Basic course information
Time: MTWF 2:00–2:50 p.m.
Place: 105 Peterson Hall.
Textbook: Multivariable Calculus by James Stewart, 8th edition.
Office hours: TBD. Subject to change.
Final exam: Per the university Final Exam Schedule
Midterm exams:
October 23 and November 7. Subject to change if necessary.
There is also WebWork homework and a Canvas webpage for tracking grades and a blog about using computer software with the course.
Prerequisites
Math 253 (Calculus III).
Description and goals
This course studies limits, derivatives, and integrals of functions from R to R^n and limits and derivatives of functions from R^n to R, as well as the basic geometry of vectors in n-dimensional Euclidean space. The first two weeks are devoted to basic tools for working with n-dimensional space: coordinate systems, vectors, dot products, cross products (for 3-dimensional space), and equations describing lines, planes, and surfaces. The next two weeks are about functions from R to R^n. These arise when studying how a vector, or collection of numbers, changes over time. The vector might represent something geometrical, like the position of an object, or something abstract, like a list of stock values. The course provides a basic language for discussing these kinds of n-dimensional motion, with an emphasis on 3-dimensions, both because we can visualize 3-dimensions and because it remains the most important case for physical applications. The rest of the course focuses on functions from R^n to R, which represent a quantity depending on several other quantities. Again, there are both physical examples, like the altitude or temperature, and non-physical examples, like the value or risk in a portfolio. The main goal of this part of the course is optimization: understanding how to find maxima and minima of such functions.
Specific “learning outcomes” include:
- Understanding how to work with vectors in 3-space and n-space, including vector addition and scalar multiplication, the dot product, and, in 3-dimensions, the cross product.
- Being able to describe lines and planes in 3-space implicitly and parametricly.
- Understanding how and why to differentiate and integrate vector-valued functions.
- Being able to compute limits of functions of several variables, test when such functions are not continuous, and, in special cases, show functions are continuous.
- Compute partial derivatives and gradients of functions of several variables and interpret the answers.
- Solve optimization problems, including constrained optimization.
A course is more than its “learning outcomes”: the goal is understanding, not the ability to perform specific manipulations.
Policies
Grading
| Written homework | 15% |
| Online homework | 10% |
| Midterm 0 | 5% |
| Midterm 1 | 20% |
| Midterm 2 | 20% |
| Final | 30% |
Homework
The course will have both written and online homework. Written homework is due at the beginning of class on Mondays, except as noted. Online homework, via WebWorks, is due before class on Mondays, except as noted. (Due dates may change.) There will be written and online homework assignments due during “dead week”. Well-prepared students should expect to spend 8 to 12 hours per week (2 to 3 hours per hour of class) outside of class on homework and review.
You may use any resources you like on the homework, but all resources except the textbook must be cited on your assignment. This includes help from your classmates, friends, or Google. Failure to cite sources constitutes plagiarism, a serious form of academic dishonesty, and will be punished and reported.
You may work together on homework assignments, but you must write up the final version of your answers by yourself. Working on the final write-ups together constitutes cheating.
Late homeworks will not be accepted, but the lowest written homework score and lowest online homework score will be dropped. Due to limited resources, only part of the homework will be graded carefully.
The WebWork homework site, for online homework, will be listed here once it has been created. Written homework assignments are posted below.
A small number of bonus points -- a maximum of 10% of the score on each homework assignment -- will be awarded for following the tutorial on using SageMathCloud alongside the class.
Exams
All exams will be given in class, and there will typically not be makeup exams. If you know in advance that you will miss an exam, contact me immediately to make arrangements. If you miss an exam because of an emergency (medical, family, ...) you will be expected to provide documentation of that emergency.
All exams are closed-note, closed-book, and without electronic assistance (including calculators and cell phones). Using any notes or electronic device or communicating with anyone except me during an exam constitutes cheating.
Students with disabilities
I, and the University of Oregon in general, are committed to an inclusive learning environment. If you have a disability which may impact your performance on exams, please contact the Accessible Education Center to discuss appropriate accommodations. If there are other disability-related barriers to your participation in the course, please either discuss them with me directly or consult with the Accessible Education Center.
Written homework
Again, all written homework is due at the beginning of class on the due date.
- Homework 1 will be posted in a few weeks. Due October 2.
Schedule
This schedule is tentative, and may change during the quarter.
| Week | Date | Topic | Sections |
| 1 | 9/25 | Introduction to the class. 3-dimensional coordinate systems. | §12.1 |
| 9/26 | Vectors. | §12.2 | |
| 9/27 | Midterm 0. Dot product. | ||
| 9/29 | More on dot product, review. |
§12.3 | |
| 2 | 10/2 | Cross product. Homework 1 due. This is the last day to drop the class without a W. |
§12.4 |
| 10/3 | Equations for lines and planes. | §12.5 | |
| 10/4 | More on equations for lines and planes. | §12.5 | |
| 10/6 | Review. | ||
| 3 | 10/9 | Cylinders and quadric surfaces. Homework 2 due. | §12.6 |
| 10/10 | Vector-valued functions. | §13.1 | |
| 10/11 | Derivatives and integrals of vector-valued functions. | §13.2 | |
| 10/13 | Review. | ||
| 4 | 10/16 | Arc length, TNB frames, and curvature. Homework 3 due. | §13.3 |
| 10/17 | More on TNB frames and curvature. | §13.3 | |
| 10/18 | Velocity and acceleration, classical mechanics. | §13.4 | |
| 10/20 | Review. | ||
| 5 | 10/23 | Midterm 1. Homework 4 due. | |
| 10/24 | Functions of several variables: graphcs, traces. | §14.1 | |
| 10/25 | Limits and continuity. | §14.2 | |
| 10/27 | Review. | ||
| 6 | 10/30 | More limits and continuity. Homework 5 due. | §14.2 |
| 10/31 | Partial derivatives. | §14.3 | |
| 11/1 | Tangent planes and linear approximation. | §14.4 | |
| 11/3 | Review. | ||
| 7 | 11/6 | More review. Homework 6 due. | |
| 11/7 | Midterm 2 | ||
| 11/8 | Taylor and McLaurin series. | §11.10 | |
| 11/10 | Review The last day to withdraw from the class or change grading option is 11/12. |
||
| 8 | 11/13 | The chain rule. Homework 7 due. | §14.5 |
| 11/14 | Directional derivatives and the gradient. | §14.6 | |
| 11/15 | More on directional derivatives and the gradient. | §14.6 | |
| 11/17 | Review. | ||
| 9 | 11/20 | Maximization. Homework 8 due. | §14.7 |
| 11/21 | More maximization. | §14.7 | |
| 11/22 | Review. | ||
| 11/24 | Thanksgiving holiday (no class). | ||
| 10 | 11/27 | Lagrange multipliers. Homework 9 due. | §14.8 |
| 11/28 | More Lagrange multipliers. | §14.8 | |
| 11/29 | Review. | ||
| 12/1 | Review. (Last day of classes.) |
Handouts
Handouts will be posted here, in case you lost the physical copy.
- First Day Handout will be posted here eventually.
Advice
Reading mathematics. You are expected to read the sections in the textbook before coming to class. It's usually only a few pages, so read it carefully. Note down the questions you have; I would expect you to have at least one per page. Read the section again after class. See which questions you now understand. Think about the remaining questions off and on for a day. See which you now understand. Ask someone (e.g., me) about the questions you still have left.
Getting help. If you're having trouble, get help immediately. Everyone who works seriously on mathematics struggles, but if you don't get help promptly you will soon be completely lost. The first places to look for help are my office hours. The Teaching and Learning Center also facilitates individual and small-group tutoring.
Teaching to learn. The best way to learn mathematics is to explain it to someone. You'll find that, particularly in office hours, I'll try to get you to explain the ideas. You should also try explaining the material to each other. The person doing the explaining will generally learn more than the explainee. Another thing to try is writing explanations to yourself, in plain English or as close as you can manage, of what's going on in the course. File them somewhere, and then look back at them a few days later, to see if your understanding has changed.