COURSE DESCRIPTION
In this course we learn how to extend the ideas of calculus to two and three dimensions.
The concepts of 1-variable calculus arise in studying the motion of a particle along a line. For a particle moving through space, not just along a line, the position, velocity, and acceleration at each moment are described by vectors, not just by single real numbers. Many other physical quantities, such as force and angular velocity, are also modeled mathematically as vectors.
We begin by studying the algebra of vectors (linear algebra), which allows us to describe the relationships between vector quantities in physics and also forms the basis of analytic geometry in 3-dimensional space. Vector-valued functions of a single real variable (time) are used to represent, for example, the velocity of a moving particle and also to study the geometry of space curves. We learn how to generalize the concepts of derivative and integral to vector-valued functions.
A real-valued function of 2 variables can be used to model quantities such as the temperature on the surface of the earth, which varies from one location to another. The graph of such a function is a surface in space. At a point of such a graph, one has a tangent plane, not just a tangent line. We learn how to describe the tangent plane in terms of ideas of calculus, and learn how the concepts of derivative and integral generalize to functions of several variables.
In the last part of the course we learn the 2-dimensional version of the Fundamental Theorem of Calculus, Green's Theorem. This is the mathematics behind the physical notions of work and potential energy, and is a big step toward understanding electric and magnetic fields.
LABS
Math 210 includes a weekly computer lab that helps students to visualize and develop intuition about the concepts being taught in the course. The lab meets in 1200 SEO on either Tuesdays or Thursdays, depending on the lecture section. Both faculty and TAs are available to provide guidance and answer questions. Each lab unit is a one-week project, and each lab contains problems to be worked with the assistance of the computer; students will submit written lab reports at the end of each lab unit.
The lab is a required part of the course, a component of the course grading. It will meet every week, starting in the FIRST week of the course. Some of the later weeks of the term may be dedicated to "open lab" and review.
More information about the computer lab is avaliable at http://www.math.uic.edu/math210/labs.html.
HOMEWORK
Homework will consist of problems assigned from the textbook (see the link below) as well as (possibly) additional problems provided by your instructor. Each lecturer will announce that section's policy on collection and grading of homework.
You are encouraged to discuss homework problems with your fellow students. Working in groups makes the explanation of approaches and solutions a part of the process and helps you learn. Your goal is to find solutions and to communicate your work in a convincing manner.
Link to Homework Assignments for this semester.
GRADES
The course grade is based on the total number of points from hour exams, homework, quizzes, computer labs, and the final exam.
| Quizzes | 50 points total |
| Homework | 50 points total |
| Computer labs | 50 points total |
| Two Midterm Exams | 100 points each |
| Final Exam | 200 points |
TEXTBOOK
Multivariable Calculus (Early Transcendentals ) by Jon Rogawski, W. H. Freeman.NOTE: If you bought the "non-early-transcendentals" version of the text, either from the Bookstore, or from elsewhere (e.g. Amazon) then the add 1 to each chapter number (so, e.g., vectors are in Ch. 13)
You are expected to read the textbook before the classroom discussion of each topic, as indicated on the schedule of reading assignments
Students with Disabilities
Students with disabilities who require special accommodations for access and participation in this course must be registered with the Office of Disability Services (ODS).
Please contact ODS at 312/413-2183 (voice) or 312/413-0123 (TTY).