to abide by UIUC's rigorous standards of academic integrity. The following affirmation will be printed on each midterm and the final exam: "In submiting this work, I have upheld UIUC policies on academic integrity." You must sign this affirmation. Submitted exams (whether midterm or final) without your signature will receive no credit.

Classroom and Course Policies

Please turn OFF the wireless/cellular feature of all electronics (cell phones, computers, PDAs, e-Readers, etc.) and refrain from eating and drinking during the lectures. During the lectures, please be mindful of the students around you and refrain from disruptive or distracting behaviors such as loud talking, joking, non-course related conversations, etc.. Please work together to foster a conducive learning environment for all students present. Those who persist in rude behaviors will be asked to leave the lecture.

There will be no make-up for any assessment (including homework) except for university-sanctioned absences and religious holidays. Unless due to sudden illness, I must be notified at least a week before the date. In case of a missed exam/quiz, I reserve the right to choose one of the three following options: make-up exam/quiz, the average of your other exams/quizzes, or your final exam score.

Getting Help

Note: If you have received help from the tutoring center or office hours, please consider posting a summary at Piazza so everyone can benefit. The process of explaining a concept or problem helps solidify your own understanding and benefits others simultaneously.

Recommendations for Learning

Some Important Links