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MATH-215 - Differential Equations - Violeta Kovacev-Nikolic

Course:Differential Equations
Professor:Violeta Kovacev-Nikolic
  • InPerson
Course Length:
  • 16 Week


Violeta with ocean and rocks in the background (Location: beach down the Lands End trail in San Francisco).

Hello and Welcome!

MATH 215 is an introductory course to ordinary differential equations and represents a basis for building mathematical models of natural phenomena that change through time and various other dynamical systems. This course is often required for mathematics, science, or engineering studies. As such, it is a relatively fast-paced and challenging course for which you will need a solid foundation in all previous mathematics, algebra, geometry, trigonometry, precalculus, and calculus. Students who attained mastery in these prerequisites and those who appreciate math, science, and their applications usually enjoy furthering their knowledge. Although it takes time, hard work, and effort, success is attainable. I am excited to assist you in learning the course topics during the upcoming term. 

I look forward to seeing you in our first class (please be sure you are present!).

Professor V. Kovacev-Nikolic

Course Description

MATH 215 includes a variety of topics. Using a few simpler mathematical models, we will introduce the concept of a differential equation and learn about the classification of differential equations. Upon the introduction, we will explore first-order differential equations and initial value problems, along with the existence and uniqueness theorem of the solution. The next segment of the course focuses on second and higher-order differential equations. We will spend some time solving homogeneous equations with constant coefficients; then, we will learn how to find particular solutions to non-homogeneous equations. Another more extensive portion of the course focuses on power-series solutions to ordinary differential equations. After that, we will learn about Laplace transforms. At the end of the semester, we will solve linear systems of ordinary differential equations.

What to Expect in this Course

Your commitment is vital for your success (much more important than talent!); with perseverance, you can succeed. To stay on task, you will need to invest time and effort. In general, you will need to spend about 2-3 hours per every hour of class time (which means 10-15 hours per week), or more, as needed. Here are some things that can help you succeed in this course. 

  • Consistently attend classes: Regular attendance is crucial! If you are not present, you are not participating and therefore missing out on the classwork. Note: You need to be present on the first day of class; there is a requirement that instructors drop no-show students, which allows waitlisted students to enroll. 

  • Participate in all class activities and discussions: Learning is deeper when students are actively involved. Throughout the semester, you will have opportunities to discuss relevant concepts, solve problems, engage in group work, and present results.

  • Prepare before the class: Research shows that the learning process is more effective when students preview a lecture ahead of time. With that in mind, I may prompt you to watch an intro video, read a portion of the course text, or fill in a short quiz before we meet. If you come prepared, our meeting will be more efficient.

  • Study and review continuously: Try to go over your notes after each class meeting. To deepen your knowledge and sharpen your math skills, try to solve homework problems without looking up the solutions.

  • Complete assignments on time: Please do your best to stay on top of your tasks! Your learning will be much smoother if you tackle your homework as soon as possible, ideally within a day from the class meeting.

  • Take all exams. We will have our tests during regular class meeting times. If a change in health-related requirements would render on-campus meetings impossible, we will have online proctored tests. 

Educational and Technological Tools

Our textbook is an open educational resource you can access online or save as a PDF file. However, reading alone is not enough - more precisely, math is not a spectator sport! You will need to take notes and write detailed calculations in quizzes or while solving problems in online homework. Thus, a pencil and an eraser are must-haves (you can also use a pen, though it makes it harder to keep the work neat). You will also need something to write on, a stack of papers or a notebook. You can also use a tablet with a stylus for writing and drawing if you have one (though you will still need more traditional writing tools in exams).

In addition to writing utensils, you will need some tech skills and equipment.

  • You will need access to an electronic device (computer, laptop, tablet, smartphone, etc.) with a network connection. You will use these resources to complete assignments, scan your written work, and submit files to Canvas. If there would be any exams online (depending on the situation with the pandemic), you may also need a secondary device with a webcam to stream a video of your surrounding workspace and to scan and upload your written work to Canvas during a limited-time window after finishing the test. 
  • Homework assignments will be in MyOpenMath, a free online learning and assessment platform.

  • We may use other educational tools (e.g., Canvas Studio, PlayPosit, PebblePad, Mentimeter, etc.); they will be at no cost to you.

Types of Assessments

Low-stakes formative assignments (e.g., quizzes, homework, and so on) will help you learn the course concepts and master the needed mathematical skills. Summative assessments (typically exams) will provide feedback on how well you understand and know the course concepts. More specifically, your progress in the course is reflected through your work on some (or all) of the following:

  • Class participation (individual or group work)

  • Online discussion boards in Canvas

  • Online and written homework assignments

  • Quizzes

  • Review assignments

  • Project(s)

  • At least three midterm tests and a cumulative final

Textbook Information

Title & Authors:

Elementary Differential Equations by William F. Trench

Link to Textbook:

You can freely download and save the book as a PDF file.

Important notice: our course is enhanced with a free online learning and assessment platform called MyOpenMath. You can access this resource without having to pay anything.

Additional Resources


This course can be accessed on the first day of class via Canvas at Log into Canvas using your CanyonsID single sign-on:

  • CanyonsID Username is your COC student email address (Ex:
  • CanyonsID Password is your COC student email password

Please visit the Get to Know Your Online Classroom page for help logging into Canvas and for tips on using Canvas and Zoom. Canvas Chat Support is also available 24/7 for any Canvas related issues.

Online Education

Check out the Online Education website for more information on a variety of topics that can help you be a successful online student such as: exam proctoring, learning styles, computer skills, and tips for student success. If this is your first online course, feel free to take our online learning readiness assessment to assess your skills.

The Learning Center (TLC)

The TLC provides FREE online tutoring resources to COC students!

Academic Accommodation Center (AAC)

College of the Canyons AAC provides educational services and access for eligible students with documented disabilities who intend to pursue coursework at COC. A variety of programs and services are available which afford eligible students with disabilities the opportunity to participate fully in all aspects of the college programs and activities through appropriate and reasonable accommodations. For more information on their services visit the Academic Accomodation Center website.

Online Counseling

The Counseling Department offers appointments online. You can schedule an appointment by visiting the Online Counseling website. Counselors can help you map out a plan to reach your educational goals as well as advise you on course selection and registration.

Management of Stress and Mental Health

Often the pressure on our students is very strong, involving academic commitments, relationships, outside jobs and family pressure to name a few. The staff and faculty of College of the Canyons are here to see you succeed academically and care about your emotional and physical health. You can learn more about the broad range of confidential student services, including counseling and mental health services available on campus by visiting the Student Health & Wellness Center in the Student Services Building (across from the bookstore). The phone number is 661-362-3259 that you can call 24/7. You can also e mail for an appointment at At the Canyon Country Campus the Health Center will be in the new Student Services Building.

Also, the National Suicide & Crisis Lifeline number is now 988. All students at COC are encouraged to enter that phone number in their cells. You can call it when you, or someone you know, is having thoughts of suicide or is in severe distress.

You can also now use the Crisis Text Line: Just text "Courage" to 741741. Someone will get back to you immediately. Its free, 24/7, and confidential.

Veterans Resource Center

The College of the Canyons Veterans Resource Center is a department within the Student Services Division at the college, created to help veterans and veteran dependents with applying to College of the Canyons, enrolling in classes, and requesting VA Education or Vocational Benefits. For more information please visit the Veterans Resource Center website, email or phone (661) 362-3469.


The Library provides live online and in-person research help, access to a full range of e-resources and physical materials that support the curriculum, individual and group study areas, and much more!

Last updated: 08/21/2022 Sub#: 1427