MULTIVARIABLE CALCULUS

                                                               Florida International University
                                                              14404 MAC 2313 (U03), Spring 2018
                                                               MULTIVARIABLE CALCULUS

Prerequisites: MAC 2311 and MAC 2312, each with a grade C or better. This course assumes that you have a basic knowledge of the limit, differentiation, and integration rules.

Instructor: Dr. Tebou
E-mail: teboul@fiu.edu
Tel: (305) 348-2939
Office hours: MF: 12:00-1:00 W: 1:00-2:00
Just drop by my office for hep, no appointment is needed.

Lectures: MF 11:00-11:50 in SASC 251
W 11:00-12:50 in SASC 251

Website:faculty.fiu.edu/~teboul/mac2313-sp18.html
Office: DM 427 Other times: by appointment only. (If you cannot make the
office hours, you can talk to me, e-mail or call me for another arrangement.)

Free Tutoring: GL 120 (MTWR 0900-2000, F 0900-1700) Tel: 305-348-2441, remember to phone for an appointment if you do not want to line up, and when you get there, ask for the mathematics tutors. For more information about math help, click here. Additionally, Hillal Ibiyemi is our Learning Assistant, and he will be helping you with course or homework questions. Meeting times: T 1:00-3:00 in PC 422 (computer lab, subject to change), W 9:30-10:30 in GC 280, R 5:00-6:00 in DM 110, F 9:30-10:30 in SASC 251. To contact the LA, just text or email him.

Communication: If need be, I will communicate with you through your FIU email account; so be sure to check it often. Attendance: Attendance is mandatory for the first two weeks as per a new university requirement for UCC courses, which include multivariable calculus. It is strongly recommended that you attend all class meetings. If you cannot attend a lecture, it is your responsibility to cover the missed material or to get the notes from a class mate.

Textbook: Multivariable Calculus, by Anton, Bivens, and Davis, 10th edition, John Wiley. The material I plan to cover includes all sections of chapters 11(Three-dimensional space, vectors), 12(Vector-valued functions), 13(Functions of several variables), 14(Multiple integrals. For a quick review of integration, click here), 15(Topics in vector calculus). The tentative order of material coverage is: 11(all), 13(all), 14(all), 15(all), 12(all). There are 40 sections; so we will try to cover as much as possible two sections on Wednesdays.

Early Alerts: The early alerts system is there to help you succeed in this course by detecting difficulties with the course early on in the semester, so that they can be addressed with your advisor. Here is how it works: if you are not performing well in the course or if you are frequently absent, I will inform your advisor so that you will be contacted to discuss either issue.

Expectations: After completing Chapter

11. I expect you to be able to:
plot points in rectangular coordinates, recognize point coordinates on a box,
recognize the equation of a sphere, and solve basic problems involving spheres,
solve basic problems involving vectors, find the area of a parallelogram, the volume of a parallelepiped, solve basic problems involving planes and lines, recognize quadric surfaces through their equations, be able to draw rough sketch of quadric surfaces, solve basic problems involving cylindrical or spherical coordinates. 12. I expect you to be able to find the domain, and solve basic limits, continuity and integration problems for vector-valued functions, find the arc length parameter, unit normal , tangent and binormal vectors on parametric curves, find the curvature of a curve, solve basic problems for motion along a curve. 13. I expect you to be able to describe in words and sketch the domain of a function of two or three
variables, solve basic problems involving
level curves and level surfaces, solve basic
problems involving limits and continuity for
functions with several variables, find partial derivatives, show that a function of two/three
variables is differentiable at a point, find
partial derivatives using the chain rule or implicit
partial differentiation, find gradients and directional derivatives, find tangent planes and normal
lines, solve basic optimization problems
using the second partials test or Lagrange multipliers.

14. I expect you to be able to evaluate simple double and triple integrals on rectangular regions
or with given integration limits, find the area of a described plane region or the volume of a described 3-dimensional region,
to solve basic integration problems involving polar, cylindrical or spherical coordinates, solve basic integration problems involving a change of variables.
Blank space.
15. I expect you to be able to solve basic problems
about vector fields, evaluate line integrals involving piecewise smooth curves, know the fundamental theorem of line integrals, show that a vector field is conservative and find corresponding potential functions, know Green's theorem, find surface areas and surface integrals, find the flux of a vector field across a given surface by using a surface integral or the divergence theorem, solve basic problems involving the Stokes' theorem.

Some old exams: Fall 06: Test 1 Test 2 Test 3 Test3-solution Test 1 soln Test 2 soln Spring 08: Test 1 Test2 Test 3 Spring 12: Test 1 Test 2

RECOMMENDED PROBLEMS : 11.1(1,2,9,10,11,12,14,15,18,19to28,51,52,53,55), 11.2(4ad,5,8ac,10b,11,14bdf,15, 17to20,21,23,27,33,37,54,56), 11.3(1cd,3,7,8,9,10,13,15,24ac,25,26bc,28-31,41,43), 11.4(1,3,4,7ab,10,13to16,18,20,22,29,30), 11.5(1,3b,5b,11to14,17,18,19,23,26,27,28,30,31,33,49,55), 11.6(3,4,7,11,13,15,17,19,21to24,26,27,30,32,34,36,37,41,44,45,48,49; be able to derive the distance formula discussed),11.7(1,4,9acdef,47), 11.8(1ad,2cd,3b,4ad,5b,6b,7d,8b,9bd,10c,12d,20,21,22,24,29,31,33), 13.1(7,16,17b,19to22,44,47,57,59), 13.2(1,4,7,,9,12,13,15,,16,19,22,24,27,29-32,35,41,42,47), 13.3(1ab,2abde,3,5,14,15,16,19,21,23,33,39,61,63,65,67,69,71,74,91,92a,107,109), 13.4(3,6,8,10,11,13,15,16,18,27-30,33,35,39,40,43,47,51), 13.5(1,3,5,7,8,14,17,19,23,25,33,39,43,54,55,59), 13.6(9,15,23,27,34,40,42,73,,76), 13.7(1,5,8,11,16,22,24,27), 13.8(1b,2bc,3,9,11,13,17,25,26,28,30,31,33,35,37,39,44), 13.9(6,8,9,11,12,17,18,24). 14.1(4,6,9,11,14,16,29,33,35), 14.2(4,7,11,15,19,20,24,29,33to36,37,40,47,51,53,55), 14.3(2,4,5,10,11,23,25,28,29,31,33,41), 14.4(1, 3,5,9,13,19,21,23,30,32,39,41,45), 14.5(3,4,6,8,9,12,16,17,27,29,39), 14.6(1,2,9,11,14,15,17,19,28), 14.7(3,4,7,9,11,13,15,16,21,23,25,30,35,37,41,45), 14.8(2,3,13,15,19,23,25,31,34,38,39,41), 15.1(1,2,3,11-14,15,17,19,23,35,36,37,41,42,43,44), 15.2(1,8,11ac,12ab,14bc,15to18,20,23,26,29,33a,34,36,39,42,43,48), 15.3(theorem 15.3.1(statement and proof), 3,4,5,7,8, 11,13,14,17,23,27,31,33), 15.4(Green's theorem, 1,3,4,9,11,12,15to18,21,25,29), 15.5(1,4,5,8,13,19,23,37), 15.6(1,5,7,8,9,11,13,16,23,26), 15.7(divergence theorem, 1,2,3,9,11,14,16,29,30,35), 15.8(Stokes theorem, 1,2,5,9,10,12), 12.1(2,3,10,12), 12.2(2,4,5,9,15,221,27,32,37,40), 12.3(2,7,9,15,26,30,33), 12.4(5,9,11,16,18,19), 12.5(5,9,15,16,23,27,30,39,45,47), 12.6(1,7,8,17,27,35,38,42), 12.7 (assigned reading). Be sure to review all those problems for the final exam. Good luck.

Solutions Manual (information on accessing this online book will be communicated in class.)

Recommendations: Begin to do your homework from today, January 08, till the last day of class. Set your goal for the course right from the beginning, and work tirelessly toward it; do not let anyone or anything divert you from your goal. Many students have trouble passing this course because there are many different notions to assimilate within one semester. However, if you put the necessary effort into it, then you'll succeed. Be sure to always come to class well prepared to tackle the topic of the day; read the section(s) to be covered beforehand; doing this will make it easier for you to understand the material to be discussed in class. Do not fall behind; it might prove very difficult to catch up afterwards. Be sure to attend classes regularly, and to diligently deal with any questions or concerns you might have. Remember that I, the LA, and other free tutoring available are here to help you succeed; so do not be shy or afraid to ask questions about a notion that you do not understand; it is absolutely normal not to be able to catch every apple as it falls from the tree, but be sure to pick up those that have escaped your grasp. It is my responsibility to make sure that your questions and concerns are swiftly addressed to your satisfaction. Avoid being a passive learner; I expect you to be active in and outside the classroom by regularly coming to class well prepared, by doing the homework as we move along the sections, and by asking questions on concepts or homework problems that you find hard. To facilitate your progress with problem solving, it would be better to note down the homework problems that you could not solve as well as the reason why (maybe you did it and your answer was not the same as that of the solution manual, or you started and could not complete, or you did it differently than the solution manual and want to ckeck whether your approach is correct, or you could not even start); that would be very helpful when you raise questions about them. You will acquire the necessary skills needed to successfully complete this course by a semester long commitment to do the homework daily. I will do my best to help you, and I expect you to do your best. Do not wait until the eve of a test to try to catch up on every thing; it would be too late. After a test has been graded, be sure to discuss your mistakes with me or the LA so that you do not make the same mistakes in subsequent tests. "Never do tomorrow what you can do today. Proscratination is the thief of time''. Commitment+Effort=Success. Always do your best.

Evaluation:
- 14 homework assignments (graded homework assigned every Wednesday and due every Friday in class; no late homework will be collected.)
- Four in-class tests ( W Jan 31; W Feb 28; W March 28; W April 18)
- Cumulative Final exam (Wednesday April 25, 2018, 9:45-11:45AM, same room.)

The assigned homeworks will amount to 5% of your course grade. They are there to check whether you are doing the homework problems listed above; you won't be ready for the tests if you only do the assigned homeworks. The four in-class tests will make up 60% of the course grade. The final exam is cumulative, and will be worth 35%. Each test will last one hour. Once you start an exam, you cannot leave the room until you're done. You will be required to produce a photo ID before taking any of the tests, and before writing the final exam. Arrange to be in the room about ten minutes before class starts; that would give you the time to cool down before starting the test. For students who took the three tests, we will also use the alternate grading scheme: Term work 50%, and final exam 50%, whichever produces the highest grade. No calculators, or ipods, or pagers or cellphones are allowed during the exams or class time; you are not allowed to use or check these devices during the exam or class time, they must be off. If you're caught with your phone during an exam, it will be considered an act of cheating, and you'll get a zero on that exam. There will be no make-up for missed exams. If you miss an exam and you produce a doctor certificate indicating that you were sick and unable to write the exam, then the corresponding grade will be added to the final exam grade, otherwise, a zero will be recorded for any missed exam.

Grading Scale:

00-39    F                      40-59    D       60-64   C
65-69   C+                    70-74    B-      75-79   B
80-84   B+                    85-89   A-      90-100 A

Academic Misconduct: FIU is a community dedicated to generating and imparting knowledge through excellent teaching and research, the rigorous and respectful exchange of ideas, and community service. All students should respect the right of others to have an equitable opportunity to learn and honestly demonstrate the quality of their learning. Therefore, all students are expected to adhere to a standard of academic conduct, which demonstrates respect for themselves, their fellow students, and the educational mission of the University. All students are deemed by the University to understand that if they are found responsible for academic misconduct, they will be subject to the Academic Misconduct procedures and sanctions, as outlined in the Student Handbook.

Incomplete grades:
It is extremely difficult to qualify for an incomplete grade. An incomplete grade is not a substitute for a failing grade. In order to be considered for an incomplete grade, the student must have completed at least seven-eighths (7/8) of the course and must be passing with a grade of C or better.

Important Dates:
March 19 is the last date to drop the course with a DR grade. It is of a great importance that you accurately assess your course performance prior to this date. The university is closed on Monday January 15 for MLK Day.
Spring Break: March 12-17, 2018.

Instructor: Dr. Tebou E-mail: teboul@fiu.edu	Tel: (305) 348-2939	Office hours: MF: 12:00-1:00 W: 1:00-2:00 Just drop by my office for hep, no appointment is needed.
Lectures: MF 11:00-11:50 in SASC 251 W 11:00-12:50 in SASC 251 Website:faculty.fiu.edu/~teboul/mac2313-sp18.html	Office: DM 427	Other times: by appointment only. (If you cannot make the office hours, you can talk to me, e-mail or call me for another arrangement.)

11. I expect you to be able to: plot points in rectangular coordinates, recognize point coordinates on a box, recognize the equation of a sphere, and solve basic problems involving spheres, solve basic problems involving vectors, find the area of a parallelogram, the volume of a parallelepiped, solve basic problems involving planes and lines, recognize quadric surfaces through their equations, be able to draw rough sketch of quadric surfaces, solve basic problems involving cylindrical or spherical coordinates.	12. I expect you to be able to find the domain, and solve basic limits, continuity and integration problems for vector-valued functions, find the arc length parameter, unit normal , tangent and binormal vectors on parametric curves, find the curvature of a curve, solve basic problems for motion along a curve.	13. I expect you to be able to describe in words and sketch the domain of a function of two or three variables, solve basic problems involving level curves and level surfaces, solve basic problems involving limits and continuity for functions with several variables, find partial derivatives, show that a function of two/three variables is differentiable at a point, find partial derivatives using the chain rule or implicit partial differentiation, find gradients and directional derivatives, find tangent planes and normal lines, solve basic optimization problems using the second partials test or Lagrange multipliers.
14. I expect you to be able to evaluate simple double and triple integrals on rectangular regions or with given integration limits, find the area of a described plane region or the volume of a described 3-dimensional region, to solve basic integration problems involving polar, cylindrical or spherical coordinates, solve basic integration problems involving a change of variables.	Blank space.	15. I expect you to be able to solve basic problems about vector fields, evaluate line integrals involving piecewise smooth curves, know the fundamental theorem of line integrals, show that a vector field is conservative and find corresponding potential functions, know Green's theorem, find surface areas and surface integrals, find the flux of a vector field across a given surface by using a surface integral or the divergence theorem, solve basic problems involving the Stokes' theorem.