Syllabus & Homework
On this page you will find a short syllabus for Math 13 indicating
the topics and sections of the text we will cover. There is also
information concerning the exams, including lists of review problems
and other updates. You should check this page frequently to obtain
your homework assignments.
Note on Homework
The information on this page with the exception of homework
assignments is for both sections of Math 13. However, the
homework assignments for Math 13 are not the same for both
sections.
The homework listed on this page is for Prof. Guentner's section
only. If you are in Prof. McAllister's section you should consult
another web page for your
homework
assignments.
Course Syllabus
The topic of the course is Multivariable Calculus. As the name
suggests we will spend our time developing the differential and
integral calculus in two and three dimensions. Thus, we will be
setting up a theory analogous to the single variable theory you
learned in Math 11.
What this means is that we will be covering most of Chapters 11-14 of
the textbook. We will try to maintain a rate of approximately one
section per class period, but will slow down somewhat and use x-hours
if this proves to be too ambitious.
We will begin in Chapter 11, where the fundamentals of geometry in two
and three dimensions are covered. We will introduce the dot and cross
products, two tools that we will be using again and again throughout
the course. In this chapter we will cover Sections 11.1-11.5.
Chapter 12 covers the differential calculus, and Chapter 13 the
integral calculus. We will cover the entirety of these chapters, with
the exception of Sections 12.8 and 13.5.
Chapter 14 is really the heart of the course. In this chapter we
discuss vector fields, and the deep generalizations of the Fundamental
Theorem of Calculus you learned in Math 11. In fact, a number of
topics in the previous chapters were omitted to save time for a
detailed treatment of the theorems of Green and Stokes, and the
Divergence Theorem. I hope we will cover the entirety of this
chapter, although if we run short of time we may have to omit Section
14.9.
Chapter 11: Vectors and Analytic Geometry
- Lecture 0 on 1/5, Introduction & Sections 11.1-11.2
- Lecture 1 on 1/7, Sections 11.3-11.4: Dot and Cross Products
Chapter 12: Differential Calculus
- Lecture 2 on 1/9, Section 11.5: Lines and Planes
- Lecture 3 on 1/12, Section 12.1: Functions of Two and Three Variables
- Lecture 4 on 1/14, Section 12.2: Limits and Continuity
- Lecture 5 on 1/16, Section 12.3: Partial Derivatives
- Lecture 6 on 1/20 (x-hour), Section 12.4: Tangent Planes
- Lecture 7 on 1/21, Section 12.5: The Chain Rule
- Lecture 8 on 1/23, Section 12.6: Directional Derivative and the Gradient
- Lecture 9 on 1/26, Section 12.7: Maximum-Minimum Problems
- Homework 9 due 1/30: click here
Corrected Version (1/26): Note new due date
First Exam
The first exam is on Tuesday, 27 January from 6:00-8:00 pm in Filene
Auditorium. There are no calculators allowed on the exam, which
is worth 125 points and 25% of your final grade. It covers the
material above, that is, Chapters 11 and 12 of the text.
The exam is not completely written yet, but the format will be
approximately as follows. Note that this may change without
notice.
- There will be 10 problems in total on the exam.
- You must write out complete solutions for 8 of the problems.
I like to call these free response problems, meaning that it's
up to you to show what you can do.
- Two of the problems are multiple part true-fals2 problems. These
will be graded on a no partial credit basis.
There are two recommended ways to prepare for the exam.
- Work the practice exam, which you will receive in class on
Monday, Jan 26.
- Work the practice problems from the
book.
Corrected Version (1/26)
When preparing keep in mind that the best way to remember the material
is to understand it. Being able to work the problems is only part of
this; another part is being able to check your work without consulting
the back of the book. In most of the practice problems, you should be
able to decide if your answer is reasonable or not. Ask yourself
questions such as: Is it a scalar when vector is called for? Does
this normal vector seem to point the right way? Is this point really
in the plane? Should the speed be negative?
- Lecture 10 on 1/28, Discussion of the Exam
Chapter 13: Integral Calculus
- Lecture 11 on 1/30, Sections 13.1 & 13.2: Double Integrals
- Lecture 12 on 2/2, Section 13.3: More Double Integrals
- Lecture 13 on 2/4, 13.4: Polar Coordinates
- Lecture 14 on 2/6, 13.6: Surface Area
- Lecture 15 on 2/9, 13.7: Triple Integrals
- Lecture 16 on 2/10 (x-hour), 13.7 & 13.8: More Triple Integrals
- Lecture 17 on 2/11, 13.9: Change of Variables
- Homework 17 due 2/17 (6:00 pm): click here
New due date
- Lecture 18 on 2/16, 13.9: Change of Variables & Review
Second Exam
The second exam is on Tuesday, 17 February from 6:00-8:00 pm in Filene
Auditorium. There are no calculators allowed on the exam, which
is worth 125 points and 25% of your final grade. It covers the
material covered since the first exam, that is, Chapters 13 of the text.
The exam is not completely written yet, but the format will be
approximately as follows. Note that this may change without
notice.
- There will be 10 problems in total on the exam.
- You must write out complete solutions for 8 of the problems.
I like to call these free response problems, meaning that it's
up to you to show what you can do.
- Two of the problems are multiple part true-false problems. These
will be graded on a no partial credit basis.
There are two recommended ways to prepare for the exam.
- Work the practice exam, which you received in class on
Wednesday, 11 Feb.
- Work the practice problems from the
book.
When preparing for the exam keep in mind that the best way to remember
the material is to understand it. Being able to work the problems is
only part of this; another part is being able to check your work
without consulting the back of the book. In most of the problems, you
should be able to decide if your answer is reasonable or not.
Chapter 14: Vector Calculus
- Lecture 19 on 2/18, 14.1 : Vector Fields & 14.2 : Curves
- Lecture 20 on 2/20, 14.2 : Line Integrals
- Lecture 21 on 2/23, 14.3 : Fundamental Theorem of Line Integrals
- Lecture 22 on 2/25, 14.5 : Curl and Divergence
- Lecture 23 on 2/27, 14.4 : Green's Theorem
- Lecture 24 on 3/2, 14.6 & 14.7 : Parametric Surfaces and Surface Integrals
- Lecture 25 on 3/4, 14.7 : Surface Integrals and 14.8 Stokes' Theorem
- Lecture 26 on 3/6, 14.8 & 14.9 : Stokes' Theorem and the
Divergence Theorem
- Lecture 27 on 3/9 : Last Day of Class
Final Exam
The second exam is on Saturday, 14 March from 12:00 to 2:00 in the
afternoon in 13 Carpenter. There are no calculators allowed on the
exam, which is worth 175 points and 35% of your final grade. It
covers the material covered during the entire term, that is, Chapters
11-14 of the text. It is, however, weighted toward the material we
covered since the second exam, that is, Chapter 14 of the text.
The exam is not completely written yet, but the format will be
approximately as follows. Note that this may change without
notice.
- There will be 10 problems in total on the exam.
- There are 10 free response problems.
- There are no short answer problems.
There are recommended methods of preparing for the exam:
- Work the practice exam, which you received together with answers
in class last Friday.
- Work the suggested practice problems
from the book.
- Attend one of the review sessions:
- Professor McAllister's review is on Thursday, from noon to
2:00 in the afternoon in 102 Bradley.
- My review is on Friday, from 4:00 to 6:00 in the afternoon
in 102 Bradley.