### Pages similar to: Function notation

- Function examples

Basic examples of functions illustrating the definition of a function. - Function composition examples

Examples of composing functions to form a new combined function. - Surfaces as graphs of functions

Illustration of how the graph of a scalar-valued function of two variables is a surface. - The exponential function

Overview of the exponential function and a few of its properties. - The function machine

The function machine metaphor helps explain the definition and properties of a function. - Introduction to changing variables in double integrals

Introduction to the concepts behind a change of variables in double integrals. The transformation is illustrated with interactive graphics. - An introduction to ordinary differential equations

An introduction using simple examples explaining what an ordinary differential equation is and how one might solve them. - Determinants and linear transformations

A description of how a determinant describes the geometric properties of a linear transformation. - Exploring the derivative of the exponential function

A guided tour into the reasons that the derivative of the exponential function with base e is the function itself. - Discrete dynamical systems as function iteration

The simplest versions of discrete dynamical systems can be viewed as evolving due to iterating a function repeatedly. - Vectors in two- and three-dimensional Cartesian coordinates

A introduction to representing vectors using the standard Cartesian coordinate systems in the plane and in three-dimensional space. - Introduction to changing variables in triple integrals

Introduction to the concepts behind a change of variables in triple integrals. - The idea of a dynamical system

The basic concept of a dynamical system as the evolution of something over time. The fundamental ideas of the state space and temporal evolution rules are illustrated with examples featuring interactive graphics. - The idea of a probability density function

A probability density function captures the probability of being close to a number even when the probability of any single number is zero. - Developing an initial model to describe bacteria growth

By analyzing some data and hypothesizing rules for cell division, we develop a discrete dynamical system for the growth of a population of bacteria. - Introduction to the multivariable chain rule

Introduction to the multivariable chain rule. The basic concepts are illustrated through a simple example. - The integrals of multivariable calculus

A summary of the integrals of multivariable calculus, including calculation methods and their relationship to the fundamental theorems of vector calculus. - From discrete dynamical systems to continuous dynamical systems

Illustration of how a discrete dynamical system approaches a continuous dynamical as the size of the time step shrinks. - Introduction to Dynamical Systems

- Level sets

A introduction to level sets. Illustrates level curves and level surfaces with interactive graphics.