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 238-002Spring 2019 | 3 Credit Hours


Shibin Dai

Contact Information

UA Campus Directory:

Office : GP 223A

Email: sdai4@ua.edu

Office Hours: MWF 8:15-9:00am, W 2:45-4:15 pm, F 1:45-3:00pm


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]

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.

Only the simple CASIO calculator, non-programmable/non-graphing, is allowed on tests. No other electronic devices, including but not limited to computers, tablets, iPads, phones, smart watches, and calculators, are allowed in exams, unless a student shows the instructor legitimate documents indicating that some specific devices are necessary for the students to take the exam. Before an exam starts, students are required to turn off their electronic devices, including smart watches, and put them away in their bags. In the case when a student does not have a bag, he/she need to turn off all his electronic devices and put them on the front desk. If a student used an electronic device in an exam without permission, the student is considered cheating, and will be prosecuted according to the university policy.

The instructor reserves the right to ban other devices from classroom or in exams.

During an exam, only one student can go to the restroom at a time, and he/she need to ask for permission from the instructor/proctor. Before a student leaves the classroom for restroom, he/she need to bring his/her bags to the front of the classroom, and leave the bags there until the end of the exam. If a student leaves the classroom without the instructor/proctor's permission, the student is considered cheating, and will be prosecuted according to the university policy.

Exam 1: Wednesday 02/06 (Chapters 1-3).

Exam 2: Wednesday 03/06 (Chapter 4).

Exam 3: Wednesday 04/10 (Chapter 5 and the first half of Chapter 7).

Final: 8:00-10:30 am on Friday, May 03 (cumulative).

Grading Policy

Homework: 10%

Matlab Projects: 10%

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

Comprehensive final exam: 35%

[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.

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.

Classroom Rules

  • The use of cell phones and laptops or any other electronic devices is strictly forbidden in class, either during lecture or testing. Those who do not abide by the rule will be asked to leave the room.

  • Only the simple CASIO calculator, non-programmable/non-graphing, is allowed on tests.

  • Formula sheets are not allowed during tests.

  • Office hours are meant for you to ask for clarification about a topic covered that you did not quite understand. They are not meant for me 
    to give you the answers to homework problems or teach you the material that you missed due to non-attandence. However, do not hesitate to drop 
    by if you wish to discuss your grade or other personal issues that you think I should know about.

  • Class attendance will be taken and recorded because university adminstration requires us to do so. No points will be awarded for just attendence.

  • The way the deadline is set for homework submission, all requests for extension will be denied. 

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.