# MATH 210: Calculus III

### 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.

### TEXTBOOK

Calculus, Early Transcendentals, by W. Briggs and L. Cochran.

NOTE: This textbook has been used since Fall 2011. It is the same textbook used in Math 181. We will cover Chapters 11 through 14.

You are expected to read the textbook before the classroom discussion of each topic, as indicated on the schedule of reading assignments.

### LABS, QUIZZES

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 either Tuesdays or Thursdays, depending on the lecture section. 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.

Starting in the second week, you will take quizzes according to schedule on the Labs page. The quizzes will be based on the lectures and will be written by your instructor. Your instructor may also give additional quizzes during the lecture.

### 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.

The course grade is based on the total number of points from hour exams, homework, quizzes, computer labs, and the final exam.

 Quizzes/Homework 100 points total Computer labs 50 points total Two Midterm Exams 100 points each Final Exam 200 points

### PREREQUISITE

Grade of C or better in MATH 181. Please make sure that you have met the prerequisite. Students without the prerequisite will not be allowed to take the course. Please take a minute to do the survey about the ALEKS placement test: https://illinois.edu/sb/sec/2457922

### 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). Students who need exam accommodations must contact ODS in the first week of the term to arrange a meeting with a Disability Specialist.