Calculus
Textbooks
Boundless Calculus
Advanced Topics in Single-Variable Calculus and an Introduction to Multivariable Calculus
Calculus Textbooks Boundless Calculus Advanced Topics in Single-Variable Calculus and an Introduction to Multivariable Calculus
Calculus Textbooks Boundless Calculus
Calculus Textbooks
Calculus

Section 1

Vectors and the Geometry of Space

Book Version 1
By Boundless
Boundless Calculus
Calculus
by Boundless
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9 concepts
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Three-Dimensional Coordinate Systems

The three-dimensional coordinate system expresses a point in space with three parameters, often length, width and depth ($x$, $y$, and $z$).

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Vectors in the Plane

Vectors are needed in order to describe a plane and can give the direction of all dimensions in one vector equation.

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Vectors in Three Dimensions

A Euclidean vector is a geometric object that has magnitude (i.e. length) and direction.

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The Dot Product

The dot product takes two vectors of the same dimension and returns a single value.

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The Cross Product

The cross product of two vectors is a vector which is perpendicular to both of the original vectors.

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Equations of Lines and Planes

A line is a vector which connects two points on a plane and the direction and magnitude of a line determine the plane on which it lies.

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Cylinders and Quadric Surfaces

A quadric surface is any $D$-dimensional hypersurface in $(D+1)$-dimensional space defined as the locus of zeros of a quadratic polynomial.

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Cylindrical and Spherical Coordinates

Cylindrical and spherical coordinates are useful when describing objects or phenomena with specific symmetries.

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Surfaces in Space

A surface is a two-dimensional, topological manifold.

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