MATH:2560 Engineering Math IV: Differential Equations

Spring 2025

Section 0102: 9:30A - 10:20A MWF in 218 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
1/22 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)

1/24 old notes for ch 1 and 2 (pdf)
Week 2
1/27 ch 1 (pptx) ,    2.2 FYI: old annotated slides (AM pptx - OLD),   (PM pptx - OLD) ,  
Video: Review of 2.1: Solving first order LINEAR differential equation using an integrating factor (15:46 min)
1/29 slope fields, 2.2 (pptx),    2.1 notes,     2.1 Integrating Factor more examples: AM notes,    PM notes,    older 2.1 notes
1/31 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
2/3 2.2 example(pptx) Video: Theorem 2.4.2/domain (28:41 min)
2/5 2.4: Existence and Uniqueness slides,   annotated slides, 2.5 Stability
2/7 2.4, 2.5, 2.5   old slides, old FYI: old annotated slides 2.4&2.5AM    2.4&2.5PM
Week 4
2/10 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)
2/12 2.8 Approximating solutions (slides), FYI: old annotated slides    2.5&2.8PM    AM,    PM 2.8, 2.7, 3.1),
2/14 2.8, 3.1 - 3.4, FYI: old annotated slides AM    PM, Quiz 2
Week 5
2/17 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''.

2/19 9y'' + 6y' +y = 0, y(0) = 1, y'(0) = 2, Wronskian.   
FYI: OLD FYI: old annotated slides AM    PM       FYI: Linearity, 3.1 - 3.4, 3.5, FYI: old annotated slides AM    PM
2/21 3.2
Week 6
2/24 Review Midterm 1 6:30PM - 8:00PM 2/27/2025 Thu
over Chapters 1 and 2 and 3.1-3.4
2/26 Problem session
2/28 3.5   FYI: 3.5,   old annotated slides PM,     
Week 7
3/3 3.5 worksheet,   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
3/5 3.7 Rcos(wt-d),   3.8 Rcos(wt-d)
3/7 Attendance Quiz 16,   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
3/10 3.8, 4.1 , FYI: old annotated slides AM,   PM 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

3/12 4.1, 4.2, FYI: old annotated slides AM,   PM
3/14 4.1, 4.2, 2023 quiz 3,  2023 answers
***** Spring Break March 16 - 23 ****
Week 9
3/24 Attendance quiz 20/21,     3.7 damping,    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

3/26 4.4
3/28 6.1 notes , ONLINE quiz 4
Week 10
3/31 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
4/2 Notes,    LaPlace table,   6.2   
4/4 6.3, notes, 6.3 answers,   6.3
Week 11
4/7 6.3 (see also 11/8)
4/9 6.4 example,    6.3, 6.6, 6.4 ,    6.4 ,    2023 notes
4/11 6.5, 6.6,    and online quiz 5
Week 12
4/14 Review,    3.8 Resonance,    resonance,    Midterm 2: 6:30PM - 8:00PM 04/17/2025 Thu in C20 PC over Chapters 3 and 4 and 6.1-6.3.
4/16 Problem session
4/18 7.3, FYI: old annotated slides AM,   PM,
Week 13
4/21 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
4/23 7.5 graphing, 7.5 graphing, 7.6
4/25 7.5graphing examples,    (2024 notes),    7.5, 7.6,   2023 notes
Week 14
4/28 7.5graphing examples part 2,    (2024 notes),    7.5graphing,   Class notes 2023,   7.6,  Fall 22 slides
4/307.5graphing examples part 3,    (2024 notes),    Class notes 2023,   2023 slides ,  OLD notes and sample quiz
5/2 9.1 summary ,   9.1, 9.2 ,    9.1, 9.2 , and online quiz 6
Week 15
5/5 7.6,   9.2 (2023 version)
5/7 9.1, 9.2 ,   7.7
5/9 Review, see also Darcy Lecture under ICON/Modules, Review, Review
Final's week
TBA Final exam TBA

Not covered: 9.3 , annotated