MATH-215 - Differential Equations - Violeta Kovacev-Nikolic
Hello and Welcome!
MATH 215 is a course that serves as an introduction 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 a requirement for undergraduate studies in mathematics, science, or engineering. As such, this is a relatively fast-paced and challenging course. To succeed in this course, 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. However, they know that it takes time, hard work, and effort to attain success. I am excited to assist you on your path of learning the course topics during the upcoming term.
I look forward to seeing you in our first class (please be sure that you are present!).
Professor V. Kovacev-Nikolic
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 spend some time exploring and solving first-order differential equations and initial value problems, along with the existence and uniqueness theorem of the solution. The next segment of the course involves second and higher-order differential equations, their properties, and techniques for finding the general solution and the solution of an initial value problem. We will spend some time solving homogeneous equations with constant coefficients and introducing the Superposition Principle. After that, we will find particular solutions of non-homogeneous equations using the Method of Undetermined Coefficients and the Method of Variation Parameters. We will also solve equations with variable coefficients in the form of a Cauchy-Euler equation. Another more extensive portion of the course focuses on power-series solutions to ordinary differential equations. The following chapter is on 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 essential for your success. To stay on task, you will need to invest time and make an effort regularly and continuously. 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. Please do your best to fulfill the following expectations:
Consistently attend classes: Regular attendance is required. Using the Zoom link on the left-hand side menu in Canvas, join a live session on time and stay until the end. Apart from the first day of class when no-show students are dropped (which allows waitlisted students to enroll), you may have two grace absences; please save them for true emergencies or illnesses. If you miss three class meetings, you may be dropped from the course unless there is a valid reason. Three late arrivals may count for one absence.
Participate in the class: Learning is more efficient when students are actively involved. During lectures, you will participate via chat. I also may ask you to provide answers verbally; there may be group work where you discuss relevant concepts with peers, solve problems and present results to the class.
Prepare before the class: To get the most of each class meeting, you should come prepared. Ideally, you should review the concepts and examples taught in the previous lesson. You may need to watch an introductory video, read the assigned portion of the eBook, or complete a short quiz before a class.
Review continuously: After each lecture, try to review your notes. Your learning and retention will be more efficient if you redo the class examples and read the relevant section in the eBook.
Complete assignments on time: Please stay on top of your tasks! To learn and retain, you should tackle your homework as soon as possible, ideally within a day from the class meeting.
Ensure you have access to WebAssign: A substantial portion of your homework assignments will be in WebAssign. This online learning platform includes an eBook and interactive problems with instant feedback and video tutorials. Without WebAssign, you will not be able to complete the required coursework and succeed in the course.
Take all exams: Supervised tests will be taking place during class meeting times on Campus. If that would not be possible (if there would be a change in health-related requirements), we will have online proctored tests. In that case, you will also need a secondary device (e.g., a smartphone or a tablet) 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.
Be proactive and seek help: During the semester, you are encouraged to ask questions, form or join a study group, attend office hours, and use tutoring services provided through the Learning Center (TLC) or MESA.
You will need to have some equipment to participate in online live classes and complete your assignments. More specifically:
You will need a computer (laptop, tablet, etc.), along with a webcam, microphone, and speakers. If you do not have a computer, please read the information about the Laptop Lending Program.
You will also need a reliable connection to the internet and a standard browser (Mozilla Firefox or Chrome).
You will use a secondary device (e.g., a smartphone) to scan your hand-written work and upload it to Canvas. If we need online exams, you may need a secondary device to stream your video via Zoom.
Access to WebAssign, which includes the course eBook and online homework.
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, there may be any or all of the following:
Class participation (individual or group work)
At least three midterm tests and a comprehensive final
WebAssign for Elementary Differential Equations (10th edition)
William Boyce and Richard DiPrima
9781945801143 (single term, $91.70)
Important notice: The course is enhanced with an online educational platform provided through WebAssign. Access to this resource can be purchased through the College of the Canyons Official Bookstore or directly from the publisher, which can be done through a link to access WebAssign in Canvas. WebAssign is required, and without it, you will not be able to complete the necessary coursework.
Other Relevant Course Information
Laptop Lending Program
You may be able to borrow a laptop from COC and use it during the semester. To find out about this, please send an Email to email@example.com and include the following information:
You will also need to sign a Laptop Lending Agreement.
This course can be accessed on the first day of class via Canvas at https://coc.instructure.com. Log into Canvas using your CanyonsID single sign-on:
- CanyonsID Username is your COC student email address (Ex: firstname.lastname@example.org)
- CanyonsID Password is your COC student email password
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.
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 StudentHealthCenter@canyons.edu. 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 email@example.com 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: 10/09/2023 Sub#: 445