Fully Online · Mathematics · Mathematics & Computer Science MULTIVARIABLE CALCULUS MATH-005C Summer 2021 Section 53226 5.0 Credits 06/21/2021 to 07/30/2021 Modified 06/11/2021  Welcome

Whether you are returning to campus, or this is your first time taking classes at PCC, we’re very glad that you have decided to pursue your education here. PCC faculty and staff are here to support you in achieving your educational goals. We are committed to seeing you succeed.  How to Reach Me How You Can Contact Me Use the Canvas Inbox or my email address ([email protected]) anytime. Use the Q&A Discussion...maybe one of your classmates will beat me to answering your question. Please don't post anything personal in the Q&A Discussion (such as grades, personal issues, etc.). Save that for a direct message to me. Use Pronto, a messaging feature that's built into Canvas For more urgent matters, you can text me: 626-344-7256. Response time: I will respond within two days (Mon-Fri), and usually the same day. If you don't hear back from me within two days, you may assume that I didn't receive your email and please resend it. How I Will Contact You I will be an active participant in this course. You can expect that I will contact you a few times each week, via the following methods:

Regular Announcements Canvas Inbox messages as appropriate Grading feedback: After each exam, you can download your marked exams. I'll also do my best to keep your grades current in the Canvas Gradebook. Instructor: Dr. Matt Henes Email: [email protected] Phone: 626-344-7256 Website: http://matthenes.com (http://matthenes.com)

I am your instructor, and you can call me Dr. Matt. I've been teaching math for 18 years and have been at PCC for the last 13 years. Previously, I taught at CSU San Bernardino, Riverside Community College, and Crafton Hills College. I'm from Riverside, Ca and went to college there, earning my Associate of Science from RCC, Bachelor of Science from UCR, and my Master of Arts from CSUSB. Ten years later, I started an Educational Leadership program at UCLA (which I completed), and that's why I get to be called doctor .

I started teaching because I think I have a way of helping people understand math, and I can't imagine doing anything else! Since spring, I've been getting used to teaching online, and I hope to help you make this a successful semester. When I'm not working, I'm exercising, playing guitar, or (yes) surfing Netflix or Amazon Prime for something to watch.

Please watch this short introductory video (https://youtube.com/playlist?list=PLjX1J0s-ZdtlBTPI8vU0y0N0KO1wu_Lxe). 1 of 9  Class Overview Course Title Math 005C Multivariable Calculus Course Description In this fully online course, we will extend the math you’ve learned—algebra, trigonometry, and calculus—into higher dimensions. We’ll see how the rules for differentiation and integration apply to functions with more than one input variable (called multivariable functions), and how they apply to curves and surfaces and solids in three-dimensional space. We will find that vectors are useful in analyzing these two- and three-dimensional objects. The concepts in this course apply to physics and engineering, and we’ll see some applications along the way. This course can be fairly visual at times, so we’ll rely on graphs in two and three dimensions to help make sense of what we’re working with. The work you’ll do is largely computational (finding limits and evaluating derivatives and integrals), but the foundation is theoretical. This will become most apparent in the last chapter. It’ll have entirely new concepts for us, but by the time we get there, it will act almost as a summary of much of the calculus you’ve learned so far. I hope you find that this course is challenging but in a satisfying way! Student Learning Outcomes By the end of this course, you will be able to:

Apply vector operations to find equations of lines and planes and analyze the motion of a particle in space. Explain limits, partial derivatives, directional derivatives, gradient vectors, and differentials and linear approximations of functions of two or more variables. Compute local and absolute extrema of functions of two variables. Compute integrals over a region, curve, solid and surface, of both scalar and vector fields, and use them to solve application problems. Apply the Fundamental Theorem for Line Integrals, Green's Theorem, Stokes' Theorem and the Divergence Theorem.  Course Description

Prerequisite: MATH 005B or MATH 005BH.

Parametric equations, polar coordinates, vectors and vector calculus, partial differentiation, multiple integration, Green's theorem, divergence theorem of Gauss, Stokes' theorem. No credit given if taken after MATH 005CH. Total of 90 hours lecture Transfer Credit: CSU; UC *C-ID: MATH 230 Grade Mode: L, P

Important Dates

Last day to add Last day to drop with a Census Last day to declare grade Last day to drop without a Last day to drop with a class: refund: Date: mode: "W": "W":

27-JUN-21 27-JUN-21 28-JUN-21 01-JUL-21 27-JUN-21 21-JUL-21

 Meeting Times

Type Meet Days Time Location Instructor Date

WEB DE Online - Henes, Matthew 06/21/2021 - 07/30/2021 Lecture

 Student Learning Outcomes

2 of 9 1. Apply vector operations to find equations of lines and planes and analyze the motion of a particle in space. 2.Explain limits, partial derivatives, directional derivatives, gradient vectors, and differentials and linear approximations of functions of two or more variables. 3. Compute local and absolute extrema of functions of two variables. 4. Compute integrals over a region, curve, solid and surface, of both scalar and vector fields, and use them to solve application problems. 5. Apply the Fundamental Theorem for Line Integrals, Green's Theorem, Stokes' Theorem and the Divergence Theorem.  Materials Textbook WebAssign for Calculus, 8th edition by Stewart (ISBN 9781305616684)

Canvas We will be using Canvas for this course, so you will need access to a computer and Internet. Canvas is also mobile-friendly and can be used on your phone or tablet through the Canvas Mobile App (https://community.canvaslms.com/docs/DOC-4048) or a mobile browser!

What are the basic computer specifications for Canvas? (https://community.canvaslms.com/docs/DOC-10721) Which browsers does Canvas support? (https://community.canvaslms.com/docs/DOC-10720) Technology Computer with internet access Webcam and microphone for exams Scanner: You will need to be able to create PDF documents. If you have an iPhone, you may want to use the built-in Notes app, which has a scanning feature that will create PDFs. Another alternative is a free application called CamScanner (https://www.camscanner.com/), which will also create PDF documents. PDF Reader: You will need to be able to view PDFs for this class. You can download a free PDF reader here, if you don't have one already on your computer: Adobe Reader (https://get.adobe.com/reader/) Other Materials Paper, pencil(s), and eraser to complete homework assignments and exams. You may find a scientific calculator useful for completing homework and exams.

3 of 9  Assignments and Grading

Grading Criteria Homework assignments, the Video Meet and Greet Check-In Assignment, the Self-Check Quiz, the Practice Submitting Exams Quiz, and Discussions: 15% (your five lowest homework scores--not the other assignments--are dropped) Exams: 55% Final Exam: 30% Total: 100% Grading Scale Assigned grades are based on performance on the work you do for this course, not on extra credit or external factors such as GPA and transfer. For a better understanding of what grades mean at PCC, please read the Grading System () document from the college catalog. Course grades will be no lower than those shown below.

A: 90-100% B: 80-89% C: 73-79% D: 60-72% F: Below 60% Late Submissions Homework is due on a daily basis. Late homework will be accepted for a reduced score, but only up to the day of the exam for that module. (In other words, homework for Module 1 can be submitted late up to the date of Exam 1; after that date, it will receive no credit.)

Please reply to assigned Discussion posts in a timely manner to give your classmates an opportunity to read them and respond with any feedback they might have. Please contact me if an exam date does not work with your schedule.  Additional Information

Participation & "Attendance"

Participation = Attendance! Online attendance is not marked by your physical presence in a classroom, but rather by your participation and engagement with the course activities and assignments. Guidelines This course is designed to take about 45 hours(!) per week (on average). This includes watching instructional videos, participating in online discussions, studying, and completing assignments, quizzes, and exams. Please plan to:

Set aside time each week to view all module materials and submit required work Log in regularly each week to check for announcements, grades, messages, and comments Participate in online discussions, and respond thoughtfully to your peers Drop Policy During the first week: Post your first Discussion response in order to mark your attendance and secure your spot! Anyone who does not complete the first Discussion post (Discussion: About You) will be dropped from the course. Throughout the term: Submit work regularly to show your active attendance. If you do not submit work for an entire module, you may be dropped for non-participation!

4 of 9 If You Fall Behind... Your participation is important for the success of this course. I do recognize that you are human, and life happens. If you've reached a point where you have fallen behind, or can't meet the due dates, please contact me. We'll work together to make a path to success.

Please click Next to go to the next page Discussion Guidelines Discussion Overview Discussion forums are used to communicate with other students on a specific topic or general course questions. Postings should be thoughtful and reflect your understanding of the subject matter. You are required to respond to your classmates each week.

If someone asks for help in the "Q&A" discussion, please feel free to respond. I will also jump in as needed. Discussion Tips For online discussions to be successful, it is recommended that you participate within the designated time period indicated in the course. As you develop your response here are a few tips you can use to avoid the "I agree or disagree" responses"

1. Share your experiences as it relates to the topic. Make connections to your own personal background and culture. 2. Identify and discuss your opinion and describe why you agree or disagree. 3. Search and share reputable sites, books, or articles that pertain to the topic. 4. Add a different view with specific examples. Netiquette Tips Avoid sarcasm. People who don't know you may misinterpret your meaning. Use appropriate language. Avoid "flaming" (online "screaming") or sentences typed in all caps. Be courteous to the other students in the class. You might find it helpful to read your posting out loud before you submit it: "tone" is a very important part of online communication. When you read your message out loud, does it sound the way you would speak to another student in the classroom? Never make derogatory comments toward another person in the class. You can disagree with ideas, but do not make personal attacks. Additional Info If you've never used Canvas discussions, you may find this 3-minute video on how to view, reply to, and edit discussion posts (https://vimeo.com/75056432) helpful.

If you prefer to read, a text transcript (http://bit.ly/2WmyDXa) is also available for this video.

Instructure Community. (2019, June 13). Discussions overview (https://vimeo.com/75056432) [video file]. Finding Grades and Feedback Finding Grades The "Grades" page in Canvas displays your grades for all course work. View this 3-minute video to see how to check your Grades (https://vimeo.com/74966156).

If you prefer to read, a text transcript (http://bit.ly/2UWzhtL) is also available for this video.

5 of 9 Finding Feedback I will be using a grading rubric to provide scores and feedback for assignments and discussions. I may also provide some written feedback to you in the "comments" area, which can be accessed by reviewing your submitted assignment, or from within your Grades page. I will do my best to provide grades and feedback within 1 week of the due date.

For additional information and questions on how to view your feedback, you may review the following Canvas Student Guides:

How do I view assignment comments from my instructor? How do I view rubric results for my assignment?

Instructure Community. (2019, April 23). Student grades (https://vimeo.com/74966156) [video file]. Academic Integrity What is Academic Integrity? Academic integrity means honesty in academic work. All of your coursework should be a result of your own efforts, so your grade reflects what you've actually learned. I understand that you can often feel pressured and overwhelmed by the demands of school, work, and personal commitments. No matter what level of stress you may be experiencing, it is still expected that you will approach your work with honesty and integrity. I believe that you want to do well in this class, and I further believe that there is a sense of pride in knowing that the grade you earn is the result of your own hard work.

Even though this course is online, academic honesty still applies. Exams are intended to be an honest assessment of what you have learned. I ask that you please maintain academic honesty for this course. For exams, you are permitted to use a scientific calculator and the textbook. Using notes or the internet or communicating with anyone about the exam during the exam are considered cheating. (You may ask me clarification questions if needed.)

PCC takes academic integrity very seriously; so do I. While I recognize that mistakes can happen, violating the college's student conduct policy (https://go.boarddocs.com/ca/pasadena/Board.nsf/goto?open&id=AM7PCG63E805) may compromise your academic career. If I learn that you have copied an assignment, you will receive zero points for the assignment. Cheating on an exam will result in a zero for the exam, and a report will be filed with the college. Students who get away with cheating will find that it will catch up with them at some point. You're in this class because you likely need the information in it for your major-- you're learning it because you'll need to use it at some point! Please keep this in mind if you become tempted to cheat. You would also be de-valuing your resulting degree or certificate when you enter the workforce or transfer and cannot meet the expectations that your degree or certification requires. Proctorio Exams will be proctored using Proctorio. You will find more information about Proctorio on the next page. Oral Follow-Up Exams After each exam, a portion of the class will meet with me one-on-one via Zoom to discuss aspects of your work. During this time I will discuss with you a couple of topics from the exam. Different students will receive different topics and questions. Advice Here are some quick tips, adapted from: What is Academic Integrity? (https://integrity.mit.edu/handbook/academic-integrity- mit/what-academic-integrity) (Massachusetts Institute of Technology, 2018): Do Trust the value of your own intellect. Demonstrate your own achievement and abilities. Do your own work for each class. Ask for help from me if you need it!

6 of 9 Don't Copy answers from the internet. Copy answers from another student. Ask another student to do your work for you. Take an exam or complete an assignment for another student. Use anything other than a scientific calculator or the textbook on exams.

Concept adapted from "Academic Integrity Example" by Fabiola Torres for Online Network of Educators, (http://onlinenetworkofeducators.org/) licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0)

Massachusetts Institute of Technology. (2018, July). What is academic integrity? (https://integrity.mit.edu/handbook/academic- integrity-mit/what-academic-integrity)  Student Resources

Accommodations If you have a disability and believe you may need an accommodation such as materials in an alternate format, sign language interpreting/real-time captioning, access to assistive technology and/or test accommodations, per the Americans with Disabilities Act, or Section 504 of the Rehabilitation Act, please contact Disabled Students Programs and Services at [email protected] or by phone at 626-720-4497 or 626-817-6133, as soon as possible. Feel free to discuss your needs with me in private. Student Support Services PCC offers many academic and personal support services to help you be more successful, including Counseling, Tutoring, Library, Financial Aid, Health Services and more. Please explore these available free services:

Remote/Online Tutoring (https://pasadena.edu/academics/support/success-centers/online-tutoring.php): Please visit Remote/Online Tutoring to get information on our student success centers for the support you need. Technology Access (https://pasadena.edu/about/president/coronavirus-updates/remote-classes-faq-for- students.php#access-to-technology): To borrow a laptop and see information about Wifi access, please visit the student information page Technical Support (https://pasadena.edu/academics/pcc-online/canvas-support.php): Find help to access and use Canvas, including guides and tutorials. Library Resources (https://pasadena.edu/library/index.php): Get help finding the resources you need, including books and articles. Meet with a librarian 24/7 to support your research needs and assist with citing sources. Counseling (https://pasadena.edu/academics/support/counseling/index.php): Our counselors can help you with educational planning, transferring to a university, academic and personal challenges, and more. Be sure to contact a counselor to complete your comprehensive student education plan before you complete 15 transferable units. This is needed to maintain priority registration and financial aid. Financial Aid (https://pasadena.edu/admissions-and-aid/financial-aid/index.php): The Office of Financial Aid and their knowledgeable advisers are here to make your education affordable. Please contact them at [email protected] Health & Well-Being Services: PCC offers a variety of free and low-cost services to help you maintain your physical and emotional well-being. Contact Student Health Services (https://pasadena.edu/campus-life/student-health- services/index.php) at [email protected] and Personal Counseling (https://pasadena.edu/campus-life/personal- counseling/index.php) at [email protected] when you need support.

View all Services for Current Students (https://pasadena.edu/current-students/index.php) on the PCC website.  College Policies

7 of 9 PCC has several policies in place to foster a positive and inclusive learning environment. These include the Academic Integrity & Student Conduct Policy, Course Attendance, Adds, Drops, and Withdrawal Policy and the Complaints, Grievances, and Student Due Process Policy. Academic Integrity and Student Conduct Policy Your thoughts and ideas are important. In order to protect your words and others’ words, we have rules about plagiarism. Students are required to cite the use of materials written by others in all communication for courses. Plagiarism is the presentation of someone else’s ideas or work as one’s own, including using ideas, words, or phrases without proper attribution. We will discuss the issue throughout the class, but feel free to contact me and/or a librarian if you are struggling to correctly combine others’ ideas with your own.

View Document: Academic Integrity & Student Conduct Policy (http://www.boarddocs.com/ca/pasadena/Board.nsf/goto? open&id=AM7PCG63E805) Course Attendance This syllabus represents one possible path our course learning may take; however, we may need to shift how and when we meet. Whatever path our course takes, I know we will spend time reflecting on how to sustain our families, communities, and ourselves through teaching and learning. Let us proceed with grace and understanding that the most important thing right now, as ever, is health and safety for the present and future of our communities.

In online classes, as in face to face classes, your contribution and attendance are valued and needed. Your active participation and completion of assignments (discussion board, quizzes, or other online based assignments) will help you successfully complete the course. Your timely submission of assignments will contribute to building a supportive learning community for all.

Some courses in the Schedule of Classes show weekly days and times that you must meet with the class live online. These class sessions are important because they’ll expand your skills through group activities and discussions. For an engaging online class, when possible please be present and ready to participate, allowing for your experiences and opinions to be shared and heard. Recordings of the live session will be posted in your class Canvas course, so that you can keep current with the learning. You will not be penalized for not attending the live sessions, but you are highly encouraged to attend. If you are unable to take an assessment during a scheduled synchronous session, please let me know so we can arrange for an alternative. Please reach out to me to discuss any challenges and resource needs you’re facing in taking this course so that I can help you succeed.

View Document: Course Attendance, Adds, Drops, and Withdrawal Policy (http://www.boarddocs.com/ca/pasadena/Board.nsf/goto?open&id=AM7P85635300) Discrimination & Complaints PCC is committed to the fair and equitable treatment of all students. There are policies in place to protect all students from discrimination. These policies include non-discrimination and sexual harassment policies which can be found at Discrimination Complaints (https://pasadena.edu/student-services/grievances.php#discrimination) on the PCC web site.

View Document: Complaints, Grievances, and Student Due Process Policy (http://www.boarddocs.com/ca/pasadena/Board.nsf/goto?open&id=AM7QWV6B5A50)  Course Schedule

Unit Title/Topic Duration in days (note Assessment there is some overlap)

Module 0 Orientation 1 day Self-Check Quiz: Module 0

Discussion: About You

8 of 9 Module 1 Ch 12 Vectors and the Geometry of Space 4 days Discussion: Academic Integrity

Exam 1 6/25

Module 2 Ch 13 Vector Functions 5 days Discussion: Muddiest Point (Group Discussion)

Exam 2 7/1

Module 3 Ch 14 Partial Derivatives 6 days Discussion: Applying the Content (Group Discussion)

Exam 3 7/9

Module 4 Ch 15 Multiple Integrals 9 days Discussion: Change of Variable Strategies (Group Discussion)

Exam 4 7/21

Module 5 Ch 16 Vector Calculus 9 days Discussion: Wrap-Up and Looking Ahead

Exam 5 7/27

Module 6 Wrap-Up and Final Exam 1 day Final Exam 7/30

Overview of Course Modules and Units

9 of 9