Instructor: Jon Simone

Email: jsimone@umass.edu

Class Meetings:
Section 01: MWF 9:05am-9:55pm in LGRT 202
Section 03: MWF 10:10am-11:00am in LGRT 202

Office: LGRT 1332

Office Hours: M: 12-1pm, W: 2-3pm, F: 11:30-12:30pm, and by appointment

Textbook: Vector Calculus (6th edition) by Marsden and Tromba


This course will explore differential, integral, and vector calculus in n-dimensional space. A strong understanding of single variable calculus, multivariable calculus, and linear algebra is expected. Please read this page for class policies.

Throughout the semester, I may cover topics and applications that are not in the textbook. Thus, it is important for you to regularly attend class.


Pre-Class Assignments:

To get the most out of class, you will often be assigned short pre-class assignments to prepare you for the upcoming class material. These assignments will either: (1) review pre-requisite concepts from calculus and linear algebra; (2) review material from a previous lecture; (3) or include short readings from the textbook. These assignments should be completed before coming to class. They are listed (and regularly updated) in the schedule at the bottom of the page.

You are to upload a picture or scanned copy of these assignments to our Moodle site before class. They will be checked for completeness. If you are unable to upload the assignment for some reason, you can hand in a hard copy of the assignment at the beginning of class. Assignments handed in after the beginning of class will not be accepted.

Since it is hard to predict exactly how much material we will cover on a given day, the pre-class assignments are subject to change. Be sure to check the schedule regularly to keep up to date. To be safe, I recommend not beginning to work on a pre-class assignment until 1pm of the day of the previous lecture.


Homework:

There will be written homework assignments (posted in the schedule below) due roughly every two weeks. These will be due at 4pm on the days listed in the schedule. Assignments are to be put in my mailbox in LGRT 1623D. Since I am teaching two sections of this class, be sure to put your assignment in the correct envelope labelled with your section (either 1 or 3).

These assignments will be graded on logical flow and clarity as well as mathematical correctness. That is to say, please write neatly and concisely. Using a pencil is alway a good idea. Late homework will not be accepted. The lowest homework grade will be dropped.

You may work on your own or collaborate with others on these assignments. If you choose to collaborate, be sure to write your solutions in your own words---solutions should not be simply copied from collaborators.

I will typically post homework at least a week in advance of the due date. It is a good idea to begin working on these assignments well before the due date. This will give you plenty of time think about the problems, collaborate, and come to office hours if you have questions.

I will post solutions to these assignments after the due date in the schedule below.


Exams:

There will be three in-class exams and a final exam. The dates and topics are as follows.

Exam 1: Friday, September 27
   Covers the differential calculus topics covered between 9/4 and 9/20.

Exam 2: Friday, October 18
   Covers the integration and parametrization topics between 9/23 and 10/11.

Exam 3: Friday, November 15th
   Covers topics between 10/15 and 11/8.

Final Exam: Check Spire for your section's final exam time and date.
   Covers vector calculus topics. More information.


Grading:

All of your grades will be posted on Moodle. The course grade is broken down as follows.

Pre-class assignments:5%
Homework:20%
Exam 1:15%
Exam 2:15%
Exam 3:15%
Final:30%


Disability Services Accommodations:

The University of Massachusetts Amherst is committed to making reasonable, effective and appropriate accommodations to meet the needs of students with disabilities and help create a barrier-free campus. If you have a disability and require accommodations, please register with Disability Services (161 Whitmore Administration building; phone 413-545- 0892) to have an accommodation letter sent to your faculty. Information on services and materials for registering are also available on their website.


Schedule (to be regularly updated and subject to change throughout the semester):

The pre-class assignment problems listed on the schedule can be found here. This problem list will be regularly updated throughout the semester.

Class Meeting Pre-class assignment Topic Other
9/4 Wed Real-valued and vector-valued functions, open sets
9/6 Fri Problems #1,2 Differentiability
9/9 Mon Review the notes from last class
Problems #3,4		 Differentiability continued
9/11 Wed Read the first definition at the beginning of Section 3.3
Problem #5		 Extreme values of real-valued functions
9/13 Fri Review notes from last class
Problem #6		 Extreme values continued
9/16 Mon Problem #7 Critical points
9/18 Wed Read definitions in the "Global Maxima and Minima" section in Section 3.3 of the text
Problem #8		 Elementary Morse Theory
9/20 Fri Problem #9 Optimization Homework 1 Solutions
9/23 Mon Problem #10 Double and triple integrals
9/25 Wed Problem #11 Triple integrals continued
9/27 Fri EXAM 1 (Covers Lectures 9/4-9/20) Some suggested practice from the text:
Section 2.3 #9, 12
Chapter 2 Review Exercise #35
Section 3.3 #19, 21, 37, 41
Section 3.4 #3, 19, 23
Exam 1 Solutions
9/30 Mon Problems #12, 13 Change of coordinates
10/2 Wed Review notes from last lecture
Problem #14		 Change of coordinates continued
10/4 Fri Applications
10/7 Mon Problem #15 Parametrized Curves Homework 2 Solutions
10/9 Wed Problems #16 Arc length
10/11 Fri Problem #17 Curvature
10/15 Tue Problems #18, 19 Parametrized surfaces
10/16 Wed Problem #20 Surface Area
10/18 Fri EXAM 2 (Covers Lectures 9/23-10/11) Textbook Sections: 2.4, 4.2, 5.5, 6.1-6.3
See the suggested practice problems at the end of Homeworks 2 and 3
Exam 2 Solutions
10/21 Mon Problem #21 Curvature of surfaces
10/23 Wed Problem #22 Vector fields Homework 3 Solutions
10/25 Fri Problem #23 Divergence and Curl
10/28 Mon Problems #24, 25 Line integrals of scalar functions
10/30 Wed Problem #26 Line integrals of vector fields
11/1 Fri Problem #27 Work, The Fundamental Theorem of Line Integrals
11/4 Mon Problem #28 Surface integrals of scalar functions
11/6 Wed Problem #29 Surface integrals of vector fields, Orientation, and Flux
11/8 Fri Problem #30 Flux continued Homework 4 Solutions
11/13 Wed Problems #31, 32 Stokes' Theorem
11/15 Fri EXAM 3 (Covers Lectures 10/15-11/8) Textbook Sections: 4.3, 4.4, 7.1-7.6, 8.3
See the relevant practice problems at the end of Homeworks 3 and 4
Exam 3 Solutions
11/18 Mon Problem #33 Green's Theorem
11/20 Wed Problem #34 Gauss's Divergence Theorem
11/22 Fri Problem #35 Applications Homework 5 Solutions
11/25-11/29 THANKSGIVING BREAK
12/2 Mon Problem #36 Differential forms  Snow Day
12/4 Wed Problem #36 Differential forms, the wedge product
12/6 Fri Problem #37 Exterior derivative, closed forms, exact forms
12/9 Mon Problem #38 Integrating forms and Generalized Stokes' Theorem
12/11 Wed Problem #39 Generalized Stokes' Theorem continued Homework 6 Solutions
See Spire FINAL EXAM (Covers Vector Calculus Topics) Review Information
Review Session Notes
Notes courtesy of Sahil Magan