Calculus for Science and Engineering III
MATH 223 -- Thomas Section
Section Summaries and Sample Problems to Work Before and In Class
Chapter 11 sections 1-6
Chapter 11 section 5: Notes on limits, continuity and differentiation for vector trajectories.
Chapter 11 sections 7-8
Chapter 12 all sections
Chapter 12: Notes on limits, continuity and differentiation for functions of several variables.
Chapter 13 all sections
Chapter 14 section 1
Chapter 14 sections 2-4
Schedule of Homework Assignments
Solutions to Sample Problems
Sample problem solutions for Chapter 11 section 1.
Sample problem solutions for Chapter 11 section 2.
Sample problem solutions for Chapter 11 section 3.
Sample problem solutions for Chapter 11 section 4.
Sample problem solutions for Chapter 11 section 5 (partial).
Sample problem solutions for Chapter 11 section 6.
Sample problem solutions for Chapter 11 section 7.
Sample problem solutions for Chapter 11 section 8.
Sample problem solutions for Chapter 12 sections 1-2.
Sample problem solutions for Chapter 12 section 3.
Sample problem solutions for Chapter 12 section 4.
Sample problem solutions for Chapter 12 section 5.
Sample problem solutions for Chapter 12 section 6.
Sample problem solutions for Chapter 12 section 7.
Sample problem solutions for Chapter 12 section 7 (alternate solutions).
Sample problem solutions for Chapter 12 section 8.
Sample problem solutions for Chapter 12 section 9.
Sample problem solutions for Chapter 13 sections 1-5.
Sample problem solutions for Chapter 13 sections 6-9.
Sample problem solutions for Chapter 14 section 1.
Sample problem solutions for Chapter 14 section 4.
Additional Review Problems
For the last class of the semester I prepared solutions to several problems including those
requested by students. During class, several students asked that I post the notes for these problems.
These are my own rough lecture notes, so they are somewhat abbreviated and are
not offered as "ideal" solution writeups. Nevertheless I hope they will be useful to you.
Here they are.
Welcome to Dr. Thomas' section of Math 223, Calculus for Science and
Engineering III, aka Multivariate Calculus! If you are majoring in
engineering, math, physics, chemistry, or biology, your hard work in
this subject will pay off in the rest of your major classes. That's a
good thing to keep in mind, because most students find this material
challenging the first time they work through it. To give you a leg up
on the challenge, I have developed a five-point plan:
- I will post reading assignments for you to complete
before each class period. Many students find their grasp of
the mathematics is strongest the third time they read through a section
of a particular textbook. I recommend that you make the first reading
happen before the class devoted to each section. The second reading should
come shortly after class. It's fine for your third reading to happen before
the corresponding midterm or final.
The reading for the first class, Monday 8/24, is section 11.1, Vectors
in the Plane.
- To help guide your reading I have written a short summary of the
key concepts in each chapter. These hand-written notes are no
substitute for reading the chapter itself (and I'm the first to admit
they're not always that legible -- they'll make more sense side-by-side
with the textbook). I will post these notes on the course web page in
advance of the reading, to assist you. Most of them also include
practice problems that you should look at with your study group.
- Study groups: I will assign each of you to a group of roughly four
students. You will work together with your group in class. And
hopefully out of class. The groups may be reorganized from time to
- I believe the best use of class time is not to have me read the
book back to you in the form of a traditional lecture. I assume (and
insist) that by now you are all able to read on your own. A better use
of class time is for me to explain what's in the book, and for
you to practice working together to solve problems (like those that are
likely to appear on your exams) with me coaching you. Since you will be
doing the assigned readings before coming to class, you can come
prepared with questions and we can spend class time discussing the
points in the text that are not clear to you, and practicing problems
together. If while reading you find some point of the text confusing,
you can e-mail me a question before class -- say by 9:00 p.m. the
evening before. In class I will sometimes choose a group to present
their solution to a randomly chosen problem from the study sheet. If we
get through all the topics and problems in a given day, we can all go
home early. (This has happened before, although not often.)
- Ultimately your best preparation for the course exams is to spend
time working out problems, both on your own and in your groups.
Therefore, I will assign short homework assignments (nearly) every class
period. They will be due back the next class period. There will
eventually be a course grader assigned, who will only be able to grade a
subset of the problems (usually just one) on each assignment. If you get
stuck on a particular problem and would like more extended comments from
the grader, you can write them a detailed note requesting feedback. I
will make available worked out solutions to all textbook problems
assigned, and also some of the non-textbook problems.
The course grade is based 100% on the exams. In the past I have tended
to give really hard exams (as measured by an unscientific sampling of
the admittedly subjective reports in past student course evaluations).
The best way to prepare for the exams is working problems, both in class
and out of class.
A Word about Proofs
Mathematics, as pursued by mathematicians, is built on proofs. Students with primary interests
in engineering or the sciences have often not been challenged to demonstrate why certain theorems
are true, but are just asked to use the results of the theorems to calculate the answers
to particular problems. In this class we will mostly follow the latter route, but not
entirely. Some problems set on homeworks and exams will say "explain why ..." or "demonstrate
that ...". Some students who have not previously encountered the notion of a proof
For more information, please contact Dr. Thomas.
Updated: August 20, 2009