LSU College of Science

Math 2057 Information

Math 2057 - Section 1 - For Spring 2019

Time 1:30--2:20 PM, MWF.
Location Room B16 Lockett Hall (in the basement)
Calendar Our class meets from Wednesday, January 9, 2019 through Friday, April 28, 2019. The Final Exam will be Saturday, May 4, 10 AM -- Noon..
Leonard Richardson Office 386 Lockett
Office Hours MWF 12:30 -- 1:30 PM and TTh 1:30--2:30 PM. I am available at many other times. Call or email first to make sure I'm able meet with you. I answer email many times daily---usually quickly.
Telephone 578--1568
Graduate Assistant Ms. Miao Zhang will grade the homework quizzes and she will assist me in grading the examinations. She will be available to answer questions in her office, Room 280 Lockett Hall, from 1:30-2:30 pm on Tuesdays. Please be sure to write your quiz and test solutions legibly so that we can read them.
Textbook Calculus: Early Transcendentals, 8th edition, by James Stewart. Please make sure you have the correct version (Early Transcendentals) and the correct edition (8) of this text since assignments will be from this book We will not be using WebAssign for homework in this class. However, if you already have access to the WebAssign e-book and wish to use it, you may register on WebAssign using this code: (8th Edition, Early Transcendentals) lsu 4658 2503. On the other hand, if you do not yet have the text, the department has negotiated some special deals for you that are available only at the following link: at which you will have 3 options from which to choose.
Free Math tutoring: Your first resource should be to see me. I am here to help each and every one of you. There are also other resources:
The Shell Tutorial Center will open its doors on TBA, in ROOM 141, Middleton Library. HOURS of Operation: M-Th, 9:30 AM to 7:00 PM. Friday, 9:30 - 3:00 pm. FOR More information on tutoring in all subjects go to: CAS also offers many on-line student resources such as study tips, time management, etc. CAS is located in B-31 Coates Hall.
CAUTION: There have been reports of unauthorized persons advertising tutoring services on campus and even in classrooms by circulating sign-up sheets. Be careful! The University does not authorize or recommend such services.
Prerequisites MATH 1552 or 1553. The student is assumed to be capable and versed in the standard Calculus I and II topics, limits, continuity, derivatives and their applications, definite integral, integration techniques and applications of integration.

Course Description

This course is a three (3) hour third semester calculus course designed for math, science and engineering majors and certain other technical majors. We will study functions of several variables, their partial and directional derivatives with applications, multiple integrals with applications and in spherical and cylindrical coordinates, vector fields including gradient fields and curl and divergence, line integrals, Green's theorem, the Divergence theorem, and Stokes' theorem concerning integration of vector fields. There will be many applications.

Attendance is required and will be counted in your final grade.

Every student's presence and participation in class is an essential part of this course. Most LSU students are conscientious and sensible about coming to class unless there is a serious, excusable reason for not being able to do so. However, there is an unfortunate tendency for some students to become discouraged as the term progresses and to cease regular attendance. This happens despite the fact that a student who is feeling discouraged has an especially great need to be in class and to ask questions. The attendance policy is intended to ensure that every student comes to class even when the going gets tough.

Attendance will be taken and recorded daily and unexcused absences will reduce your final average as follows. If UA is the number of your unexcused absences, UA/4 will be subtracted from your final average. If you need to be absent you must tell me why so that I can determine whether or not such an absence is excused. Depending on circumstances I may require documentation for your absences and documentation will always be required if you are absent from a quiz, an hour test, or the Final Examination.

Organization of this Class

Please understand that it is from the effort of working your way through assigned problems on paper that you learn mathematics. It is by no means sufficient to read solutions in a solutions manual! Although I hope you benefit from seeing solutions presented in class, you must not expect to learn how to solve problems just from watching. You must work out problems yourself, the hard way, in order to learn this work. Examination problems will be very similar to assigned homework problems. Thus your daily effort on homework problems will be strongly reflected in your test grades. It is very important that you maintain a notebook with all your homework problems worked out fully by yourself. If you email me about a pending assignment, I may send a hint to the whole class in answer to your question, not giving your name of course!
It is very important to come to class every day from the first class of the semester to the last day, and to do all the assignments on time to the best of your ability. Lax attendance or laxity in doing the homework are two of the earliest warning signs of academic failure. Please arrive on time for class. However, anyone may need to be late on some days for reasons beyond your control---such as transportation breakdown or a preceding class running overtime. If you need to be late, please do not wait outside in the hall. Please come in right away, late or not, and take a seat. You should not miss any more class time than necessary and no apology is needed for being late. Just come in right away --taking care to minimize noise-- and be sure to sign the attendance sheet after class if you have not done so already.

When class begins, be sure to put away all cell phones, smart phones, head phones, wrist watch communication devices, tablets, laptops, etc. You are not an internet-connected android. You are a human being and I need your real-time living engagement with the work in class.

When should you ask questions?

You should ask questions every time you do not understand something and also every time you are curious about something. Ask questions in class. If I am looking the other way and you have a question--PLEASE call out to me so I can have the opportunity to answer your question! Ask questions after class. Ask questions in my office. Ask questions by email. Please consider this: If you are approximately 20 years old, then I have been teaching this subject for approximately 2 and 1/2 times as long as you have lived thus far. So I ask you to consider that I just may be able to help you with whatever is causing you difficulty if you will permit me to do so. Please give me a chance to help you to the best of my knowledge and ability.

Tests and Homework Quizzes

There will be 3 in-class closed-book hour tests (100 points each) and a two hour final examination (200 points). To ensure that everyone works on every homework problem assigned, there will be homework quizzes. These weekly quizzes will consist of one recent homework problem, with some of the numbers changed so that the answer will be changed accordingly, and each quiz will count for 10 points. Collectively, the homework quizzes will be counted as a fourth hour test worth 100 points. No cell phones, computers, or internet or any other communication devices are allowed during quizzes, hour tests, and the final exam. You must keep your eyes on your own paper and do your own work. Do not communicate with your classmates during an examination. No books or notes are permitted, electronic, paper, or on any other medium. No electronic devices are permitted on tests other than a scientific calculator (with no symbolic calculations or graphing capability) and a watch to check the time. The problems will be similar to those in the homework. There will be no short-answer questions. All tests will be graded by me with the assistance of the course TA, and there will be partial credit, since the work is at least as important as the answer.


If you miss a test, it is your responsibility to speak to me as soon as possible to determine whether or not your excuse is acceptable. Here is some General Guidance regarding appropriate reasons for absence from a test or examination. If you are in doubt, ask me as soon as possible. However, please note that leaving early for a holiday, making plane reservations to leave early while classes or examinations are scheduled by the University, or planning to attend a social event during University scheduled class times is not a legitimate excuse for missing a test or a quiz.

Lateness Policy

It is important to arrive on time. However, there are occasions when a student must be late for reasons beyond his or her control. If you arrive late, please just come right into the room as quietly as possible and take a seat. Please do not stand outside in the hall --- just come right in. Every student should have the benefit of as much class time as possible.

Classroom Conduct!

There are approximately 78 students registered for this class, but the classroom seats 195! If you sit in the back, you will not be able to hear me clearly and you will not be able to read the board adequately. For your own good please be sure to sit ONLY in the front half of the room.
There are rules of common courtesy to bear in mind. If you have a question, ask it to me. Class time is not for conversation with your neighbor. In a large class, once individual conversations get started the din makes it impossible for other students to hear the day's lesson. So please do not forget: As a courtesy to your fellow students, questions during class time must be addressed to me. Conversations with your classmates are for before class starts or after class ends.


There will be three in-class hour tests, worth 100 points each. The homework quizzes will count as a fourth 100 point hour test. One half your final exam grade (which has a 200 point maximum score) will replace your lowest hour test grade if there is an hour test grade lower than one half your final exam grade. But beware: The final exam will be comprehensive so please do your best to prepare for each hour test! Our TA and I will grade your hour tests and return them to you as soon as possible, usually the very next class meeting. Your Test Average (TA) will be the sum of all your test grades and the final exam grade plus your homework quiz average on a 100 point scale, divided by 6 since the maximum possible number of points will be 600. Your Final Average will be FA=TA - UA/4, where UA is the number of unexcused absences. The minimum Final Average (FA) for each letter grade is as follows:
A+, 97
A, 93
A-, 90
B, 83
B-, 80
C+, 77
C, 73
C-, 70
D+, 67
D, 63
D-, 60
F, below 60
You should save all your graded work for future study and in case you think your final grade is in error.

Unhappy with your grades in Math?

Click here for a Plan to improve your grades!


It is especially important not to fall behind. It is very important to attend class and to ask questions. Please do not assume you can take care of difficulties later---see me for help as soon as possible if there is something you do not understand! You are responsible for all assigned problems---not just those which we go over in class!

It is not possible to anticipate each student's difficulties so you need to bring them to my attention.

Calculators, Collaboration, and Computer Support

You can use any technology available to help with homework, and you may collaborate with others while doing homework, provided that you maintain a notebook with your own handwritten solutions of each homework problem. However, on in-class exams you may only use a scientific calculator that does not do graphing or symbolic manipulation, such as solving equations and symbolically calculating derivatives and integrals. Also, work on in-class exams must be your own work with no assistance from anyone else. During an exam, attempts to look at other students' exams and the use of crib sheets or formula sheets will be considered to be a violation of the LSU Code of Student Conduct and will be reported to the Student Advocacy and Accountability Office.

The full power of Mathematica is available on many LSU computers, including those in the Math Department's computer labs and in the Library as well. Students can access Mathematica on Tigerware through their MYLSU accounts.
There is a simplified Web Mathematica which is free to use online if you click on the link in this sentence. If you have not already had the Math Department's course in Mathematica, you might find it simpler to figure out how to use the Web Mathematica. However, it is not as versatile as the full version. But do remember, this is an auxiliary resource. The time you spend working on problems on paper is the most important part of homework when it comes to learning the subject. With that understanding, Mathematica can be fun and helpful too.

Homework Assignments and Downloads

The assignments in the table below will be revised daily for the current semester. When you see a valid due-date supplied in the left-hand column, then you will know the assignment is current for this semester. A star (*) next to a problem indicates that it is more challenging than the others. Be sure to reload this page from the website each time you visit, since it is updated daily!
January 9 Read this syllabus so you can ask questions about it in class. Bookmark this page and be sure to get the latest daily version each time you access it to find assignments. Obtain a copy of the correct text book so you will be ready for work from the very first day. Not having the text on time is not a valid excuse from doing the homework and being ready for and taking the homework quizzes.
January 11 14.1 / 9, 11, 13, 15, 17, 19, 21, 23, 25, 29, 45, 47, 49, 51, 67, 69. These exercises focus on ways of picturing functions of several variables. Please download an illustration of the completion of the Example of Level Surfaces that we did not complete in class January 9.
January 14 14.2 / 5, 7, 9, 11, 13, 17, 19, 21, 29, 31, 33, 39, 41. Please download an illustration of how a limit can fail to exist if one approaches a point along a parabolic path as discussed in class Friday.
January 18 14.3 / 15, 17, 19, 21, 27, 29, 33, 39, 41, 47, 49, 51, 57, 61.
January 23 14.4 / 1, 3, 4, 5, 6.
January 25 14.4 / 11, 13, 15, 17, 19, 25, 27, 29, 33, 35. Also, please download an example of a non-differentiable function. Although the download refers to a different text, it is helpful also in connection with the current text. Homework Quiz today!
January 28 14.5 / 7, 9, 11, 13, 15, 17, 19, 21, 23.
January 30 14.5 / 27, 29, 31, 33, 49, 58.
February 1 14.6 / 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 29. Friday homework quiz today.
February 4 14.6 / 41, 43, 45, 49, 55.
February 6 -- 8 Continue study of 14.7 / 1, 5, 7, 9, 11, 13, 15, 17. Note: Problem 17 may be hard to complete. Can you find a way to reach the author's conclusion in the answer section? Download 14.7/17: an example of failure of the second derivative test. Also, please download an example of a saddle point and also an example of the second derivative test from class. Homework Quiz February 8 will go only as far as the exercises listed above for 14.7.
February 11 14.7 / 31, 33, 35, 37, 41, 43, 45, 47, 49, 51, 53. Also, please download the example of a minimum with an with unbounded domain.
February 13 Bring questions to review for the first hour test.
February 15 First Hour Test: covering sections 14.1 -- 14.7.
February 19 Download Spring 2019 Solutions and Statistical Results for Test #1. You will find the solutions and class statistics at the end of the pdf document. Work out on paper the solutions to test problems you think you missed, following the sketches online at the link listed above. Ask questions in class.
February 20--22 14.8 / 3, 5, 7, 9, 11, 15, 17, 21, 23, 31, 35, 39. Quiz Friday on Sec. 14.8. Download picture for Exercise 14.8 #11: the Boxy Ball.
February 27 15.1 / 9 -- 33 (odd), 39, 47, 49.
March 1 -- March 6 15.2 / 1 -- 9 (odd), 15, 17, 21, 23. 27, 29, 31, 45, 47, 49, 51, 53, 55. Download picture for Exercise 15.2 #29. Friday quiz, as usual.
March 8 15.3 / 1 -- 25 (odd), 29. Friday quiz, as usual.
March 11 15.4 / 1 -- 15 (odd).
March 13 15.5 / 1, 3, 5, 7, 9, 11(Number 11 is harder!).
March 15 15.6 / 3 -- 21 (odd), 27, 35. Friday quiz as usual.
March 18 15.7 / 1--11 (odd), 17, 19, 21, 23, 25, 27, 29.
March 21 No office hours this Thursday, March 21. Sorry.
March 22 15.8 / 1 -- 29 (odd), 35, 41, 43. Also: Bring questions to review for the second hour test, covering 14.8 -- 15.8 inclusive. No quiz this Friday because of Monday hour test.
March 25 Second Hour Test
March 29 Please download Solutions and Statistical Results for Test #2, Spring 2019. Solutions and overall class statistics appear at the end.
March 29 16.1 / 5, 7, 9, 21, 22, 23, 24, 33, 35.
April 1 16.2 / 1 -- 15 (odd); 19, 21, 33, 39, 45.
April 3 16.3 / 3 -- 23 (odd), 29.
April 5 16.4 / 1 -- 13 (odd), 17, 19. No quiz today: we need the time to focus on the new work.
April 8 16.5 / 1 -- 7 (odd), 12, 13 -- 21 (odd).
April 10 16.7 / 23, 25, 27, 29. Use the methods learned in class today. If a surface S encloses a region of space, choose the outward normal to calculate the flux of the vector field F across S.
April 12 16.8 / 1, 3, 5, 7, 9. (If asked to use Stokes' theorem to find one side of the equation of Stokes' theorem, this instruction means that it will be easier to evaluate the other side of the Stokes' equation instead.) Bring questions to review for the hour test! No quiz this Friday. > Please download The Moebius Strip - a non-orientable surface!
April 22 Third Hour Test.
April 23 Please download Solutions and Statistical Results for Test #3, Spring 2019. Solutions and overall class statistics appear at the end.
April 26 16.9 / 3, 5, 7, 9, 11, 13.
Remember that the instruction "Use the Divergence theorem to calculate the flux across the closed surface S in the outward direction" MEANS calculate the integral of the divergence of F over the enclosed volume with respect to volume.
Begin reviewing for the Final Exam. It is important to review ALL the homework problems assigned in this course. The final exam will be divided evenly over the whole course. Bring questions.
April Final Exam Week Office Hours:
Mon: 1--2:30
Tues: 3--4:30
Wed: 12--2
Thurs: 1:30--3
Fri: 1:30--3
in Room 386 Lockett Hall. For other times, call or email first.
Study for the Final Exam! This 200-point exam will cover the whole course in a uniform manner, so remember to review from the beginning of the course. Your final grade for the course will be the larger of the following two:
1. The grade guaranteed by the formula provided higher on this page.
2. One letter below the final exam grade.
Thus the final exam provides a safety net that supplements the calculations specified above.
Saturday, May 4 Final Exam, Saturday, May 4, 10 AM -- Noon, in our normal classroom.
May 6 Download 2019 Solutions and Statistical Results for Final Exam and Final Grades