# 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

#### Chapter 11

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.

#### Chapter 12

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.

#### Chapter 13

Sample problem solutions for Chapter 13 sections 1-5.
Sample problem solutions for Chapter 13 sections 6-9.

#### Chapter 14

Sample problem solutions for Chapter 14 section 1.
Sample problem solutions for Chapter 14 section 4.

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 message

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:
1. 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.
2. 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.
3. 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 time.
4. 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.)
5. 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.