Math 276: Calculus III
Fall 2018
Section 01, CRN 915

Schedule: MWRF 10:00am-10:50pm
Location: Fitzelle Hall 204
Text: Calculus Early Transcendentals, by Stewart (8th edition).

Professor: Jonathan Brown
Office: Fitzelle Hall 260
Email: jonathan.brown@oneonta.edu
Phone: 436-3720
Office Hours: Wednesday 12:00-12:50, Thursday 11:00-11:50, Friday 12:00-12:50, or by appointment
Website: http://employees.oneonta.edu/brownjs/

Catalog Description:
Math 276 constitutes the last third of the standard 12-credit calculus sequence, 173-174-276. Topics include functions of two or more variable, partial derivatives, multiple integrals.

Prerequisite: Pass Math 174 with a C or better.

Course Goals and Objectives:
Math 276 provides an introduction to the functions of several variables using vector space calculus. The goals of the course are to understand the fundamentals of vector functions and their derivatives and integrals, directional derivatives, gradients, tangent planes, and the Chain Rule, multiple integrals, line and surface integrals with Green and Stoke's Theorem. Historical references will be made when appropriate.
To achieve these goals, students will:
1) use a problem-solving approach to investigate and understand the mathematical content;
2) demonstrate an understanding of the principles and techniques of applying mathematics to other disciplines and to real world problems;
3) understand and apply numerical, computational, and estimation techniques;
4) use mathematical modeling to solve problems from such fields as natural sciences, social sciences, business, and engineering;
5) use computer software to explore and solve mathematical problems;
6) understand the historical development of calculus and the contributions of Newton, Leibniz and others.

Course content: We will cover Chapters 12 - 16, and as much of Chapter 17 as we are able.

SUNY Learning Outcomes:
Students will show competence in the following quantitative reasoning skills: arithmetic, algebra, geometry, and data-analysis.

Grades:
Homework: 10%
Quizzes: 15%
3 in class exams: 15% each
Final: 30%

Your letter grade will be determined from the following heuristic:
A : 93 - 100
A-: 90 - 92.99
B+: 87 - 89.99
B : 83 - 86.99
B-: 80 - 82.99
C+: 77 - 79.99
C :73 - 76.99
C-: 70 - 72.99
D+: 67 - 69.99
D : 63 - 66.99
D-: 60 - 62.99
E : 0 - 59.99

Quizzes:
There will be a quiz during the last 10 minutes of class on most Fridays. I will drop your lowest quiz score.

Homework: Each week I will assign two types of homework in the course: practice problems from the text, and WeBWork problems.
WebWork: Your homework grade is completely determined by WebWork problems. Here is the link the WebWork website for this course: https://webwork.oneonta.edu/webwork2/276-01-f18/
Your login id for WeBWork is your oneonta.edu username with all lowercase letters, that is the part of your email address before the '@' sign.
Your initial password is your A number (with a capital A).
Book Problems: The practice problems will be from the text, and they will not be collected or graded. It is mandatory that you do these problems as we cover the corresponding sections in class. The list of practice problems can be found below. Note that the odd numbered problems have answers in the back of the book. I don't expect you to do all of the assigned problems, instead do problems from each subsection until you are completely confident that you can do the rest with little effort, accounting for the fact that the later problems are usually harder. It is essential that you do these problems in addition to the WeBWork problems. Learning, development, and growth require time and sustained effort. Most of the knowledge and skills you obtain from this course will come from the time you spend with these problems. Furthermore the quiz problems will often closely resemble (or even be copied from) the problems from the text.

Tentative Exam Schedule:
Exam 1: 9/27 (Thursday)
Exam 2: 10/26 (Friday)
Exam 3: 11/30 (Friday)

Final Exam:
The final exam will take place Monday December 17, 8:00am - 10:30am.
The final exam is cumulative.

Calculators:
While calculators may occasionally be useful while doing the homework, they are not allowed to be used during quizzes and exams (unless you have a note from Student Disability Services).

Attendance Policy:
Missing class is a very bad idea. Anyone who misses more than 25% of classes starting in week 2 may be removed from the course.

Getting Help
You are expected to spend anywhere between 6 and 12 hours per week outside of class on the material. The amount of time necessary to pass, or obtain the grade you expect, depends heavily from person to person. Typically, a student spending less than 6 hours per week outside the class should expect to earn a "C" or worse.

If you are struggling with the material, be aware that you have options:
(1) Struggle a bit. Part of the learning process is the internal struggle of trying to understand how all of the pieces fit together. It can be frustrating, but it can also be rewarding. If you make progress, however slow, then it is time well spent. If you feel that your time is not productive, then you should talk to me, or other students, about how you can make better use of your study time.
(2) Visit my office hours. It is part of my job to be available to help you understand the material. There is not enough time in the classroom to get everything across, and you are not expected to do it all on your own.
(3) Find alternate instructional material online. Different people have different styles, and while you might have found my way of discussing something to be confusing, there may be someone else out there who can discuss it in a away that makes sense to you. There are a number of free text books, lessons, and video lectures available online. Feel free to ask me about other sources.
(4) Visit the tutors in CADE. They have drop in tutoring for this course 3 nights a week.
(5) Talk to your fellow students who are taking or who have taken the class. Learning is a social activity; you are not expected to do it all on your own.
(6) If after availing yourself of the above options, you still find that you are struggling regularly to understand the material, find a regular tutor. If you are in this situation, you will likely have to spend significant extra time on the material to ensure a passing grade.

ADA (American with Disabilities Act):
Students Diagnosed with a Disability, all individuals who are diagnosed with a disability are protected under the Americans with Disabilities Act, and Section 504 of the Rehabilitation Act of 1973. As such, you may be entitled to certain accommodations within this class. If you are diagnosed with a disability, please make and appointment to meet with Student Disability Services, 209 Alumni Hall, ext. 2137. All students with the necessary supporting documentation will be provided appropriate accommodations as determined by the SDS Office.

Emergency Evacuation Procedures:
In the event of an emergency evacuation, classes meeting in this building are directed to reassemble in the IRC Lobby so that all persons can be accounted for. Complete details of the College's emergency evacuation, shelter-in-place, and other emergency procedures can be found at http://www.oneonta.edu/security/.

Tentative Schedule
Date Section Topic Suggested Textbook Problems for each Section
8/27 12.1 Three-dimensional coordinate systems #3, 5, 7, 11, 15, 21, 25, 31
8/29 12.2 Vectors #5, 7, 11, 17, 21, 25, 35
8/30 12.3 The dot product #1, 3, 5, 9, 11, 17, 23, 27, 29, 35, 41
8/31
9/5 		12.4 The cross product #3, 7, 11, 13, 17, 19, 29, 33, 35, 39
9/6
9/7 		12.5 Equations of lines and planes #1, 5, 9, 19, 21, 25, 29, 37, 41, 45, 51, 55, 57, 67, 73
9/10 12.6 Cylinders and quadric surfaces #1, 5, 7, 15, 21, 23, 25, 27, 33, 35, 43
9/12 13.1 Vector functions and space curves #1, 7, 19, 21, 25, 29, 41
9/13 13.2 Derivatives and integrals of vector functions #5, 13, 19, 25, 37, 41,47
9/14
2/6 		13.3 Equations of lines and planes #3, 5, 11, 13, 19, 23, 25, 29, 31, 39, 45, 47
9/17 13.4 Motion in space: velocity and acceleration #3, 7, 11, 13, 21, 25, 29, 39, 45
9/19 14.1 Functions of several variables #5, 7, 11, 17, 20, 25, 29, 32, 33, 35, 45, 47, 59, 61, 63, 67
9/20 14.2 Limits and continuity #5, 9, 13, 17, 19, 21, 25, 35
9/21
9/24 		14.3 Partial derivatives #5, 7, 9, 17, 21, 25, 33, 37, 47, 51, 55, 59, 65, 74, 95
9/26 14.4 Tangent planes and linear approximations #3, 5, 13, 21, 29, 39
9/27 Exam 1
10/1
10/3 		14.5 The chain rule #3, 5, 9, 11, 13, 17, 21, 25, 27, 31, 39
10/4 14.6 Directional derivatives and the gradient vector #1, 5, 7, 9, 13, 17, 23, 25, 38, 43
10/5
10/10 		14.7 Maximum and minimum values #3, 7, 11, 15, 19, 31, 33, 39, 45, 51
10/11 14.8 Lagrange multipliers #3, 5, 7, 9, 11, 15, 17, 19, 23
10/12 15.1 Double integrals over rectangles #1, 3, 5, 7
10/15 15.2 Iterated integrals #3-31 odd
10/17
10/18 		15.3 Double integrals over general regions #1-9, 15-31, 43-47 odd
10/19
10/22 		15.4 Double integrals in polar coordinates #1-31 odd
10/24 15.5 Applications of double integrals #3-15 odd
10/25
10/29 		15.6 Surface area #1-11
10/26 Exam 2
10/31
11/1 		15.7 Triple integrals #3-21 odd, 29
11/2
11/5 		15.8 Triple integrals in cylindrical coordinates #1-29 odd
11/7
11/8 		15.9 Triple integrals in spherical coordinates #1-29 odd
11/9 15.10 Change of variables in multiple integrals #3-33 odd
11/12 16.1 Vector fields #1-9 odd, 11-18, 21, 25, 29-32
11/14 16.2 Line integrals #1-21 odd
11/15 16.3 The Fundamental Theorem for Line Integrals #1-9 odd, 13-19 odd, 23, 25
11/26
11/28 		16.4 Green's Theorem #1-13 odd, 17
11/29 16.5 Curl and divergence #1-21 odd
11/30 Exam 3
12/3 16.6 Parametric surfaces and their areas #1-5, 13-25 odd, 35, 39-49
12/5 16.7 Surface integrals #1-31 odd
12/6 16.8 Stokes' Theorem #1-10, 13, 15
12/7 16.9 The Divergence Theorem #1-13
12/10 Review
12/17 Final Exam: 8:00-11:30