MATH 3321 Engineering Mathematics, Spring 2024

Meeting time: Asynchronous, Room: online

1. Instructor: Demetrio Labate

Office Hours (Teams): by appointment
Phone Number: (713) 743-3492
E-mail address: dlabate@math.uh.edu
Homepage: http://www.math.uh.edu/~dlabate

TA: JI SH, e-mail: jshi24@cougarnet.uh.edu
TA Office hours:

2. Goals and Objectives: Course Description: First order ordinary differential equations and initial value problems; higher order differential equations; vector spaces, matrices, determinants, eigenvectors and eigenvalues; applications to systems of first order equations; Laplace transforms.

3. Teaching Material:

Lecture Notes (with annotations) (this list will be updated during the semester):

Lecture Set 1: Introduction

Lecture Set 2: IVPs and Finding ODEs

Lecture Set 3: First Order Differential Equations

Lecture Set 4: Separable Differential Equation

Lecture Set 5: Extensions to Other First Order Equations

Lecture Set 6: Applications of First Order Equations

Lecture Set 7: Introduction to Second Order Linear ODEs

Lecture Set 8: Homogeneous Equations with Constant Coefficients

Lecture Set 9: Second Order Linear Nonhomogeneous Equations

Lecture Set 10: Nonhomogeneous Equations with Constant Coefficients

Lecture Set 11: Higher Order Linear Differential Equations

Lecture Set 12: Vibrating Mechanical Systems

Lecture Set 13: Introduction to the Laplace Transform

Lecture Set 14: Inverse Laplace Transforms and Initial-Value Problems

Lecture Set 15: Laplace Transforms of Piecewise Continuous Functions

Lecture Set 16: Initial-Value Problems with Piecewise Continuous Nonhomogeneous Terms

Lecture Set 17: Systems of Linear Equations. Part I

Lecture Set 18: Systems of Linear Equations. Part II

Lecture Set 19: Matrices and Vectors. Part I

Lecture Set 20: Matrices and Vectors. Part II

Lecture Set 21: Eigenvalues and Eigenvectors

Lecture Set 22: Systems of Linear Differential Equations

Lecture Set 23: Homogeneous Systems with Constant Coefficients. Part I

Lecture Set 24: Homogeneous Systems with Constant Coefficients. Part II

Lecture Set 25: Homogeneous Systems with Constant Coefficients. Part III

VIDEOS of Lecture Notes (this list will be updated during the semester):
Videos of Lecture Notes: Sharepoint Folder

Useful background material:
Very brief linear algebra review [from http://alumni.media.mit.edu]

Another linear algebra review (with Matlab examples) [by G. Recktenwald Portland State University]

4. Prerequisites:

Calculus II

5. Homework, tests, exams and grading:

The only way to understand and master the material presented in class is by working out the homework problems on your own. You are strongly encouraged to work out the homework problems that are assigned regularly and carefully. Copying the homework or watching someone else doing the work for you will bring you minimal benefit.

Homework Problems (list to be updated during the semester - solutions are posted aftrer the due date):

Midterm Tests:

March 30, April 27 and May 25.

Test 1 with Solution

Test 2 with Solution

Test 3 with Solution

Final Exam:

6. Grading:

Each student will receive a score based 30% on the homework/quizzes, 40% on the tests and 30% on the final. The grade will be determined according to a set point scale:
90%-100%: A, 80%-89%: B, 70%-79%: C, 60-69% D; F is less than 60% (+ and - will also be used).
Policy on grades of I (Incomplete): The grade of "I" (Incomplete) is a conditional and temporary grade given when a student, for reasons beyond his or her control, has not completed a relatively small portion of all requirements. Sufficiently serious, documented situations include illness, death in the family, etc.

7. Course outline:

Introduction to Differential Equations
- 1.1 Basic Terminology
- 1.2 n-Parameter Family of Solutions; General Solution; Particular Solution
- 1.3 Initial-Value Conditions; Initial-Value Problems
First Order Differential Equations
- 2.1 Linear Equations
- 2.2 Separable Equations
- 2.3 Some Applications
Second Order Linear Differential Equations
- 3.1 Introduction; Basic Terminology and Results
- 3.2 Homogeneous Equations
- 3.3 Homogeneous Equations with Constant Coefficients
- 3.4 Nonhomogeneous Equations
- 3.5 Nonhomogeneous Equations with Constant Coefficients; Undetermined Coefficients
- 3.6 Vibrating Mechanical Systems
Laplace Transforms
- 4.1 Introduction
- 4.2 Basic Properties of Laplace Transforms
- 4.3 Inverse Laplace Transforms and Initial-Value Problems
- 4.4 Applications to Discontinuous Functions
- 4.5 Initial-Value Problems with Piecewise Continuous Nonhomogeneous Terms
Linear Algebra
- 5.1 Introduction
- 5.2 Systems of Linear Equations; Some Geometry
- 5.3 Solving Systems of Linear Equations
- 5.4 Solving Systems of Linear Equations, Part 2
- 5.5 Matrices and Vectors
- 5.6 Square Matrices; Inverse of a Matrix and Determinants
- 5.7 Vectors; Linear Dependence and Linear Independence
- 5.8 Eigenvalues and Eigenvectors
Systems of First Order Linear Differential Equations
- 6.1 Higher-Order Linear Differential Equations
- 6.2 Systems of Linear Differential Equations
- 6.3 Homogeneous Systems
- 6.4 Homogeneous Systems with Constant Coefficients
- 6.5 Nonhomogeneous Systems
- 6.6 Some Applications

UH Email: Email communications related to this course will be sent to your Exchange email account which each University of Houston student receives. The Exchange mail server can be accessed via Outlook, which provides a single location for organizing and managing day-to-day information, from email and calendars to contacts and task lists. Exchange email accounts can be accessed by logging into Office 365 with your Cougarnet credentials or through Acccess UH. They can also be configured on IOS and Android mobile devices. Additional assistance can be found at the Get Help page.

Academic Integrity: University of Houston students are expected to adhere to the Academic Honesty Policy as described in the UH Undergraduate Catalog. “Academic dishonesty” means employing a method or technique or engaging in conduct in an academic endeavor that contravenes the standards of ethical integrity expected at the University of Houston or by a course instructor to fulfill any and all academic requirements.
Academic dishonesty includes, but is not limited to, the following: Plagiarism; Cheating and Unauthorized Group Work; Fabrication, Falsification, and Misrepresentation; Stealing and Abuse of Academic Materials; Complicity in Academic Dishonesty; Academic Misconduct.
Please, refer to UH Academic Honesty website and the UH Student Catalog for the definition of these terms and university’s policy on Academic Dishonesty. Anyone caught cheating will be reported to the department for further disciplinary actions, receive sanctions as explained on these documents, and will have an academic dishonesty record at the Provosts office. The sanctions for confirmed violations of this policy shall be commensurate with the nature of the offense and with the record of the student regarding any previous infractions. Sanctions may include, but are not limited to: a lowered grade, failure on the examination or assignment in question, failure in the course, probation, suspension, or expulsion from the University of Houston, or a combination of these. Students may not receive a W for courses in which they have been found in violation of the Academic Honesty Policy. If a W is received prior to a finding of policy violation, the student will become liable for the Academic Honesty penalty, including F grades.
Cases of using websites/apps like GroupMe and Chegg to facilitate cheating will be punished to the maximum degree possible. This includes grades of 0 on any assignments or exams and potentially a grade of F for the course.