# MT 4410: Differential Equations.

Overview: This course is an introduction to the modern theory of differential equations from both theoretical and applied viewpoints. We will learn how to solve explicitly a wide variety of differential equations, and how to predict the qualitative behavior of those equations that cannot be solved in closed form. We will also see how differential equations can be used to model and predict diverse scientific phenomena. Topics will include basic first and second order equations, existence and uniqueness of solutions, linear systems, power series solutions.

Lectures: MWF 2:00-2:50 in GASSON 306.

Instructor: Dubi Kelmer, Maloney Hall 526. Email address: dubi.kelmer@bc.edu

Office Hours: MW 12:00-13:00 and Th 13:00-14:00.

I am very happy to answer your questions and to help you with the homework during these office hours. These times are always reserved for you and there is no need for an appointment. I am also available on other times by appointment. Please email me for one. I am always happy to work with students, so don't hesitate to contact me (email is also good for short questions).

Course Syllabus in PDF

Textbook: Elementary Differential Equations by W. E. Boyce and R. C. DiPrima, 10th Edition

Grading: Homework 30%; Each midterm 20%; Final 30%.
Exams: Two in-class exams and one final exam .

Homework: There will be weekly homework assigned and collected every week.
HOMEWORK WILL NOT BE ACCEPTED AFTER THE DAY IT IS DUE!

You are encouraged to typeset your HW in LATEX. Though it takes a while to get the hang of it, this is recommended as it will help you write mathematics clearly. If you want to give it a try, here are some helpful resources

Windows

Homework problems:
• Problem set 1: Section 1.1 problems 4,8,11,23,24; Section 1.2 problems 4,9,15 and section 1.3 problems 4, 6, 12, 17
Solutions due on Friday Sep 9 in class.
• Problem set 2: Section 2.1 problems 4,14,22,30,38; Section 2.2 problems 6,17,21,26,30abcde.
Solutions due on Friday Sep 16 in class.
• Problem set 3: Section 2.3 problems 3, 12, 18 ; Section 2.4 problems 2,13,16,32,33; Section 2.5 problems 3,4,8
Solutions due on Friday Sep 23 in class.
• Problem set 4: Section 2.4 problems 27,28; Section 2.5 problems 15,16; Section 2.6 problems 6,10,15,20,26,28
Solutions due on Friday Oct 7 in class.
• Problem set 5: Section 3.1 problems 4,6,10,18,24; Section 3.2 problems 4,8,28; Section 3.4 problems 6,14,18,23,28
Solutions due on Friday Oct 14 in class.
• Problem set 6: Section 3.3 problems 4,11,15,25,36; Section 3.5 problems 3,4,6,9,15,21
Solutions due on Friday Oct 21 in class.
• Problem set 7: Section 3.6 problems 3, 5, 10, 14, 20; Section 3.7 problems 2, 6, 10 and Section 3.8 problems 4, 7, 10
Solutions due on Friday Oct 28 in class.
• Problem set 8: Section 7.1 problems 2,5,10; Section 7.2 problems 7, 10,21,22 and Section 7.3 problems 8,13,16
Solutions due on Friday Nov 11 in class.
• Problem set 9: Section 7.5 problems 4,15,16,18; Section 7.6 problems 2,7,14 (there is no need to draw direction fields for any of the problems, but do sketch a few trajectories and described behavior of solutions as t grows).
Solutions due on Friday Nov 18 in class.
• Problem set 10: Section 7.7 Problem 1; Section 7.8 Problem 2c; Section 7.9 problems 1,11,14; Section 6.2 problems 11,23; Section 6.3 problems 1, 9, 20; and section 6.4 problems 1, 9. Solutions due on Friday Dec 02 in class.
• Problem set 11: Section 6.5 Problems 1,14,17,18,18; Section 6.6 problems 4,10,13. No need to hand in solutions.