M, Tu, W, Th, 2:45 a.m. - 4:20 a.m.

520 Mathematics building

July 7 - August 15

Course Information

Assignments

Homework: There will be homework assignments every week. The homework will be due on Tuesdays before class or at the beginning of class. There will be a deposit box (turn in) on the fourth floor and a pick up box for graded homework. No late homework will be accepted. No exceptions. Please staple your homework. Extra credit problems will be given for all assignments. These are harder problems, designed to test your understanding. These will only be graded if you have completed all the problem set, you cannot substitute them for another exercise (nor is it in you interest: they are harder).

Quizzes: There will be short quizzes (about 10 minutes) every Monday. These should be easy if you study regularly. I just want to make sure nobody is falling behind.

Exams: There will be one midterm on July 24 and one final exam on August 14. These will last 1 hour and 15 minutes.

Grading Scheme: The final grade will be determined from the following (tentative) weights

Homework: 20%

Quizzes: 15%

Midterm: 25%

Final exam: 40%

Help Room: 406 Mathematics Building. The schedule is available here.

Policies

Summer Session: The class will only last six weeks and meet four times a week. This is very fast and makes the class both demanding and comforting. You will have to work every day to keep up with the class, but your efforts should have almost immediate results.

Assignments: Even though the homeworks only make up a relatively small portion of the final grade, they are probably the most important part of your work. Doing the homework is the only way you can really test your knowledge of the material. If you do not like abstract statements, examples and homework are the mean to understand the theory and gain respect for it. As for the quizzes, I like to ask for definitions. When solving exercises, many students have no idea where to start. If you know the definitions of the objects at play, you can start by writing them down. Then write down what you are asked. Once this is done, the path from one to the other is often already clear to you.

Calculators: It might be helpful to have a graphic calculator during the class. A scientific calculator will be needed for some computations in the exercises, although it is not strictly necessary to have one as you can use websites instead (like google). Calculators will not be allowed during the exams/quizzes.

Grading Policies: Your homework should show your work, not only the end result. You are expected to detail your computations, write sentences that explain what you do, quote the theorems you are using and verify their assumptions. You will loose credit if you fail to do so, even if you get the right answer. You may work with your classmates on the homework. However, you are supposed to write up your own copy, and indicate who your worked with on your copy, so that we are not too surprised by the similarities.

Reading Assignments: I will regularly assign reading. If we do not have time to cover some material in class, I might assign reading it for the following week. In any case, we will go by the book, maybe not in the same order but I will update the syllabus often, so you can read in advance and feel like you understand everything at the lectures. Or you can come to the lectures and open the book afterwards with the happy feeling you have already read it. In any case, I encourage you to read the sections in the book on your own.

Class Participation: Attendance is not required, but strongly encouraged. Ask questions. A lot. Please. I like questions. On occasion, I might stop the class if I do not have any question. There is no stupid question. Do not spend the class feeling like you are watching a foreign movie with no subtitles because you did not dare to ask a question in the first five minutes. Also, do not hesitate to tell me if I am going too fast, too slow, etc. If anything, you are doing me a favor for improving my teaching.

Make-up Exams: If you are not present at an exam, you will get 0. There will be no make-up exam without a note from a doctor or the dean.

Lectures Schedule

Disclaimer: The following schedule is only tentative and will change. The homework will be posted as we go.

Course Announcements

Please check this section regularly for updates.

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Reference: Call number 77029. Here is the course page on the directory of classes.

Instructor: Thibaut Pugin (206B Mathematics, pugin@math.columbia.edu)

Teaching Assistant: TBA

Textbook: Elementary Differential Equations and Boundary Value Problems, by William E. Boyce and Richard C. DiPrima (8th edition). Note that this book is available as an e-book for a substantially inferior cost on the publisher’s website.

Office Hours: M, Tu, W, Th, 4:30 p.m. - 5:30 p.m. in 206B Mathematics or by appointment.

Course Description: This course is an introduction to differential equations. We will define what differential equations are and study their solutions. When do they exist? How do we find them? We will study various special types of equations, and the presentation of the material will use Linear Algebra. We will do some review of the latter, although this should be familiar to you already. Later on, we will study more solving techniques, some numerical. We will finish the course with a discussion on stability. See the (prospective!) syllabus below for a more detailed outline.