SYLLABUS MA 2051 Ordinary Differential Equations (ODEs), Mayer Humi, Term A 2025 PLEASE READ THIS DOCUMENT CAREFULLY. Instructor:Professor M.Humi,SL405F, e-mail - mhumi@wpi.edu Tel:831-5213 Office Hours: Mon,Tue Thursday and Friday, 5-6PM. Other times are available by appointment. Please always send an e-mail before you come to see me during office hours. PLEASE USE MASH, TA OR PLA OFFICE HOURS AND MATH TUTORING CENTER IN Gordon library TO GET HELP IN THIS COURSE. If you need tutoring please contact the "Academic Resource Office" to make arrangements. My office hours are intended PRIMARILY to answer questions about the lectures.(Please email me if you have to see me to make an appointment) PLEASE send ALL emails to me to mhumi@wpi.edu NOT through canvas. I am definitely NOT available in the mornings 8-12. RESOURCES: TEXT: S.J. Farlow -An Introduction to Differential Equations ISBN: 978-0-486-44595-3 . OR Polking et al -Differential equations ISBN: 0-13-143738-0 The book by Polking et al is FAR SUPERIOR to the one by Farlow but it is more expensive. Two copies of this book will be available at the reserve shelf in the library and you can scan(for free) those pages that you find useful to you in this book. If you use this "option" you do not need to purchase the book by Farlow. I (STRONGLY) recommend that you buy a book for this course ONLY at the end of the first week of classes. LECTURES RECORDINGS: The recordings of the lectures will be published to MA2051 CANVAS site > ECHO 360 ALSO my (typed/hand written) lecture notes will be available on CANVAS (in the files section) usually within 24 hours after the actual lecture. TAs and PLAS and office hours: Dina Kalmanson dkalmanson@wpi.edu office hour Stratton Hall 429 from 12-1pm on Thursdays Math Tutoring Center: The Math Tutoring Center (MTC) in Stratton Hall 206 will re-open for the academic year on Monday, August 25th. Hours are Monday - Thursday 11am - 5pm and Friday 10am - 2pm. It is drop-in style tutoring and is a helpful resource for students. The full schedule linked on canvas and the website MASH and Tutoring: The Academic Resources Center (ARC) offers individual tutoring and Math and Science Help (MASH, group drop-in tutoring) in person on the 5th floor of Unity Hall for undergraduate students. Some MASH sessions that occur after 6pm may take place in the Exam Proctoring Center (EPC, UH 505). Tutoring sessions are 50 minutes long and are facilitated by peer undergraduate students. Tutoring availability is dependent on tutor’s schedules within the ARC hours of operation. Students should use Tutortrac to sign up for 1-on-1 tutoring appointments that fit their schedule. Students are encouraged to schedule 1-on-1 appointments in advance. No appointments are needed for MASH group drop-in sessions. A Term 2025 tutoring will start on Sunday August 24, 2025 and will end on Wednesday October 8, 2025. There will be NO tutoring in A term on: September 1, 2025; September 19, 2025. Information about MASH and tutoring offered by the ARC is located on the Academic Resources Center Canvas Page and on the Academic Resources Center WPI Webpage COURSE GOALS The main goal of this course is to provide students with an understanding of both the theory and applications of Differential equations and methods of their solution. In many ways this course is the "cap-stone" of the basic mathematics sequence. You will use many of the concepts introduced in previous calculus courses and gain further insights regarding their applications in Science and Engineering. The topics covered by this course provide essential background and preparation for many other courses at WPI and you will use them throughout your career. Accordingly students are required to UNDERSTAND and be PROFICIENT in the material covered. Students in this course must realize that they need to become intentional architects of their own learning, actively setting goals, exploring, reflecting, and integrating acquired knowledge and experiences into their career goals and expectations in life to become leaders in their profession. HERE ARE SOME MYTHS I WANT TO DISPEL: 1. AI and Education Each of us is born with a wonderful "blank computer" viz. BRAIN. This "computer" can learn quickly and the main objective of education is to empower it to perform tasks which are more and more complex (like steps on a ladder). Without mastery of these tasks one will not be able to be creative and come up with innovations which require more complex patterns of thinking. The present course provides a key step in this evolutionary process. Do not use AI to impede your creative progress. 2. I do not have to attend lectures and can read the book instead. NO YOU CAN NOT LEARN MATH by reading a book(even if you consider yourself to be a super-genius). It is essential TO MAKE A COMMITMENT TO ATTEND ALL LECTURES IN THIS COURSE. Be FOREWARNED if you plan to "fudge" this course then you came to the wrong address. 3. I do not have to come class and can listen instead to the class capture on CANVAS. Experience shows that this is a VERY BAD choice. 4. The course is about integration. On the contrary the course is about algorithms that avoid integration and still get solutions of Differential equations. 5. I understand the material and therefore I do not have to solve problems or do homework. You might be able to read musical notes but this will NOT enable you to play a piano. Same here. 6. I did not understand the lecture perhaps I should give up. SEEK HELP. Go for help to MASH, the PLA, the Math tutoring center or contact ARO for tutoring. DO NOT BE a "jelly fish". DO NOT GIVE UP. Worthwhile achievements in life do not come on a silver platter. 7. I am not a math major "I just want to pass the course". Without a strong background in ODEs you will be a "second class professional" in whatever discipline you choose. Besides you are spending the best years of your life here why not be the BEST? 8. "I want A-grade" I congratulate you for your motivation and drive for excellence. However remember that to get 'A' you must do 'A-work' and have a complete mastery of the course material. Doing a "B-work" and expecting 'A-grade' is a pie-in-the-sky. EXPECTED LEARNING OUTCOMES: By the end of this course you should be able to do the following: 1. Solve linear differential equations(DE) with constant coefficients 2. solve first order linear DE with non-constant coefficients. 3. Use Laplace transform methods to solve ODEs and systems of ODEs. 4. Have a basic introduction to Numerical methods for ODEs (and learn to use MATLAB). 5. Solve systems of linear DE with constant coefficients by vector and matrix methods. 6. Apply these methods to model and solve problems in science and engineering. (7. Solve some classes of nonlinear differential equations.) COURSE SETTINGS: Cell-Phones etc PLEASE make sure ALL your ringing devices are turned OFF during the lectures. EXAMS**.(See notes at the bottom of the page). There will be two exams Midterm and Final exam: Each of these exams will count for 27% of your final grade. Exams dates are: Sept 16 for the midterm and Oct 10 for the final (both exams are during class time) THESE TESTS ARE CLOSED BOOK AND NOTEBOOKS AND NO Electronic Devices ARE ALLOWED. YOU MUST SHOW ALL YOUR STEPS. OTHERWISE ZERO CREDIT WILL BE GIVEN. All test problems are to be worked using techniques presented in this course. THERE WILL BE NO OTHER EXAM DATES. UNLESS YOU BRING A (VERIFIABLE) NOTE FROM ACADEMIC ADVISING THAT YOU WERE SICK ON THE EXAM DATE. QUIZZES There will be 35min weekly quizzes during class on the following dates: Aug 29 Sept 9 Sept 23 Oct 2 NO ELECTRONIC DEVICES ARE ALLOWED DURING THESE QUIZZES. Students who miss a quiz (due to VERIFIED extenuating circumstances) should notify me (for approval) and make an arrangement with their TA to take a (modified) quiz during the TA office hour or time at the MTC during the following week. IF YOU CAN NOT VERIFY YOUR extenuating circumstances YOU WILL NOT BE ELIGIBLE TO TAKE THE QUIZ AT A LATTER DATE. The rest of the class will be used to provide solutions for the quiz questions and answer any additional questions you might have. Each of these quizzes will count for 10% of the final grade (for a total of 40%). Homeworks. Problems will be assigned weekly to give you practice . Doing these problems regularly is essential for your understanding and mastery. Some of these problems will be designated as optional and will not be collected or graded. The other HW problems should be submitted in one PDF file through canvas by the upcoming discussion session. There will be six homeworks which shall count for 6% of the total grade. THERE WILL BE A PENALTY OF 20% A DAY FOR late submission (UNLESS YOU BRING A (VERIFIABLE) NOTE FROM ACADEMIC ADVISING THAT YOU WERE SICK). GRADES: Ranges for grades are given by A: 100% - 90+% B: 90-% - 80+% C: 80-% - 65+% Please note that NO grades will given out by phone or e-mail. EXAMS, HOMEWORKS that were not collected by students by Oct 22,25 WILL BE DESTROYED. TOPICS TO BE COVERED(Polking) Chapter 1, chapter 4:Secs 4.1-4.5(4.6) chapter 2:Secs 2.2 2.4, chapter 3:Secs 3.1 (3.4), chapter 5:Secs 5.1-5.2,5.3,5.6 (5.5), Chapter 6:Secs 6.1, 6.2 (6.3) 6.4 Chapter 7:(Secs.7.1,7.2,7.3,7.4) Chapter 9:Secs 9.1,9.2 (Sections in brackets will be covered lightly) TOPICS TO BE COVERED(Farlow): Chapter 1:Secs 1.1,(1.2) Chapter 3: Secs 3.4 - 3.12 Chapter 2: Secs 2.1, 2.2, 2.3 Chapter 6: Secs (6.2) 6.3-6.5, (6.9) Chapter 5: Secs 5.1-5.4 5.7. (Secs in brackets will be covered lightly). INTEGRITY/HONESTY CODE: Please note that the integrity/honesty code will be strictly enforced in this class. For more please read http://www.wpi.edu/Pubs/Policies/Honesty/ *** 1. Special needs students should identify themselves to me (in person or email) at the beginning of the course to make proper arrangements. 2. Students who for religious reasons can not take an exam or a Quiz or Discussion at the scheduled time should inform me about this (in person or email) at the beginning of the course to make proper arrangements.