MTH 277 S01 (primarily seated hybrid)/277 V01 (online): Vector Calculus, Fall 2017

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1 Blue Ridge Community College MTH 277 S01 (primarily seated hybrid)/277 V01 (online): Vector Calculus, Fall 2017 Lynne Ryan Course Meets: MW 2:00 3:15 in ( S01 section) My : T RyanL@brcc.edu Phone: (540) Hours: See block schedule at end Course Website: I. COURSE DESCRIPTION: A. MTH 277 presents vector valued functions, partial derivatives, multiple integrals, and topics from the calculus of vectors. Designed for mathematical, physical, and engineering science programs. B. Prerequisite: MTH 174 or equivalent. C. Distance Learning Policy ( V01 section): Students will be required to take three proctored tests. The tests will be given in the BRCC Testing Center, or you may make arrangements with your instructor to take the proctored test/exam at any other college, university or military testing center. Tests/Exams taken at the BRCC testing center are at no charge. Students that live outside the BRCC service area and arrange to take the test or exam at another site are responsible for any fees associated with test proctoring at the selected site. Test dates are published in the syllabus. You must take the test/exam during the allotted dates and times given. Do not wait until the last minute to take the test/exam as seats are limited. You must present a photo ID to take the test. For BRCC testing center hours and other testing information see D. Hybrid note ( S01 section): This class is scheduled as a primarily seated hybrid it is a four credit hour class that is scheduled to meet in a three hour block each week. The remaining hour of instruction is provided through online content students should expect to spend time each week working through additional lecture materials on topics that are not covered within the class meeting period.

2 II. COURSE OBJECTIVES: Course Major Topics/Units A. Vectors and the Geometry of Space B. Vector Functions C. Partial Derivatives D. Multiple Integrals Specific Student Learning Outcomes for Topic/Unit The student will be able to Identify and apply the parts of the three dimensional coordinate system, distance formula and the equation of the sphere Compute the magnitude, scalar multiple of a vector, and find a unit vector in the direction of a given vector Calculate the sum, difference, and linear combination of vectors Calculate the dot product and cross product of vectors, use the products to calculate the angle between two vectors, and to determine whether vectors are perpendicular or parallel Determine the scalar and vector projections Write the equations of lines and planes in space Draw various quadric surfaces and cylinders using the concepts of trace and cross section Sketch vector valued functions Determine the relation between these functions and the parametric representations of space curves Compute the limit, derivative, and integral of a vector valued function Calculate the arc length of a curve and its curvature; identify the unit tangent, unit normal and binormal vectors Calculate the tangential and normal components of a vector Describe motion in space Define functions of several variables and know the concepts of dependent variable, independent variables, domain and range. Calculate limits of functions in two variables or prove that a limit does not exist; Test the continuity of functions of several variables; Calculate partial derivatives and interpret them geometrically, calculate higher partial derivatives Determine the equation of a tangent plane to a surface; calculate the change in a function by linearization and by differentials, Determine total and partial derivatives using chain rules, Calculate directional derivatives and interpret the results Identify the gradient, interpret the gradient, and use it to find directional derivative Apply intuitive knowledge of concepts of extrema for functions of several variables, and apply them to mathematical and applied problems. Lagrange multipliers. Define double integral, evaluate a double integral by the definition and the midpoint rule and describe the simplest properties of them. Calculate iterated integrals by Fubini s Theorem Calculate double integrals over general regions and use geometric interpretation of double integral as a volume to calculate such volumes. Some applications of double integrals may include computing mass, electric charge, center of mass and moment of inertia

3 Evaluate double integrals in polar coordinates to calculate polar areas, evaluate Cartesian double integrals of a particular form by transforming to polar double integrals Define triple integrals, evaluate triple integrals, and know the simplest properties of them. Calculate volumes by triple integrals Transform between Cartesian, cylindrical, and spherical coordinate systems; evaluate triple integrals in all three coordinate systems; make a change of variables using the Jacobian E. Vector Calculus Describe vector fields in two and three dimensions graphically; determine if vector fields are conservative, directly and using theorems Identify the meaning and set up of line integrals and evaluate line integrals Apply the connection between the concepts of conservative force field, independence of path, the existence of potentials, and the fundamental theorem for line integrals. Calculate the work done by a force as a line integral Apply Green's theorem to evaluate line integrals as double integrals and conversely Calculate and interpret the curl, gradient, and the divergence of a vector field Evaluate a surface integral. Understand the concept of flux of a vector field State and use Stokes Theorem State and use the Divergence Theorem Within the context of the topics covered above, students should be able to Effectively use technology as an aid to modeling, visualizing, understanding, and applying the concepts presented. Communicate mathematical concepts clearly and correctly through the use of precise terminology and notation. III. EVALUATION AND REQUIREMENTS: Grading Policy: Your grade will be calculated using a weighted average. The types of assignments and weights are given below: Nine graded assignments* (40%) Three tests (60%) *I ll drop the lowest graded assignment with the caveat that all assignments must be attempted. In other words, you can t skip an assignment / chunk of material and say just make that my drop. You re responsible for all the material, but as long as you make a reasonable stab at all nine of them, I will drop the lowest. Skip one, and I won t drop it it ll go in as a zero! Letter grades are assigned on the ten point scale: A = B = C = D = F = below 60 Late policies: First, the instructor reserves the right to accept or refuse late assignments, depending on circumstances. General guidelines are that written assignments are due on their scheduled due dates,

4 have a one day grace period after that to allow for minor mishaps (please submit the assignment by any means possible, such as dropping off by my office or scanning and ing), and then lose 10% a day for each day late. Tests should be taken in the week that they are scheduled, preferably on the scheduled class day, but I will put one up in the Testing Center for you in the event of an emergency. IV. COURSE ATTENDANCE AND PARTICIPATION POLICY: Attendance Policy (seated S01 section): The student is expected to attend all classes. If an absence is unavoidable, it is the student s responsibility to contact the instructor regarding material covered and assignments made. Permission to make up missed exams is granted at the discretion of the instructor. The circumstances causing the absence from an exam must be discussed with the instructor before the next regularly scheduled class meeting, and if permission to make up the exam is granted, it must be done in a timely manner in the Learning Assistance Center (G202). Attendance Policy (online V01 section): Attendance in an online section is defined by some evidence of participation in the course. Actions such as submitting assignments on time, and communicating with your instructor demonstrate that you are actively engaged in the course. Please be aware that BRCC policy allows for students to be dropped for non participation in the first few weeks of the course, and that for virtual sections, merely logging into Blackboard does not constitute participation. If you re in an online section of any course, be sure to check your VCCS daily your instructor may be trying to communicate something important to you, and a lack of response can be taken as not participating! For both sections, notes, lectures, and worked problems will be available online. The three tests are on site proctored assessments, in accordance with VCCS recommendations for distance learning. Seated section exams are in class at scheduled class times. Virtual section exams may be taken in the Testing Center at BRCC, or you may make arrangements with the testing center of your local college. Cancelled Classes: Unscheduled class cancellations may occur, sometimes college wide (e.g. weather) and sometimes due to instructor emergencies. Online sections are generally unaffected by class cancellations (unless the event manages to take out our power, and thus, our server!), but for the seated section, be aware that if we have a cancellation, the expectation is that you will make up the missed class by working through the posted material that was scheduled for that day s class session. Notification of college wide closures will be posted on the main BRCC home page, and you are encouraged to sign up for BRCC s Emergency Alert Service to receive texts: In the event I need to cancel, I ll try to both post as an announcement and you all as well. That s another reason to check your VCCS daily! V. COURSE ETIQUETTE: Correspondence: To protect your privacy, your business with Blue Ridge Community College is conducted only through your college provided account. Please use this account to contact your instructors, or when you are conducting other business with BRCC. Your instructors will use this address to contact you as well.

5 VI. HONOR POLICY: As an academic community we are committed to holding ourselves to the highest standards of ethical integrity. Blue Ridge Community College values truthfulness, honesty in academic work, and respect for the person and property of others [ ] BRCC Honor Code: code/index.html As a member of this community, you are responsible for understanding and adhering to the Honor Code. Violations include (but are not limited to) cheating on tests and quizzes, unauthorized collaboration on assignments, and plagiarism. For this course, collaborative work on written assignments and takehome tests is permitted and encouraged, and you may even submit group copies of assignments with multiple names on one assignment however, it is expected that each member of the group is individually responsible for knowing all the material covered by each assignment. In class tests are not collaborative, and should be completed with no outside help. Please consult me if you have any questions or concerns about what is permitted. Violations of the Honor Code may result in a grade penalty and or disciplinary action. For further information on your rights and responsibilities as a student, and the disciplinary guidelines and procedures, please consult the Student Handbook ( student rights/index.html ). VII. TEXT AND INSTRUCTIONAL MATERIALS: Course content is web based and not text specific. A Calculus text which covers the topics in the objectives list is necessary as a reference i.e. use whatever your freshman Calc textbook was. Internet access is required, and access to high speed Internet (cable, DSL) is strongly recommended. Software requirements are detailed on the course website. This course has both a Blackboard shell (access through MyBRCC: ) and a supplementary website ( ). The Blackboard site is where the secure stuff lives, like your grades, and solutions to assignments. The supplementary website is where most of the content (lectures, practice problems, etc) lives, and is a free and open public resource. You can get to it directly from the link (and can access the material there at any time, even after this course ends), and it s also linked from within the Blackboard shell. Additional BRCC Information, Policies, and Links VIII. ACADEMIC CALENDAR: The academic calendar gives the start and end dates for semester sessions and important deadlines for withdrawing from classes, etc. IX. BLACKBOARD COURSE ACCESS: X. COURSE RECORDINGS: Meetings of this course might be recorded; these recordings will be available to students registered for this class and are intended to supplement the classroom experience. Students

6 are expected to follow appropriate BRCC policies and maintain the security of passwords used to access recorded lectures. Recordings may not be reproduced, shared with those not in the class, or uploaded to other online environments without prior written instructor permission; doing so would be a breach of the BRCC Honor Code. If the instructor or any other BRCC personnel or departments plan for other uses for the recordings beyond this class, students identifiable in the recordings will be asked for consent prior to such use. XI. BRCC POLICIES: A. Academic Honesty: As a college student, you are expected to show integrity in your work and interactions with others. code/index.html B. Academic Support: BRCC is committed to making sure you get responsive, effective answers to your questions. We re here to help you succeed online. Click the link below to see resources available to you. support/index.html C. Non attending Policy: Attendance is considered a measure of progress as defined by federal financial aid regulations. In order to maintain eligibility for financial aid, Blue Ridge must proactively monitor course progress. Non attendance will be reported to the Dean of Student Services at the conclusion of the first week of the course, at midterm, and at the conclusion of the course. Students who receive federal financial aid and are not attending classes may be administratively withdrawn from the course. Failure to demonstrate active participation within the first seven days of an online class may result in administrative withdrawal from the course. For online courses, never attending is defined as never participated in any class discussions, blog postings, or other learning activities. If the student has logged into blackboard less than 2 times and has never contributed, they may be counted as never attending. D. Disability Services: We provide academic accommodations and support for students with documented disabilities. Students must submit current documentation of a disability by a qualified professional to Disability Services before academic accommodations can be requested. Qualified professional evaluations by physicians, psychologists, audiologists, etc., must have been completed within the last three years. E. Final Course Grade Appeal Policy: 1. The student should submit his/her complaint in writing to the appropriate administrative unit. 2. The College will respond in writing within the designated time frame. 3. Documentation of written complaints and the College's written response will be kept in a secure location for three years and then will be destroyed. F. Faculty Expectations: Enrolling in classes at Blue Ridge Community College is a serious investment of money, time, and effort. To be successful, students must be aware of the challenges ahead of them and be willing and able to work toward meeting those challenges. Knowing what faculty expect helps students get the most out of the learning experience in the classroom and online. G. Student Expectations: College instructors have encountered most of the challenges, frustrations, stresses, and triumphs that students will face. Faculty members know what students need to do to succeed in their courses and will work with students to that end. expectations/index.html

7 XII. BRCC ALERT REGISTRATION: Blue Ridge Community College uses BRCC Alert to immediately contact you during a major crisis or emergency. BRCC Alert delivers important emergency alerts, notifications and updates to you on all your devices.

8 CLASS SCHEDULE AND SEQUENCE OF INSTRUCTION: WEEK COMPLETE MODULES ASSIGNMENT DUE DATES Week 1: 8/21/17 Week 2: 8/28/17 Week 3: 9/4/17 Week 4: 9/11/17 Week 5: 9/18/17 Week 6: 9/25/17 Week 7: 10/2/17 Week 8: 10/9/17 Week 9: 10/16/17 Module 1: Defining a vector Module 2: Vector addition and scalar multiplication Module 3: The dot product Module 4: The cross product Module 5: Lines and planes Module 6: Vector valued functions Module 7: Calculus of vector valued functions Module 7: Calculus of vector valued functions Module 8: Applications of vector valued functions Catch up and review for test one Module 9: Functions of several variables Module 10: Calculus of multivariable functions Module 11: The chain rule Module 12: Applications of partial differentiation No class 10/16 FALL BREAK Module 13: Optimization Graded assignment 1 (modules 1 3) 8/28/17 Graded assignment 2 (modules 4 5) 9/4/17 *see assignment page for schedule note Graded assignment 3 (modules 6 8) 9/18/17 Test one covers modules 1 8 9/25/17 Graded assignment 4 (modules 9 11) 10/18/17 Week 10: 10/23/17 Module 14: Iterated and double integrals Graded assignment 5 (modules 12 13) 10/23/17 Week 11: 10/30/17 Week 12: 11/6/17 Week 13: 11/13/17 Week 14: 11/20/17 Week 15: 11/27/17 Week 16: 12/4/17 Catch up and review for test two Module 15: Triple integrals Module 15: Triple integrals Module 16: Applications of double and triple integrals Module 17: Vector fields and line integrals Module 17: Vector fields and line integrals No class 11/22 THANKSGIVING Module 18: Green's Theorem, Stokes' Theorem, Divergence Theorem Catch up and study for "final" (test three) Graded assignment 6 (module 14) 10/30/17 Test two covers modules /6/17 Graded assignment 7 (modules 15 16) 11/20/17 Graded assignment 8 (module 17) 11/27/17 Graded assignment 9 (module 18) 12/4/17 Exam week: 12/11/17 In class final (test three) covers modules TBD Important Dates: Last day to add is August 20; last day to drop with refund is September 7; last day to drop w/o grade penalty is October 26. A complete academic calendar is at

9 Homework policy, for emphasis (extended threatening version!) There s a long story about why I m cranky about homework in this class, and if you re in the in class class, you ll have to hear all about it Believe me. I m going to try to terrify you into compliance. The summary is ASSIGNMENTS ARE DUE THE DAY THAT THEY ARE DUE. Not some other day. Not three weeks later. Not right after I have my Physics test. You get a day s grace period to allow for short term right before class emergencies, like a car breakdown if you get it to me the day after it s due, there s no penalty. How you get it to me is up to you under my office door, or scanned and ed to me, or faxed. If you drop it in the US mail and it s postmarked that day, I ll consider it OK. After that, assignments lose 10% a day for every day late. I will drop the lowest assignment grade at the end. This is on the condition that all assignments have at least been attempted. You can t skip an assignment and the corresponding chunk of material. If something unfortunate happens to you that you re out long term well, the nice thing is, this originally started out as an online class, and all the content is online. So while you re sitting at home with that broken leg, you can still keep up with the material, and hand your assignments over to a friend to turn in. Got the flu? Well, you don t have to come in and infect us all! Isn t that great how that all works out?! And if you re dysfunctional for a week or two, you have a sick day assignments only come due every week or two, so the drop has you covered that s your sick day. If you go on vacation, I suggest you book a hotel with wireless access and bring a laptop. If you are in a coma for three or more weeks, then I d recommend a medical withdrawal at that point anyway. If you are dead, and subsequently resurrected, follow the procedure for coma. Thank you.

10 Blue Ridge Community College Lynne s Fall 2017 Schedule Monday Tuesday Wednesday Thursday Friday before 11:00 11:00-12:15 MTH MTH :30-1:45 Unavailable reserved assessment meeting time SDV 101-H02 G215* Unavailable reserved assessment meeting time (appt. only) 2:00-3:15 MTH 277-S01 MTH 277-S01 (appt. only) 3:30-5:35 MTH MTH :35-6:30 *SDV 101-H02 is a mostly online hybrid course that only meets in person twice: 8/22 and 9/12. All other Tuesday dates in this time block are office hours.

SOUTHWEST COLLEGE Department of Mathematics

SOUTHWEST COLLEGE Department of Mathematics COURSE SYLLABUS MATH 2415: CALCULUS III (DISTANCE EDUCATION) SPRING 2015 / SS TERM / CRN 48306 / FEBRUARY 14 MAY 17/ INSTRUCTOR: Dr. Jaime L. Hernández CONTACT