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