Course description: MT202 is an introduction to multivariable calculus, generally taken by mathematics and science students. The goal of the course is to extend topics from single variable calculus to multivariable settings.
In single variable calculus we study functions of the form y=f(x), where the independent variable (or input) x is a real number and the dependent variable (or output) y is a real number. In mutivariable calculus, either the independent variable or the dependent variable or both are lists of real numbers. For example, let x be the longitude, y be the latitude, and z be the height above sea level. Further, let t represent time (measured from a convenient initial time). Then we may be interested in studying a temperature function,
f(x,y,z,t), whose value is the temperature measured at location (x,y,z) and time t.
The temperature function above is an example of a scalar-valued function, since the output is a real number (or scalar). By contrast, the output of a vector-valued function is a list of real numbers (known as vectors). For example, we can represent wind speed and direction at a given position and time using a list of three real numbers, say (u,v,w), and study a vector-valued function of the form
f(x,y,z,t)=(u,v,w), whose value is the wind velocity vector at position (x,y,z) and time t.
Note that students in MT202 are expected to have a working knowledge of the techniques of single variable calculus, including differentiation, integration, sequences and series.
Fall 2008 course information: The required text for this course is Vector Calculus, Third Edition, Plus Student Solutions Manual by Oberlin College Professor Susan Jane Colley (Prentice Hall, 2006).
Students are encouraged to browse through other multivariable calculus books, including Multivariable Calculus by James Stewart (Brooks-Cole Publishing), and Multivariable Calculus by Brian Blank and Steven Krantz (Key College Publishing).
Course notes: notebook1, notebook2, notebook3, notebook4, notebook5.
Emails to all class members: email01, email02, email03,
Course syllabus (important information you need to know; posted 9/1/2008).