List of all pages
- Data modeling versus mathematical modeling
Discussion of the difference between data modeling, in which one fits a function to data, and mathematical modeling, in which one fits a model that describes the process underlying the data. - The degree distribution of a network
The degree distribution is introduced as a simplified measure that characterizes one aspect of a network's structure. - Definition: Dependent variable definition
A dependent variable is a variable that represents a quantity that changes based on other quantities being manipulated in an experiment. In the context of a function, the dependent variable is the output to the function. - The derivative, critical points, and graphing
- Solutions to elementary derivative problems
Solutions to sample problems illustrating the ordinary derivative. - Elementary derivative problems
Sample problems illustrating the ordinary derivative. - Developing intuition about the derivative
An intuitive exploration into the properties of the derivative, illustrated by interactive graphics. - The derivative of an inverse function
How to write the derivative of an inverse function in terms of the derivative of the original function. - Calculating the derivative of a linear function using the derivative formula
Exploring how the limit definition of the derivative gives the slope of a linear function. - The derivative matrix
The derivative matrix is presented as a natural generalization of the single variable derivative to multivariable functions. - Examples of calculating the derivative
Examples showing how to calculate the derivative and linear approximation of multivariable functions. - The derivative of the natural logarithm
Determining the derivative of the natural logarithm from the fact that it is the inverse of the exponential function. - The derivative of a power function
Using the limit definition of the derivative to calculate the derivative of a power function. - Calculating the derivative of a quadratic function
Using the limit definition of the derivative to calculate the derivative of a quadratic. - Derivatives of more general power functions
How to compute the derivative of power functions. - Derivatives of polynomials
How to compute the derivative of a polynomial. - Derivatives of transcendental functions
A list of formulas for taking derivatives of exponential, logarithm, trigonometric, and inverse trigonometric functions. - Geometric properties of the determinant
Explanation of some of the basic geometric properties of the determinant. - Determinants and linear transformations
A description of how a determinant describes the geometric properties of a linear transformation. - The determinant of a matrix
The calculation of the determinant of a matrix, a single number that gives useful information about the matrix.
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