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The Identity Matrix

"When dealing with matrix computation, it is important to understand the identity matrix. We can think of the identity matrix as the multiplicative identity of square matrices, or the one of square ma ...

Hyperbola Graphs

"Graphing a transformed hyperbola combines the skills of graphing hyperbolas and graphing transformations. With hyperbola graphs, we use the formula a^2 + b^2 = c^2 to determine the foci and y= + or - ...

The Hyperbola

"A hyperbola is a type of conic section that is formed by intersecting a cone with a plane, resulting in two parabolic shaped pieces that open either up and down or right and left. Similar to a parabo ...

The Greatest Integer Function

"One of the most commonly used step functions is the greatest integer function. The greatest integer function has it's own notation and tells us to round whatever decimal number it is given down to th ...

The Ellipse

"An ellipse is an important conic section and is formed by intersecting a cone with a plane that does not go through the vertex of a cone. The ellipse is defined by two points, each called a focus. Fr ...

The Cross Product of Vectors

"In Calculus we often use the cross product of vectors to find orthogonal vectors and the area of parallelograms in three dimensions. The cross product of vectors is found by identifying the 3x3 deter ...

The Complex Plane

"Imaginary numbers arise frequently in mathematics, but in order to do much with them we need to know more about the complex plane and the rectangular form of complex numbers. The complex plane is a m ...

The Angle Between Vectors

"The vector formula to find the angle between vectors is a useful formula to memorize. This formula uses the dot product, magnitude and cosine to give us the angle between vectors. We can use this for ...

The Angle Between Planes

"We can use knowledge of how to find the angle between vectors to help us find the angle between planes. We can use the dot product to find the angle between planes, or determine whether or not the pl ...

Tangent Transformation

"When graphing a tangent transformation, start by using a theta and tan(theta) t-table for -pi/2 to pi/2. In the case of y=Atan(Bx) or y=Atan(B(x-h)), define Bx or B(x-h) to be equal to theta and sol ...

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