Multivariable Calculus

MATH2202 course description: MATH2202 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 MATH2202 are expected to have a working knowledge of the techniques of single variable calculus, including differentiation, integration, sequences and series.

Fall 2015 course syllabus (includes textbook information).

Fall 2015 course notes: notebook1, notebook2, notebook3, notebook4.

Updated: January 21, 2019 — 10:50 pm