MATH-213 - Calculus III - Violeta Kovacev-Nikolic
Hello and Welcome!
MATH 213 is the last in the sequence of calculus courses and is essential for further studies in STEM. 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
MATH 213 represents multivariable or multivariate calculus, which focuses on functions of two or more variables. We will start the course by getting acquainted with three-dimensional coordinate systems and vectors; this will allow us to introduce the dot and cross product. We will also explore equations of lines and planes and various surfaces. The next segment of the course focuses on vector functions, their derivatives, and integrals, and we will also calculate quantities such as arc length, velocity, and acceleration. A rather extensive portion of the course will be about partial derivatives, the Chain Rule, equations of tangent planes, directional derivatives, and the gradient. We will find local and global maxima and minima on various surfaces and learn about Lagrange multipliers. We will also explore double and triple integrals using Cartesian, polar, and spherical coordinates; at the end of that chapter, we will learn about a change of variables. In the final chapter, our focus will be on vector fields. We will learn about curl and divergence and how we can evaluate line, surface, and volume integrals. At the end of the course, we will explore and apply theorems that connect these various types of integrals - namely, Green's Theorem, Stokes Theorem, and the Divergence Theorem.
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. Notice that our tests are supervised and on-Campus 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
You may have already heard that mathematics is not a spectator sport. Indeed, the best way to learn math is by taking notes and writing detailed calculations. 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 a reliable network connection and an electronic device (computer, laptop, tablet, smartphone, etc.) with a microphone and speakers (and, if possible, a webcam). You will use these resources to join and participate in our online-live classes, complete homework, scan your written work, and submit assignments 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.
You will also need access to WebAssign, an online learning platform that includes an eBook and online homework with interactive problems with instant feedback and video tutorials. WebAssign is vital for your success in the course; without it, you will not be able to complete the necessary coursework. If you have already used WebAssign for Stewart Calculus, you can reuse the resource if you have a multi-term version (if you have a single-term version, you will need to pay for the price difference between the two versions).
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
At least three midterm tests and a cumulative final
Textbook Information / Link to ZTC Textbook
Title & Author:
WebAssign for Calculus by James Stewart (8th ed.)
URL by author:
URL by publisher:
Important notice: The course is enhanced with an online educational platform called WebAssign. Access to this resource can be purchased through the College of the Canyons Official Bookstore or directly from the publisher (at a lesser cost), using a link within the WebAssign. WebAssign is required; without it, it will be impossible to complete the necessary coursework. Students who have already used WebAssign for Stewart Calculus can reuse the resource, though they may need to pay the price difference between the single and multi-term options.
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
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.
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
College of the Canyons cares about your emotional and physical health. Learn more about the broad range of confidential student services, including free counseling and mental health services available during this time by visiting the Student Health & Wellness Center website or by calling them at: 661-362-3259.
The National Suicide Lifeline number is 1-800-273- 8255 (TALK). Please call it if you or someone you know is having thoughts of suicide or is in severe distress - it could save someone's life.
You can also use the Crisis Text Line: Just text "Courage" to 741741. It's free, available 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: 08/21/2022 Sub#: 1428