Multivariable Calculus, MATH W53 2018
Multivariable Calculus, MATH W53 2018Four (4) semester credits. This course counts the same as the usual version ofMath 53 to satisfy prerequisite or major requirements.Course DescriptionThis course has the same content as the usual, face-to-face version ofMath 53. The official description in the course catalog is as follows:Parametric equations and polar coordinates. Vectors in 2- and 3dimensional Euclidean spaces. Partial derivatives. Multiple integrals.Vector calculus. Theorems of Green, Gauss, and Stokes. The purposeof this course is to introduce the basic notions of multivariable calculuswhich are needed in mathematics, science, and engineering.PrerequisitesMath 1B or equivalent. In particular, students should have a solidcommand of single variable calculus including trigonometric andexponential functions, limits and continuity, differentiation, the chainrule, integration and its applications, the fundamental theorem ofcalculus, substitution, and integration by parts.Course ObjectivesAfter successfully completing this course, you will be able to Demonstrate understanding of the basic notions of multivariablecalculus that are needed in mathematics, science, and engineeringInstructor Information, Contact, Office Hours,& CommunicationCourse InstructorInstructor Name: Professor Michael HutchingsOffice Hours: See announcementPage 1
Graduate Student Instructors (GSIs)While the instructor will interact with the whole class and will overseeall activities and grading, as well as being available to resolve anyissues that may arise, the GSIs will be your main point of contact.Your GSIs are responsible for assisting you directly with your questionsabout assignments and course requirements, as outlined in theAssignments and Calendar. The GSIs will also facilitate ongoingdiscussion and interaction with you on major topics in each module.You can always send a message to your GSI through the coursemessage system.GSI Name: Archit Kulkarni Felix Gotti Nic Brody Jeremy Meza Thunwa TheerakarnOffice Hours: See announcementsOffice HoursThe course instructor and GSIs will offer virtual office hours, wherestudents can communicate in real time (synchronously) using the Chattool. While these chats are optional they can be valuable fordiscussion, answering questions, and reviewing for exams. Chats areoptional; no points are awarded for participation. In person officehours may be offered at the discretion of the instructor and GSIs.The session will be for one hour. However, if no one shows up in thefirst 10 minutes, then that office hour will be cancelled.Course MailMake sure to check the Course Mail for messages from the instructor.You can access course email within the Learning Management Systemby clicking on the Inbox link or choose to have your course mailforwarded to your personal email account or your cell phone.Page 2
Course Materials and Technical RequirementsRequired MaterialsCalculus: Early Transcendentals by Ian Stewart, 8th edition.A custom edition of the book, containing only the chapters needed forthe course and costing much less than the full book, is available fromCengage and the Cal Student Store. The custom edition is entitledMultivariable Calculus: Early Transcendentals for UC Berkeley, 8thedition, and its ISBN is 9781305749986. There are many otherversions and editions of Stewart’s Calculus; unfortunately these willnot work with this course.Technical RequirementsThis course is built on a Learning Management system (LMS) calledCanvas and you will need to meet the computer specifications listed inbcourse to participate within this online platform.Technical SupportIf you are having technical difficulties please alert the GSIimmediately. However, understand that neither the GSIs, nor theprofessor can assist you with technical problems. You must call oremail tech support and make sure you resolve any issues immediately.In your course, click on the "Help" button on the bottom left of theglobal navigation menu. Be sure to document (save emails andtransaction numbers) for all interactions with tech support.Extensions and late submissions will not be accepted due to“technical difficulties.”Learning ActivitiesVERY IMPORTANTYou won't be able to access your course material until you read andmake your pledge to Academic Integrity in the Orientation Module.You are expected to fully participate in all the course activitiesdescribed here.Page 3
1. Read the assigned sections of the textbook.2. Watch and listen to the lecture presentations.3. Answer the "Check Your Understanding" questions after eachlecture segment.4. Complete homework assignments.5. Complete biweekly quizzes.6. Read web-based announcements posted during the course.7. (Optional but strongly recommended) Participate in onlinediscussions on piazza.8. (Optional but strongly recommended) Participate in online officehours.9. Complete the final examSectionsFor grading purposes, each of you has been assigned to one of thecourse GSIs and placed within his/her section. Your particular GSI willgrade all of your work, as well as that of your section-mates, andengage with you in the course discussions. You can see whose sectionyou've been placed in by exploring the "Section" column within the"People" page or by examining your discussion group's title, whichincludes your GSI's nameModulesPart 1: Introduction to the course. Geometry of curves. (Stewartchapter 10.) Geometry of vectors, dot product, cross product. Planesand quadric surfaces. (Stewart chapter 12.) Vector-valued functions.(Stewart chapter 13.)Part 2: Differentiation. Limits and continuity, partial derivatives, chainrule, directional derivative and gradient, optimization, Lagrangemultipliers. (Stewart chapter 14.)Part 3: Integration. Double and triple integrals in Cartesian, polar,cylindrical, and spherical coordinates, change of variables. (Stewartchapter 15.)Part 4: Vector calculus. Line integrals and surface integrals,fundamental theorem for line integrals, Green's theorem, Stokes'stheorem, divergence theorem. (Stewart chapter 16)Part 5: Review and Final Exam. August 7 and 8 will be devoted toreview and practice for the final exam on Thursday August 9.Page 4
Reading AssignmentsEach module includes assigned readings relevant to each topic coveredin that module.Lecture and Check Your UnderstandingThere will be a number of short video lecture segments each week.Each lecture segment will be followed by one or more multiple choicequestions to check your understanding of the material, with instantfeedback and explanations of the answers. Sometimes these will besurvey questions instead. Completion (but not correctness) of thesequestions counts towards the participation component of the grade.While the lecture segments can be viewed at any time, each lecturesegment and its accompanying check your understanding questionsmust be completed before a fixed deadline to receive full credits.Homework AssignmentsSince extensive practice is essential for mastering this material, therewill be a number of substantial homework assignments, which will bedue twice a week. These will be given a pass/fail grade based oncompleteness. Collaboration on homework with fellow students ispermitted, as long as each student writes their own solutionsindependently. The homework grade is determined by the percentageof homework assignments that are completed on time. (The lowestthree assignments will be dropped. Here an "assignment" consists ofthe homework for one section of the course. Sometimes more thanone assignment will be due on the same day.)ParticipationThe participation grade is determined by the percentage of check yourunderstanding questions (including those that are survey questions)that are answered (correctly or not) on time.QuizzesThere will be two quizzes each week, on Mondays and Thursdays.However there will be no quiz on the first Monday or on the lastThursday. Quizzes will be similar to homework, except that they will beshorter and will be graded by the GSIs, who will provide detailedpersonalized feedback. Each quiz may be taken at any time during thePage 5
day for which it is assigned. There is a one hour time limit forcompleting the quiz, plus an additional hour for dealing with anytechnical issues in submitting it. Thus, after a quiz is started, it mustbe submitted within two hours. The quizzes will be "open book": thetextbook and course materials may be used. However the internet andelectronic devices may not be used except as needed to access thecourse materials. The lowest two quiz scores will be dropped.Discussion ForumsGeneral Discussion on PiazzaStudents are encouraged to use Piazza to discuss questions of generalinterest regarding the course content. Messages not tied to anyspecific homework assignment should be posted with the tag "GeneralQ and A". The GSI's and the professor will periodically check in andhelp answer questions.Final ExamThe final exam will take place on Thursday August 9, 2018 at 9:00am- 12:00pm PDT. Students must take the final examination in person orpossibly arrange to have the examination proctored if you cannotcome to campus. For more information on getting a proctor, look atthe Proctor Info on the left navigation menu. Off-site proctorapplications must be submitted prior to July 13th, 2018 PDT. If youmiss taking the final or try to take it in a manner for which you havenot received permission, you will fail this class automaticallyReminder: Your Course End DateYour course will end on August 10. As you work through the course,please keep the end date in mind, and if you want to save anycommentary or assignments for future reference, please make sure toprint or copy/paste those materials before your access ends.Grading and Course PoliciesYour final course grade will be calculated as follows:Table 1: Final Grade PercentagesPage 6
CategoryPercentageof GradeHomeworkThe homework grade is determined by the percentage ofhomework assignments that are completed on time.(The lowest three assignments will be dropped. Here an 20%“assignment” consists of the homework for one sectionof the course. Sometimes more than one assignmentwill be due on the same day.)ParticipationThe participation grade is determined by the percentageof check your understanding questions (including those 5%that are survey questions) that are answered (correctlyor not) on time.QuizzesThe lowest two quiz scores will be dropped.25%Final ExamA passing grade (at least C-) on the final exam isrequired to pass the course50%The four items above will be curved to a common scale, and then thecurved grades will be averaged to determine the course grade.There is no regrading of quizzes and the final exam. Grades cannot bechanged unless an egregious error was made such as adding up thepoints incorrectly.It is important to note that not all components are graded online andincluded in the online course grade book. Because of this, the onlinecourse grade book will not display your overall course grade at anygiven time or your final grade. It should simply be used to assess yourperformance on the components that are included within it. Your finalletter grade will be mailed to you by the registrar's office.Page 7
Course PoliciesPromptnessHomework assignments all have specific final due dates and times. Youwill not receive credit if assignments are submitted after the indicateddue date.Further, each online activity must be submitted through the coursewebsite by the due date. Fax or mail submission will not be accepted.Students who wait until the final hours prior to a submission deadlinerisk having problems with their ISP, hardware, software, or variousother site access difficulties. Therefore, it is advisable to submitassignments and tests through the course website early. Studentsshould plan accordingly and get into the habit of checking the coursewebsite several times each week, and submitting and posting early.Academic IntegrityCheating on exams and plagiarism are two common examples ofdishonest, unethical behavior. Honesty and integrity are of greatimportance in all facets of life. They help to build a sense of selfconfidence, and are key to building trust within relationships, whetherpersonal or professional. There is no tolerance for dishonesty in theacademic world, for it undermines what we are dedicated to doing furthering knowledge for the benefit of humanity.Incomplete Course GradeIncomplete grades can only be given if (1) unanticipatedcircumstances (e.g.illness) prevent a student from completing thecourse, and (2) the student is otherwise passing with a grade of atleast C-. In this case the student must make arrangements with theprofessor for completing the coursework before the start of thefollowing spring semester. For example, if the missing courseworkconsists of the final exam, then one can make it up by taking the finalexam for Math 53 at the end of the fall semester. Note that this will bewith another professor, and their final exam might be more difficult.Page 8
Students with DisabilitiesAny students requiring course accommodations due to a physical,emotional, or learning disability must contact the Disabled Students'Program (DSP). They will review all requests on an individual basis. Request your Disabled Student Program Specialist to send theinstructor a formal request before the official course start date byemail.In addition, notify the instructor and your Online Learning SupportSpecialist, which accommodations you would like to use.o Your Online Learning Support Specialist is Tracie Allen and heremail is summer online support@berkeley.eduEnd of Course EvaluationBefore your course end date, please take a few minutes to participatein the Course Evaluation to share your opinions about the course.The evaluation does not request any personal information, and yourresponses will remain strictly confidential. A link to the evaluation willbe made available via bCourses on July 26th, 2018 and will beavailable until August 8th, 2018. You will also be emailed a link to thecourse evaluation.To access the course evaluation via bCourses: Enter the course in bCoursesChoose Course Evaluation from the left-hand navigation menu.Complete evaluation and submit. Course OutlinePage 9
Vector calculus. Theorems of Green, Gauss, and Stokes. The purpose of this course is to introduce the basic notions of multivariable calculus which are needed in mathematics, science, and engineering. Prerequisites Math 1B or equivalent. In particular, students should have a solid command of single varia
MATH 210 Single Variable Calculus I Early Transcendentals (4) o Allan Hancock College : MATH 181 Calculus 1 5 o American River College : MATH 400 Calculus I 5 o Berkeley City College : MATH 3A Calculus I 5 o Cabrillo College : MATH 5A Analytic Geometry and Calculus I 5 o Canada College : MATH 251 Analytical Geometry and Calculus I 5
Math 1B or equivalent. In particular, students should have a solid command of single variable calculus including trigonometric and exponential functions, limits and continuity, differentiation, the chain rule, integration and its applications, the fundamental theorem of calculus, substitution, and integration by parts. Course Objectives
Lectures on Multivariable Feedback Control Ali Karimpour Department of Electrical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad (September 2009) Chapter 2: Introduction to Multivariable Control 2-1 Multivariable Connections 2-2 Multivariable Poles 2-2-1 Poles from State Space Realizations 2-2-2 Poles from Transfer Functions
3 Linear Algebra in Multivariable Calculus Linear maps play a big role in multivariable calculus and are used in a number of ways to clarify and understand certain constructions. The fact that linear algebra is the basis for multivariable calculus should not be surprising as linear algebra is merely a gen
Calculus is an essential tool in many sciences. These questions are designed to ensure that you have a su cient mastery of the subject for multivariable calculus. We rst list several results you should know and then many review problems, which are followed by detailed solutions.
2224H or MATH 2204 or MATH 2204H), Co: MATH 2214 3 MATH 2114(3) Introduction to Linear Algebra Pre: MATH 1225 (min grade of B) or MATH 1226 3 (1) MATH 2214 Introduction to Differential Equations Pre: (1114 or 2114 or 2114H or 2405H), 1226 3 MATH 2204(3) Introduction to Multivariable Calculus Pre:
2224H or MATH 2204 or MATH 2204H), Co: MATH 2214 3 MATH 2114 (3) Introduction to Linear Algebra Pre: MATH 1225 (min grade of B) or MATH 1226 3 MATH 214 (1) I ntr od uc iD f e alEq s Pre: (1114 or 2114 or 2114H or 2405H), 1226 3 MATH 2204 (3) Introduction to Multivariable Calculus Pre:
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