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- Two dimensional autonomous differential equation problems
Sample problems involving analysis of a two coupled autonomous differential equations. - Definition: Uncountable definition
A set is uncountable if it contains so many elements that they cannot be put in one-to-one correspondence with the set of natural numbers. In other words, there is no way that one can count off all elements in the set in such a way that, even though the counting will take forever, you will get to any particular element in a finite amount of time. - Definition: Undirected graph definition
An undirected graph is graph, i.e., a set of objects (called vertices or nodes) that are connected together, where all the edges are bidirectional. - Definition: Definition of union
The union of a set $A$ with a $B$ is the set of elements that are in either set $A$ or $B$. The union is denoted as $A \cup B$. - Definition: Unit vector definition
A unit vector is a vector of length one. - Using the Forward Euler algorithm to solve pure-time differential equations
By pretending that the slope of a function is constant over small intervals, we following tangent lines to estimate the solution to pure-time differential equations. - Definition: Variable definition
A variable is a quantity that may change within the context of a mathematical problem or experiment. - Vector fields as fluid flow
Interpretation of vector fields as velocity fields of fluids. - Vector field overview
An overview introducing the basic concept of vector fields in two or three dimensions. - An introduction to vectors
A introduction to the concept of a vector as an object with magnitude and direction. - Vectors in arbitrary dimensions
A brief introduction to n-dimensional vectors. - 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. - Visualizing the solution to a two-dimensional system of linear ordinary differential equations
An interactive plot of the the solution trajectory of a 2D linear ODE, where one can explore the behavior of the solution in the phase plane and versus time. - Volume of surfaces of revolution
Calculating the volume of created by rotating a plane region around some axis. - Volumes by cross sections
Calculating the volume of a solid by integrating the area of its cross sections. - The zero vector
The zero vector is the unique vector having zero length. The direction of the zero vector is undefined.
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