This course is a study of the calculus of functions of several variables (vector arithmetic and vector calculus). License: Creative Commons BY-NC-SA More information at ocw.mit.edu/terms
Herb Gross introduces 3-dimensional vectors.
Herb Gross reviews the definition of vectors and vector arithmetic.
Herb Gross discusses Green's Theorem: the relationship between line integrals and double integrals over a region in 2-space.
Herb Gross illustrates the equivalence of the fundamental theorem of the calculus of one variable to the fundamental theorem of the calculus of several variables.
Herb Gross illustrates how the Jacobian arises when changing coordinates in order to calculate a double integral.
There is more than one type of integral in calculus of more than one variable. In this lesson, Herb Gross discusses line integrals.
Herb Gross teaches us how to calculate infinite double (multiple) sums (for topics in calculus of several variables). This topic is analogous to the use of infinite sums in calculus of a single variable.
Herb Gross illustrates how to invert a square matrix and its relevance to Calculus of several variables.
With our knowledge of Matrix Algebra to help, Herb Gross teaches how to find maxima and minima of functions of several real variables.
Herb Gross describes the mathematical structure of matrix algebra.
Herb Gross considers linearity in spaces of greater than 2 variables including a discussion of local linearity.
Herb Gross demonstrates how to invert systems of non-linear equations.
Herb Gross defines the Directional Derivative and demonstrates how to calculate it. Herb also emphasizes the importance of this topic in the study of Calculus of Several Variables
Herb Gross discusses Exact Differentials.
Herb Gross shows examples of the Chain Rule for several variables.
Herb Gross show how the Chain Rule is involved in finding some integrals involving parameters.
Herb Gross introduces us to the traditional Calculus of Several Variables
Herb Gross defines and demonstrates the use polar coordinates.
Herb Gross describes n-Dimensional Vector Spaces relating definitions to the concept of a mathematical structure.
Herb Gross discuss tangential and normal vectors to a point on a function in 2-space analagous to x-y coordinates.
Herb Gross describes Vectors and Polar Coordinates.
Herb Gross introduces the topic of Vector Functions of Scalar Variables.
Herb Gross defines the cross product of two vectors.
Herb Gross motivates the definition of the dot product and shows how to calculate the dot product of two vectors in 3-space.
Herb Gross discusses the topic of lines and planes in 3-dimensional space.
Herb Gross introduces Calculus Revisited part 2 - functions of several variables and discusses the over-arching theme "The Game of Mathematics"