1. Contact Information
  2. Prerequisites
  3. Course Description and Credit Hours
  4. Required Texts
  5. Course Objectives
  6. Student Learning Outcomes
  7. Other Course Materials
  8. Outline Of Topics
  9. Exams and Assignments
  10. Grading Policy
  11. Policy on Missed Exams and Coursework
  12. Attendance Policy
  13. Notification of Changes
  14. Custom Sections
  15. Statements on Academic Misconduct
  16. Statement On Disability Accommodations
  17. Severe Weather Protocol
  18. Pregnant Student Accommodations
  19. Religious Observances
  20. UAct Statement

Appld Diff Equations I

MATH 238-050Summer 2022 | 3 Credit Hours


Shibin Dai

Contact Information

UA Campus Directory:


UA Course Catalog Prerequisites:

C- or higher in MATH 126 or C- or higher in MATH 146

Course Description

Course Description and Credit Hours

Introduction to analytic and numerical methods for solving differential equations. Topics include numerical methods and qualitative behavior of first order equations, analytic techniques for separable and linear equations, applications to population models and motion problems; techniques for solving higher order linear differential equations with constant coefficients (including undetermined coefficients, reduction of order, and variation of parameters), applications to physical models; the Laplace transform (including intial value problems with discontinuous forcing functions). Use of mathematics software is an integral part of the course. Computing proficiency is required for a passing grade in this course.

Required Texts

Required Texts from UA Supply Store:

Course Objectives

Students will learn how to solve first order differential equations, second order initial value problems and model physical phenomena with differential equations.

Student Learning Outcomes

  1. Students will use analytical methods to solve linear ordinary differential equations.

  2. Students will classify an ordinary differential equation in terms of its degree, linear or nonlinear, homogeneous non-homogeneous and pick the technique most likely to solve it.

  3. Students will model simple physical and biological phenomena.

  4. Students will use basic numerical techniques to solve linear initial value problems.

  5. Students will use MATLAB to solve initial value problems, and study the qualitative and quantitative properties of differential equations.

Other Course Materials

Outline of Topics

Chapter 1. Introduction [Sections 1.1-1.4]

Chapter 2. First Order Differential Equations [Sections 2.1-2.3, and Bernoulli equations]

Chapter 3. Mathematical Models [Sections 3.1-3.3]

Chapter 4. Linear Second Order Equations [Sections 4.1-4.6, 4.9, 4.10]

Chapter 5. Introduction to Systems [Sections 5.1, 5.2 (2 by 2 systems only)]

Chapter 7. Laplace Transforms [Sections 7.1-7.8, (and if time permits, 7.9)]

Exams and Assignments

  1. Homework will be assigned after each section. You have to complete the homework using MyMathLab. You will need to purchase an access code. You must do all the assignments on time - this is a very important way to learn the material. The majority, but not all, test questions will be minor variations of the assigned homework problems and the problems done in class.

  2. Group Projects: There will be two computer-based (MATLAB) assignments done by yourself or in groups. Your assignments should be done independently and not copied from others. MATLAB is available at Gordon Palmer 152, Rodgers library, Gorgas library, McLure Education library and Hoole Special Collections library.

  3. Exams: There will be three in-class exams during the semester and a comprehensive fnal exam. In-class exams and the final will be closed book and will be based on the material covered in class.

Exam 1: Thursday June 9 (Chapters 1-3).

Exam 2: Thursday June 16 (Chapter 4).

Exam 3: Thursday June 23 (Chapter 5 and the first half of Chapter 7).

Final: Thursday June 30 (cumulative).

Grading Policy

Homework: 14%

Matlab Projects: 6%

3 in class exams: 45% (15% each)

Comprehensive final exam: 35%

Eight or more missing lectures without legitimate excuses will guarantee a penalty of -3% from the final grade.

[97, 100)


[87, 90)
























Policy on Missed Exams and Coursework

There will be no extensions of the deadline for homework, unless there are documented legitimated reasons.

A makeup exam may be given in the following cases subject to verification: a medical emergency, a University-sponsored event, a religious event, or a family emergency. A makeup exam should be scheduled at least one week in advance, unless it is due to emergency situations. You must present the documentation either before the exam or as soon as you return to class.

Attendance Policy

Class attendance is required. Class participation is strongly encouraged. Students are solely responsible for any work missed during an absence. At the beginning of every class the instructor will pass an attendance sign up sheet. Everyone need to initial on the sheet.

Notification of Changes

The instructor will make every effort to follow the guidelines of this syllabus as listed; however, the instructor reserves the right to amend this document as the need arises. In such instances, the instructor will notify students in class and/or via email and will endeavor to provide reasonable time for students to adjust to any changes.

Department of Mathematics Academic Misconduct Policy

  1. During tests you may only use a calculator that has been specifically approved by the instructor.  Using or being in possession of an unauthorized calculator will be considered academic misconduct. 
  2. Taking a test for another student will be treated as academic misconduct by both parties.  In particular, showing an instructor a fake ID or another student’s ACT card will be treated as academic misconduct.
  3. Receiving or providing assistance of any kind during an exam will be treated as academic misconduct by both parties.
  4. Cellphones must be turned completely off and placed with other belongings on the floor.  All watches must be taken off and put away.  DO NOT put your phone or watch in your lap or on your chair or desk.  Physically holding or concealing on your person a phone, watch or other unauthorized technological device (including but not limited to headsets, earphones, earbuds, microphones, cameras, or scanning pens) will be treated as academic misconduct.
  5. If you are seen using an unauthorized device, the instructor may request that you turn it over.  It will be returned at the end of the exam.  However, the instructor does not have to request your device in order to charge you with academic misconduct.
  6. If for any reason you must have access to your phone while taking a test, you must inform an instructor prior to accessing your phone.  The instructor must be present while you use the phone.  Failure to do so will be treated as academic misconduct.
  7. If necessary, scratch paper will be provided.  No other paper is allowed; being in possession of any unauthorized papers will be treated as academic misconduct.
  8. You may review your test before leaving the exam.  You may not photograph your exam or write down or copy any information pertaining to the test, nor may you share any information about the test with anyone by any means.  This includes sharing information by word of mouth, written correspondence, electronic device or any type of social media.  Providing information about the test to other students will be treated as academic misconduct.  Also, having in your possession information about any test prior to the test that was not given to you by the instructor will be treated as academic misconduct. 
  9. You may not leave your place during a test for any reason.  This includes getting water or going to the restroom.  You must take care of these things before the start of the test.  If you leave your test without permission, your test will be collected and you will not be allowed to continue working on it.
  10. Interrupting the exam or creating a disturbance to cause a distraction during the exam will be treated as academic misconduct. 
  11. In order to enforce these rules, an instructor may require you to do any of the following.  Failure to comply will be treated as academic misconduct.
    1. Remove hats, hoods, scarves, or other head coverings.
    2. Remove bulky coats, sweaters or other over-garments.
    3. Roll up sleeves.
    4. Remove anything seen in your ears or on your person.
    5. Empty your pockets and display the contents.
    6. Sit in assigned seats prior to the start of the exam.
    7. Require you to move to a new seat during the exam.

If you wear a hat, head covering or long-sleeved garment for religious reasons, the instructor may still request to examine under them.  If you would prefer to have this done privately, or by an instructor or staff member of the same sex, you will be accommodated.  To ensure accommodation, you must discuss this with your instructor prior to the test.

If you use a hearing aid or other adaptive technology that could be mistaken for an earbud or other unauthorized electronic device, please notify your instructor prior to the test.  You may be asked to provide documentation of your need to use such a device.

MTLC Specific Policies

  1. In the MTLC, you may only use either the Casio fx-SOLAR SCHOOL or the Casio fx-260 SOLAR II.
  2. In the MTLC, swiping another student’s ACT card will be treated as academic misconduct. 
  3. In the MTLC having any other website other than the test open during a test will be treated as academic misconduct.
  4. In the MTLC, if you leave your computer during a test without permission, your exam will be closed and you will forfeit any remaining exam time.

Statement on Academic Misconduct

Students are expected to be familiar with and adhere to the official Academic Misconduct Policy provided in the Online Catalog.

Statement On Disability Accommodations

Contact the Office of Disability Services (ODS) as detailed in the Online Catalog.

Severe Weather Protocol

Please see the latest Severe Weather Guidelines in the Online Catalog.

Pregnant Student Accommodations

Title IX protects against discrimination related to pregnancy or parental status. If you are pregnant and will need accommodations for this class, please review the University’s FAQs on the UAct website.

Religious Observances

Under the Guidelines for Religious Holiday Observances, students should notify the instructor in writing or via email during the first two weeks of the semester of their intention to be absent from class for religious observance. The instructor will work to provide reasonable opportunity to complete academic responsibilities as long as that does not interfere with the academic integrity of the course. See full guidelines at Religious Holiday Observances Guidelines.

UAct Statement

The University of Alabama is committed to an ethical, inclusive community defined by respect and civility.  The UAct website (www.ua.edu/uact)  provides extensive information on how to report or obtain assistance with a variety of issues, including issues related to dating violence, domestic violence, stalking, sexual assault, sexual violence or other Title IX violations, illegal discrimination, harassment, hate or bias incidents, child abuse or neglect, hazing, threat assessment, retaliation, and ethical violations or fraud.

Wellness Resources

College can be a stressful time

If you or someone you know is facing a challenging time or dealing with academic or personal stress, anxiety, depression, or other concerns, we strongly encourage and support you to seek assistance or to help friends find the care that they may need.

Also, If you are experiencing a personal crisis and need urgent assistance, you can also contact the following resources:

Counseling Center

  • Monday-Friday during routine Center hours (205-348-3863).
  • Weekends, holidays, after-hours (contact UAPD at 205-348-5454 and ask to speak with the on-call counselor).
  • You may also text BAMA to 741-741 to text with a trained volunteer.

Women and Gender Resource Center

  • Monday-Friday during routine Center hours (205-348-5040).
  • Weekends, holidays, after-hours (contact UAPD at 205-348-5454 and ask to speak to the on-call advocate for the WGRC.