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:

Integration Pre-requisites:

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:

Tentative ScheduleAnnouncements
Week 1
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 notes (2025) ,    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,   answers,  3.5 guess summary,   notes Fall2025 8:30am,  notes Fall2025 9:30am,  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 4.4 derivation 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),    2025 notes
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 Sun, Nov 23, 2025 - Sun, Nov 30, 2025 ****
Week 14
12/1 7.5graphing examples part 2,    (2025 notes),    (2024 notes),    7.5graphing,   Class notes 2023,   7.6,  Fall 22 slides
12/37.5graphing 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