MATH:2560 Engineering Differential Equations

Fall 2025

Section 0091: 9:30A - 10:20A MWF in 217 MLH

Section 0103: 8:30A - 9:20A MWF in 217 MLH

Instructor: Dr. Isabel K. Darcy
Department of Mathematics and AMCS
University of Iowa
Office: 25J MLH
Phone: 319-335- 0770
Email: isabel-darcy AT uiowa.edu

Ways to get help:

Get help during class. Please ask questions.
Get help during office hours.
Make an appointment outside of office hours.
E-mail me questions. You can also take a picture with your phone, computer, etc to show me your work.
Math Tutorial Lab in 125 MacLean Hall
Engineering Tutoring, 6:00 PM - 9:00 PM, Sunday - Thursday in 3612 Seamans Center
Tutor Iowa
Math Platoon (for military-connected students)
Other tutoring resources

Integration Pre-requisites:

Integration by substitution
Integration by parts
Integration by partial fractions

The following free supplemental online book contains many nice examples and good explanations: Paul's Online Notes: Differential Equations

TENTATIVE CLASS SCHEDULE-ALL DATES and CONTENT SUBJECT TO CHANGE:

Week 1
Tentative Schedule		Announcements
8/25	1.1, 1.2 = 2.2 , notes	Partial Fractions Review Videos: Integration by parts (12:44 min), Linear algebra + partial fractions review (25:45 min), Slope fields (45:18 min)
8/27	old notes for ch 1 and 2 (pdf)
8/29	ch 1 (pptx) , 2.2 FYI: old annotated slides (AM pptx - OLD), (PM pptx - OLD) ,
Week 2
9/1	Labor Day Holiday	Video: Review of 2.1: Solving first order LINEAR differential equation using an integrating factor (15:46 min)
9/3	slope fields, 2.2 (pptx), 2.1 notes, 2.1 Integrating Factor more examples: AM notes, PM notes, older 2.1 notes
9/5	Quiz 1, more 2.1 notes, more 2.1 notes (Marked), 2.2 + HW2 hints (pptx), 2.3 notes, 2.3 example from p. 9 of old notes for ch 1 and 2 (pdf)
Week 3
9/8	2.2 example(pptx)	Video: Theorem 2.4.2/domain (28:41 min)
9/10	2.4: Existence and Uniqueness slides, annotated slides, 2.5 Stability
9/12	2.4, 2.5, 2.5 old slides, old FYI: old annotated slides 2.4&2.5AM 2.4&2.5PM
Week 4
9/15	3.1: 2nd order linear homog, 2.7: Approx 1st order solns ,	Video: 2.7: Euler's method for approximating a function using tangent lines (27:00 min)
9/17	2.7 notes
9/19	2.8 Approximating solutions (slides),FYI: old annotated slides 2.5&2.8PM AM, PM 2.8, 2.7, 3.1), Quiz 2
Week 5
9/22	2.8, 3.1 - 3.4, FYI: old annotated slides AM PM, notes for 3.1, 3, 4, FYI: 3.1 - 3.2, 3.1 - 3.4 (old), FYI: old annotated slides AM PM	For HW 5, notice the behavior of the solutions. Some of these solutions will model mechanical/electrical vibration problems (section 3.7) Hint for problem 15: to use recommended substitution, note y' = dy/dt = (dy/dx)(dx/dt). Use chain rule to calculate y''.
9/24	3.1, 2, 4 summary FYI: OLD FYI: old annotated slides AM PM FYI: Linearity, 3.1 - 3.4, 3.5, FYI: old annotated slides AM PM
9/26	3.2
Week 6
9/29	3.5	Midterm 1 6:30PM - 8:00PM 10/02/2025 Thu over Chapters 1 and 2 and 3.1-3.4
10/1	Review
10/3	3.5 FYI: 3.5, old annotated slides PM,
Week 7
10/6	3.5 worksheet, 3.5 guess summary, notes Sp2025, answers, Attendance Quiz 14, 3.7 , FYI: old annotated slides AM, PM	Practice problems (not HW, but will help) 3.5 worksheet, answers with explanations. 3.5 worksheet 3.5 worksheet answers
10/8	3.7 Rcos(wt-d), 3.8 Rcos(wt-d)
10/10	3.7, 3.8 , FYI: old annotated slides AM, PM 3.7, 3.8 review, 4.1, FYI: old annotated slides AM, PM
Week 8
10/13	Quiz 3, 3.7 damping, FYI: old annotated slides AM, PM 2023 quiz 3, 2023 answers	For section 3.6 HW,use matrix form if you use a formula (this will make section 4.4 much easier). 3.7 worksheet (optional -- includes more advanced topics NOT covered) 3.7 worksheet ANSWERS
10/15	Attendance Quiz 16, 3.8 Resonance, resonance, FYI: old annotated slides AM, PM
10/17	4.1, 4.2
Week 9
10/20	Attendance quiz 20/21, 4.3, 3.6, FYI: old annotated slides AM, PM	Mechanical Vibration review Solving higher order linear homogeneous DE (See also 4.1/4.2 slides) Intro to Ch 6: LaPlace Transform
10/22	4.4
10/24	6.1 notes , ONLINE quiz 4
Week 10
10/27	6.1 - 6.3, 6.2 Warning: Announcements made in slides (recorded or unrecorded) do not apply to current course.	Some review problems including answers
10/29	Notes, LaPlace table, 6.2
10/31	6.3, notes, 6.3 answers, 6.3
Week 11
11/3	6.3 (see also 11/8)
11/5	6.4 example, 6.3, 6.6, 6.4 , 6.4 , 2023 notes
11/7	6.5, 6.6, and online quiz 5
Week 12
11/10	Review, , 3.8 Resonance, resonance,	Midterm 2: 6:30PM - 8:00PM 11/13/2025 Thu over Chapters 3 and 4 and 6.1-6.5.
11/12	Problem session
11/14	7.3, FYI: old annotated slides AM, PM,
Week 13
11/17	7.1, 7.4, FYI: old annotated slides AM, PM, 2022 notes	For 7.5 graphs, you might consider using this pdf for your graphs
11/19	7.5 graphing, 7.5 graphing, 7.6
11/21	7.5graphing examples, (2025 notes), (2024 notes), 7.5, 7.6, 2023 notes
*** Thanksgiving Break March 16 - 23 **
Week 14
12/1	7.5graphing examples part 2, (2025 notes), (2024 notes), 7.5graphing, Class notes 2023, 7.6, Fall 22 slides
12/3	7.5graphing examples part 3, (2025 notes), (2024 notes), Class notes 2023, 2023 slides , OLD notes and sample quiz
12/5	7.5, 7.6, 9.1 summary , 9.1, 9.2 , 9.1, 9.2 , and online quiz 6
Week 15
12/8	7.6, 9.2 (2023 version)
12/10	9.1, 9.2 , 7.7
12/12	Review, see also Darcy Lecture under ICON/Modules, Review, Review
Final's week
	Final exam TBA

Not covered: 9.3 , annotated