Math 285
Spring 2026 University of Nevada Reno
285 DIFFERENTIAL EQUATIONS (3+0) 3 credits
Theory and solving techniques for constant and variable
coefficient linear equations and a variety of non-linear
equations.
Emphasis on those differential equations arising from
real-world phenomena.
Prerequisite: MATH 283 (or 182 with permission of instructor).
Instructor Course Section Time Room
------------------------------------------------------------------------
Eric Olson Math 285 Differential Equations MWF 11-11:50am PE104
Course Information
- Instructor:
- Eric Olson
- email:
- Please contact me through WebCampus
- Office:
- MWF 12:30-1:30pm in DMS 238 and through Zoom by appointment
- Homepage:
- http://fractal.math.unr.edu/~ejolson/285/
- Course Textbook:
-
Dennis G. Zill, Differential Equations with Modeling
Applications, 10th Edition, 2013,
Brooks Cole Thomson Learning.
- Supplemental References:
-
Boyce and Diprima, Elementary Differential Equations and
Boundary Value Problems, Seventh Edition, 2001,
John Wiley & Sons, Inc.
-
An Introduction to Ordinary Differential Equations
by James C. Robinson, Cambridge University Press, 2004.
Student Learning Outcomes
We will cover selected sections in Chapters 1 through 5, 7 and 8
of the textbook.
Upon completing this course, a student shall be able to
- Use qualitative methods to assess the behavior of solutions without
solving an equation.
- Demonstrate understanding of some of different techniques for solving
first and higher order homogeneous and non-homogeneous equations: e.g. the
integrating factor method, separable variables, the Laplace transform.
- Solve systems of differential equations with constant coefficients.
Information about Software
I will occasionally use the Julia programming language in class to
draw graphs and perform simple calculations. This software is
free to download for Windows, MacOS and Linux.
Class Handouts
Course materials specific for this section of Math 285 are available
by clicking on this link. Details for how to
access these files may be found on our course page in WebCampus.
Lecture Notes
Homework
Homework is available on Webassign to help you learn the material.
There are also exercises at the end of the each chapter in the text.
Solutions to homework problems will not be part of your grade.
The goal of homework is to help you to understand key concepts
and to master the skills you will need to succeed in this course.
To access the online homework go to
www.webassign.net and use
the code
unr 5078 7833
You will be asked to set up a Webassign account if you do not
already have one. Please use exactly the same name and email you
use to register for courses at UNR.
Following is a list of homework problems from the 10th edition of
the textbook that should help prepare you for the quizzes. Similar
problems appear in the online homework and can also be created by
typing a representative question into generative AI and asking
the model to create a similar problem for you to practice.
Quiz 1 will focus
on Homework 1 and similar problems, Quiz 2 will focus on Homework 2
and so forth. All exams are comprehensive and include material from
earlier quizzes and exams plus the indicated additional sections.
- Homework 1 (Quiz 1)
- Section 1.1#3,5,8,9,11,13,15,27,29,31,55
- Section 1.2#1,3,5,9,13,17,23,31,32,33,34
- Homework 2 (Quiz 2)
- Section 2.1#1,2,21,26
- Section 2.2#1,7,15,17,23,25
- Homework 3 (Quiz 3)
- Section 2.3#1,3,5,7,23,25
- Section 2.4#1,5,8,12,15,16,28
- Homework 4 (Quiz 4)
- Section 2.3#27,31
- Section 2.4#31,33,34
- Section 2.5#1,5,7,9,15,17,21,27,29
- Homework 5 (Quiz 5)
- Section 2.6#1,3,5,7
- Section 9.1#1,4,9
- Section 9.2#5,9,11
- Homework (included on Exam 1)
- Section 4.1#1,15,21,23,27,29
- Section 4.2#3,7,11,13
- Section 4.3#1,3,6,9,12,17,21,29,31,37
- Section 4.4#3,5,11,13
- Homework 6 (Quiz 6)
- Section 4.6#3,5,19
- Section 4.7#3,5,13,15
- Homework 7 (Quiz 7)
- Section 7.1#1,21,23,26,37,39,
- Section 7.2#1,3,5,15,19,23,31,33,35,36
- Homework 8 (Quiz 8)
- Section 7.3#2,3,5,11,13,15,17,40,41,43,47,49,53,55,57
- Section 7.4#1,3,9,21,25,27
- Homework 9 (Quiz 9)
- Section 7.5#1,3
- Appendix II Matrices#2,3,4,8,11,12,13
- Section 8.1#1,7,19,20
- Homework (included on Exam 2)
- Section 8.2#1,3,7,9,13
- Appendix II Matrices#25,26,47,48,49,51,52
- Homework 10 (Quiz 10)
- Section 8.2#19,21,25,35,37
- Homework (included on Final)
- Section 8.3#1,3,9,11
- Section 8.4#1,9,15,17
Announcements
[03-May-2026] Sample Final
The Final will be given at on Wednesday, May 13, 2026
from 10:15-12:15pm in PE104.
It is comprehensive and covers the entire course.
I have prepared a sample exam
to help you prepare.
[19-Apr-2026] Sample Exam 2
Exam 2 will be given in class Wednesday, April 22.
It covers Sections 4.6 up to and including Section 8.2 on our syllabus.
I have prepared a sample exam
to help you prepare.
[08-Mar-2026] Sample Midterm
The Midterm will be given in class Wednesday, March 11.
It covers up to and including Section 4.4 on our syllabus.
I have prepared a sample exam
to help you prepare.
[18-Feb-2026] Snow Day
Following an assessment of the anticipated overnight weather and road
conditions around the University of Nevada, Reno campus,
nonessential campus operations and in person classes are suspended today.
[21-Jan-2026] Welcome Spring 2026
I am looking forward to seeing you January 26 starting
the first week of class.
In person
attendance is mandatory for all
computing labs, quizzes, exams and the final.
Grading
2 Exams 50 points each
10 Quizzes 10 points each
Final 100 points
------------------------------------------
300 points total
Exams and quizzes will be interpreted according to the following
grading scale:
Grade Minimum Percentage
A 90 %
B 80 %
C 70 %
D 60 %
The instructor reserves the right to give plus or minus grades and
higher grades
than shown on the scale if it is believed they are warranted.
Calendar
Jan 21 1.1-1.2 Initial Value Problems
Jan 23 1.2 Existence of a Unique Solution
Jan 26 2.1 Direction Fields
Jan 28 2.2 Separation of Variables (quiz 1)
Jan 30 2.3 Variation of Parameters
Feb 2 2.3 Variation of Parameters
Feb 4 2.4 Exact Equations (quiz 2)
Feb 6 2.5 Solution by Substitution
Feb 9 2.6 Numerical Solutions
Feb 11 9.1 Error Analysis (quiz 3)
Feb 13 9.2 Runge-Kutta Methods
Feb 16 President's Day
Feb 18 4.1.1 Initial-Value and Boundary-Value Problems
Feb 20 4.1.2-4.1.3 Homogeneous and Nonhomogeneous Equations
Feb 23 4.2 Reduction of Order
Feb 25 4.3 Constant Coefficients (quiz 4)
Feb 27 4.3 Constant Coefficients
Mar 2 4.4 Superposition Approach
Mar 4 4.6 Variation of Parameters (quiz 5)
Mar 6 4.7 Cauchy-Euler Equations
Mar 9 Review
Mar 11 EXAM 1
Mar 13 7.1 Definition of the Laplace Transform
Mar 16 7.2 Inverse Transform
Mar 18 7.2 Inverse Transform (quiz 6)
Mar 20 7.3 Translation on the s-axis and t-axis
Mar 23 Spring Break
Mar 25 Spring Break
Mar 27 Spring Break
Mar 30 7.4 Additional Operational Properites
Apr 1 7.4 Additional Operational Properites (quiz 7)
Apr 3 7.5 Dirac Delta Function
Apr 6 7.5 Dirac Delta Function
Apr 8 8.1 Systems of Linear First Order Equations (quiz 8)
Apr 10 8.1 Systems of Linear First Order Equations
Apr 13 8.2.1 Distinct Real Eigenvalues
Apr 15 8.2.2 Repeated Eigenvalues (quiz 9)
Apr 17 8.2.3 Complex Eigenvalues
Apr 20 Review
Apr 22 EXAM 2
Apr 24 8.3 Variations of Parameters
Apr 27 8.3 Variations of Parameters
Apr 29 8.4 Matrix Exponential (quiz 10)
May 1 8.4 Matrix Exponential
May 4 Recitation
May 13 Final Exam at 10:15-12:15pm
Course Policies
Communications Policy
Lectures and classroom activities will held in person.
If you wish to set up an appointment for office hours
please send me a message through
WebCampus.
Late Policy
Students must have an approved university excuse to be eligible for a
make-up exam. If you know that you will miss a scheduled exam please
let me know as soon as possible.
AI Policy
In this course you are welcome to use generative artificial
intelligence/large language model tools (such as ChatGPT, Claude, Gemini,
Grok, Perplexity, etc.). Using these tools aligns with the course learning
outcomes/student goals for an in-depth understanding of calculus.
Please be aware that many AI companies collect and store personal
information. Please do not enter your confidential information as part
of a prompt.
Also, please note that some of these large language models may make up
or hallucinate information. These tools may reflect misconceptions and
biases of specific data. Students are responsible for checking facts,
finding reliable sources for, and making a critical examination of any
work that is submitted.
Plagiarism
Students are encouraged to work in groups and consult resources outside
of the required textbook when doing the homework for this class. Please
cite any sources you used to complete your work including Wikipedia, other
books, online discussion groups, generative AI such as ChatGPT as well
as personal communications. Note that answers obtained from any source
should be verified and fully understood for homework to have a positive
learning outcome. In all cases your sources need to be cited.
Exams and quizzes, unless otherwise noted, will be closed book, closed
notes and must reflect your own independent work.
Plagiarism
Students are encouraged to work in groups and consult resources outside
of the required textbook when doing the homework for this class. Please
cite any sources you used to complete your work including Wikipedia, other
books, online discussion groups, generative AI such as ChatGPT as well
as personal communications. Note that answers obtained from any source
should be verified and fully understood for homework to have a positive
learning outcome. In all cases your sources need to be cited.
Exams and quizzes, unless otherwise noted, will be closed book, closed
notes and must reflect your own independent work.
Academic Conduct
Bring your student identification to all exams.
Work independently on all exams and quizzes.
Behaviors inappropriate to test taking may disturb other
students and will be considered cheating.
Don't send electronic messages, talk or pass notes with other
students during a quiz or exam.
Homework may be discussed freely.
When taking a quiz or exam
don't read notes or books unless explicitly permitted.
Sanctions for violations are specified in the
University Academic Standards Policy.
If you are unclear as to what constitutes cheating,
please consult with me.
Diversity
This course is designed to comply with the UNR Core Objective 10
requirement on diversity and equity. More information about the core
curriculum may be found in the
UNR Catalog.
Statement on Academic Success Services
Your student fees cover usage of the
University Math
Center, (775)
784-4433; University
Tutoring Center, (775) 784-6801; and
University
Writing & Speaking Center, (775) 784-6030. These centers support your
classroom learning; it is your responsibility to take advantage of their
services. Keep in mind that seeking help outside of class is the sign
of a responsible and successful student.
Equal Opportunity Statement
The University of Nevada Department of Mathematics and Statistics
is committed to equal opportunity in education
for all students, including those with documented physical disabilities
or documented learning disabilities.
Statement of Disability Services
Any student with a disability needing academic adjustments or
accommodations is requested to speak with me or the
Disability Resource
Center (Pennington Achievement Center Suite 230) as soon as possible to
arrange for appropriate accommodations.
This course may leverage 3rd party web/multimedia content, if you
experience any issues accessing this content, please notify your
instructor
Mental Health Support Statement
There are times when you may experience difficulties in life,
and you may benefit from seeking help. Mental health services are
available to you as a student at no additional cost through Counseling
Services at the Pennington Student Achievement Center. This includes
same-day in-person and tele mental health initial consultations, brief
individual counseling, and group counseling sessions. Limited same-day
appointments can be scheduled online via
Counseling Services or
by calling 775-784-4648. Additional brief drop-in "Let's Talk" student
consultations are also available in the Counseling Services Annex located
at the southwest corner of Great Basin Hall.
Veteran Statement
Veterans, Reservists, National Guard and military connected family members
may wish to check the office of
Veteran Services for benefits and
support. Besides processing VA educational benefits, the department
offers a variety of programs year-round to support student academic and
personal success while transitioning to higher education and throughout
your educational experience. They welcome inquiries regarding VA benefits
and assist in navigating resources, the campus, and in the Reno community.
Statement on Audio and Video Recording
Surreptitious or covert video-taping of class or unauthorized audio
recording of class is prohibited by law and by Board of Regents
policy. This class may be videotaped or audio recorded only with the
written permission of the instructor. In order to accommodate students
with disabilities, some students may be given permission to record class
lectures and discussions. Therefore, students should understand that
their comments during class may be recorded.
Final Exam
The final exams will be held in person at the time listed in
the standard schedule of final exams for this section. Namely,
the final exam is Wednesday, May 13, 2026
from 10:15-12:15pm in PE104.
Last Updated:
Sun Jan 18 02:57:49 PM PST 2026