Welcome To Pengtao Sun's Home!

Math 431, Mathematics for Engineers and Scientists I

Section 1004, Spring 2026

(01/21/2026-05/09/2026)

Breakout Session

CATALOG DESCRIPTION: Mathematics for Engineers and Scientists I (3 semester hours) contains theory and solution techniques for solving: first order linear and non-linear ordinary differential equations (ODEs), second and higher order ODEs with constant coefficients, Laplace transforms and applications, solutions of systems of ODEs.

The topical outline of course objectives is the following:

PREREQUISITE: Math 283.
 

LEARNING OUTCOMES: The following is only a set of the most important objectives of the course students shall be able to grasp.

I: First Order Differential Equations.

1. Distinguish between linear, nonlinear, partial and ordinary differential equations.
2. State the basic existence theorem for 1st order ODEs and use the theorem to determine a solution interval.
3. Recognize and solve a variable separable differential equation.
4. Recognize and solve a homogeneous differential equation.
5. Recognize and solve an exact differential equation.
6. Recognize and solve a linear differential equation by use of an integrating factor.
7. Recognize and solve equations of Bernoulli, Ricatti and Clairaut.
8. Make a change of variables to reduce a differential equation to a known form.
9. Find particular solutions to initial value problems.
10. Solve basic application problems described by first order differential equations.

II: Linear Differential Equations of Higher Order.

1. Use the existence theorem for boundary value problems to determine uniqueness of solutions.
2. Use the Wronskian to determine if a set of functions is linearly independent.
3. Build solutions to differential equations by superposition of known solutions.
4. Find the complete solution of a nonhomogeneous differential equation as a linear combination of the complementary function and a particular solution.
5. Construct a second solution to a second order differential equation by reduction of order.
6. Find the complete solution of a homogeneous differential equation with constant coefficients by examining the characteristic equation and its roots.
7. Find the complete solution of a nonhomogeneous differential equation with constant coefficients by the method of undetermined coefficients.
8. Write a differential equation with constant coefficients in operator form and find the complete solution by using an annihilator operator.
9. Find the complete solution of a differential equation with constant coefficients by variation of parameters.
10. Solve basic application problems described by second order linear differential equations with constant coefficients.

III. Systems of Differential Equations.

1. Write a system in operator notation and solve by elimination.
2. Solve a system by the Laplace transform method (optional).
3. Solve a homogeneous linear system by the eigenvalue method.
4. Solve a nonhomogeneous linear system by variation of parameter.

IV. The Laplace Transform.

1. Find the Laplace transform of a function by definition and by use of a table.
2. Find the inverse Laplace transform of a function.
3. Write piecewise functions using the unit step function.
4. Find transforms using the first and second translation theorems.
5. Find the convolution of two functions and the transform of a convolution.
6. Find the transforms of derivatives and integrals.
7. Find the transform of a periodic function.
8. Solve a basic integrodifferential equation using the Laplace transform.
9. Solve linear differential equations with constant coefficients and unit step input functions using the Laplace transform.

TEST AND GRADING POLICY: There will be six (50 minutes) quizzes, a  (1 hour and 15 minutes) midterm exam, and a (2-hour) final exam. The two lowest quizzes will be dropped, eventually. Each quiz is worth 10%, and each exam is worth 25%. The midterm exam will test Chapters 1 & 2, and the (noncumulative) final exam will test Chapters 3, 4 & 6.

Grades will be assigned on the basis of total 100 points, distributed as follows:

Final course letter grades will be assigned as follows:

NOTE: Your grade will be based EXCLUSIVELY on the homework, quizzes and examinations.

CLASS POLICIES:

HOMEWORK:

Homework problems are given on the assignment list after every lecture class. You are required to do the homework outside of class. Homework will be collected on Monday, the teaching assistant will partially grade your homework by randomly picking a few questions as well as check your completion. You will get your homework back in the coming breakout session on Friday, during which homework problems will be reviewed by the teaching assistant.

 

ATTENDANCE:

You are expected to attend class regularly. If you miss a class for any reason, you are responsible for all material covered, announcements made in your absence, and acquiring materials that may have been distributed in class.

 

MISSED EXAMS:

You have an opportunity to make up a missed quiz or midterm exam if you can provide an officially documented reason to excuse for your absence at least two days before the scheduled testing day. Note that the instructor is the only one who can judge and grant you the permission to make up a missed test.

CALCULATORS:

Scientific (non-programmable and non-graphing) calculators are allowed during quizzes and exams.

TUTORING:

(1)  Visit https://www.unlv.edu/math/tutoring or click here for UNLV Math Tutoring Clinic's location, hours and more information.

 

(2) The Academic Success Center (ASC) provides tutoring and academic assistance for all UNLV students taking UNLV courses. Students are encouraged to stop by the ASC to learn more about subjects offered, tutoring times and other academic resources. The ASC is located across from the Student Services Complex, #22 on the current UNLV map. Students Dec learn more about tutoring services by calling (702) 895-3177 or visiting the tutoring web site at http://academicsuccess.unlv.edu/learningsupport/Tutoring/Tutoring.html,

and a full schedule of subjects at:

https://www.unlv.edu/news-story/llb-tutoring-subject-availability.

(3) The Tutoring Center in Lied Library offers tutoring this semester. Please find a full schedule of subjects available at https://www.unlv.edu/news-story/asc-lied-library-llb-tutoring-spring-2020.

CLASS COURTESY:

Please use basic common courtesy and mute or turn off your cell phone before class. Private conversations cannot be allowed in class.

ASSISTANCE:

If you have a documented disability that Dec require accommodations, you will need to contact the Disability Resource Center (DRC) for the coordination of services. The DRC is located in the Student Services Complex (SSC), Room 137, and the contact numbers are: VOICE (702) 895-0866, TTY (702) 895-0652, FAX (702) 895-0651. For additional information, please visit: http://studentlife.unlv.edu/disability/.

ACADEMIC INTEGRITY:

Academic integrity is the pursuit of scholarly activity in an open, honest and responsible manner. Academic integrity is a basic guiding principle for all academic activity at University of Nevada, Las Vegas, and all members of the University community are expected to act in accordance with this principle. Consistent with this expectation, the University's Code of Conduct states that all students should act with personal integrity, respect other students' dignity, rights and property, and help create and maintain an environment in which all can succeed through the fruits of their efforts.

Academic integrity includes a commitment not to engage in or tolerate acts of falsification, misrepresentation or deception. Such acts of dishonesty violate the fundamental ethical principles of the University community and compromise the worth of work completed by others. Based on the University's Student Academic Misconduct Policy, a range of academic sanctions may be taken against a student who engages in academic dishonesty.

LECTURE-BY-LECTURE BREAKDOWN (Tentatively):