Multivariable Calculus

In this course, we build on previously defined notions of the integral of a single-variable function over an interval. Now, we will extend our understanding of integrals to work with functions of more than one variable. First, we will learn how to integrate a real-valued multivariable function over different [...]

This course is an applications-oriented, investigative approach to the study of the mathematical topics needed for further coursework in single and multivariable calculus. The unifying theme is the study of functions, including polynomial, rational, exponential, logarithmic, and trigonometric functions. An emphasis is placed on using these functions to model [...]

As rates of change, derivatives give us information about the shape of a graph. In this course, we will apply the derivative to find linear approximations for single-variable and multi-variable functions. This gives us a straightforward way to estimate functions that may be complicated or difficult to evaluate. We [...]

This course offers a brief introduction to the multivariate calculus required to build many common machine learning techniques. We start at the very beginning with a refresher on the “rise over run” formulation of a slope, before converting this to the formal definition of the gradient of a function. [...]

Vector Calculus for Engineers covers both basic theory and applications. In the first week we learn about scalar and vector fields, in the second week about differentiating fields, in the third week about multidimensional integration and curvilinear coordinate systems. The fourth week covers line and surface integrals, [...]