MATH 219 Introduction to Differential Equations
Credit: (40) 4
Catalog description: First order equations and various applications. Higher order linear
differential equations. Power series solutions. The
Course Objectives: By the end of this course, a student will:
Course Coordinator: Özgür Kişisel (Office: 128, Phone: (312) 210 5388) akisisel@metu.edu.tr
Course Assistant: Levent Aybak (Office: Z43, Phone: (312) 210 5360) aybak@metu.edu.tr
Course Website: http://ma219.math.metu.edu.tr/ and https://metuclass.metu.edu.tr/
Textbook: “Elementary Differential Equations and Boundary Value Problems”, Boyce, W. E., DiPrima, R. C., 9^{th} ed.
Exams and Grading:
Midterm 1 : 35 % (8^{th} of April, Saturday, 17:00)
Midterm 2 : 30 % (13^{th} of May, Saturday, 17:00)
Final : 40 % (to be announced)
Total : 105 (5 points bonus)
Attendance: Attendance is required. Policy varies from section to section.
Suggested Problems:A list of suggested problems will be announced on the course website. Students are encouraged to attempt to solve all of these problems in a timely manner, and ask the instructors about the ones that they cannot solve. At least 25% of the exam problems will be chosen among these problems.
NA Policy: A student who misses all exams will receive a grade of NA for the course. In addition, a student with weighted average of Midterm 1 and Midterm 2 grades less than 15% will not be eligible to take the final examination and receive a grade of NA from the course (assuming that midterm 1 and 2 grades are M1 and M2 respectively, this condition is (0.30*M1+0.30*M2)/0.60<15).
Makeup Policy: In order to be eligible to enter a makeup examination for a missed examination, a student should have a documented or verifiable, and officially acceptable excuse. A student cannot get makeup examinations for two missed exams. The makeup examination for all exams will be after the final exam, and will include all topics.
Lectures:
Section, Instructor 
Lecture Time and Place 
Instructor email, Office (Math building), office phone 
S1. Özgür Kişisel 
Tue 10:4012:30 (U3) Fri 8:4010:30 (U3) 
128, (312) 210 5388 
S2. Semra Pamuk 
Mon 10:4012:30 (G111) Thu 8:4010:30 (G111) 
228, (312) 210 2990 
Office Hours: To be announced on the website.
Important Dates:
· February 20: Classes start
· February 27March 3: Adddrop period
· April 8: Midterm 1
· April 23: National Sovereignty and Children’s Day (Sunday)
· April 30: Course withdrawal
· May 1: Labor and Solidarity Day (Monday)
· May 13: Midterm 2
· May 19: Commemoration of Atatürk & Youth and Sports Festival (Friday)
· May 26: Classes end
· May 29June 9: Final Exams
· June 19: Grades announced
Course Schedule
The table below is a rough guideline for
the content of course lectures. Instructors may reorder their lectures as
necessary/desired. Section and page numbers below are from the textbook, Elementary
Differential Equations and Boundary Value Problems, Boyce and DiPrima, 9^{th} ed., 2010.
Week
1: Feb.2024 
1 
§1.1, §1.3: Introduction, Direction Fields Chapter
2. First Order Differential Equations §2.2: Separable equations (also homogeneous equations  see p49 #30). 
2 
§2.1: Linear equations; Method of integrating factors. 

Week
2: Feb.27Mar.3 
3 
§2.3: Modeling with first order equations 
4 
§2.4: Differences between linear and nonlinear equations 

Week
3: Mar.610 
5 
§2.6: Exact equations and integrating factors. 
6 
Chapter
7. Systems of First Order Linear Equations §7.1:
Introduction. 

Week
4: Mar.1317 
7,8 
§7.3: Systems of linear algebraic equations; Linear independence, eigenvalues, eigenvectors. 
Week
5: Mar.2024 
9 
§7.4:
Basic theory of systems of first order linear equations. §7.5: Homogeneous linear systems with constant coefficients. 
10 
§7.6: Complex eigenvalues. 

Week
6: Mar.2731 
11 
§7.7: Fundamental matrices. §7.8: Repeated eigenvalues. 
12 
§7.9: Nonhomogeneous linear systems (variation of parameters only). 

Week
7: Apr.37 
13 
Chapter
4. Higher Order Linear Equations §4.1: General theory of n^{th} order linear equations 
14 
§4.2: Homogeneous equations with constant coefficients. 

MIDTERM 1 (April 8, Saturday) 

Week
8: Apr.1014 
15 
§4.3: The method of undetermined coefficients. 
16 
§4.4: The method of variation of parameters. 

Week
9: Apr.1721 
17 
§3.7: Mechanical and electrical vibrations. §3.8: Forced Vibrations. 
18 
Chapter
5. Series Solutions of Second Order Linear Equations §5.1: Review of Power Series §5.2: Series Solutions Near an Ordinary Point, Part I §5.3: Series Solutions Near an Ordinary Point, Part II 

Week
10: Apr.2428 
19 
§5.4: Euler Equations, Regular Singular Points 
20 
§5.5: Series Solutions Near a Regular Singular Point, Part I 

Week
11: May.15 
21 
Chapter 6. The Laplace Transform §6.1: Definition of the Laplace transform. 
22 
§6.2: Solution of initial value problems. §6.3: Step functions. 


Holiday: May 1^{st} , Monday 

Week
12: May.812 
23 
§6.4: Differential equations with discontinuous forcing functions. 
24 
§6.5:
Impulse functions. 

MIDTERM 2 (May 13, Saturday) 

Week
13: May.1519 
25 
Chapter
10. Partial Differential Equations and Fourier Series 

Holiday: May 19^{th} , Friday 

Week 14: May.2226 
26 
§10.2:
Fourier series. 
27 
§10.4: Even and odd functions. §10.5: Separation of variables, heat conduction in a rod. 

FINAL EXAM (between May 29June 9) 