 TOPICS   # Topics in a Pre-Calculus Course

To learn more about a topic listed below, click the topic name to go to the corresponding MathWorld classroom page.

### General

 Asymptote An asymptote is a line or curve that approaches a given curve arbitrarily closely. Curve A curve is a continuous map from a one-dimensional space to an n-dimensional space. Loosely speaking, the word "curve" is often used to mean the function graph of a two- or three-dimensional curve. Determinant The determinant of a square matrix is a scalar (commonly computed using so-called expansion by minors) which is nonzero if and only if the matrix has an inverse. Parametric Equations Parametric equations are a set of equations that together express a set of quantities as explicit functions of a number of independent variables, which are known as parameters. Plane A plane is a two-dimensional surface defined by linear equations. Plane Curve A plane curve is a curve that lies in a single plane. A plane curve may be closed or open. Polar Coordinates Polar coordinates are a two-dimensional coordinate system in which points in two dimensions are given by an angle and a distance from the origin. Rational Function A rational function is a function that can be written as the quotient of two polynomials. Reflection In mathematics, reflecton is the operation of exchanging all points of a mathematical object with their mirror images. Rotation A rotation is the turning of an object or coordinate system about a fixed point. Rotation Matrix A rotation matrix is a matrix that corresponds to the linear transformation of a rotation. Scalar A scalar is value (such as a measurement) that has only magnitude but not direction. This contrasts with a vector, which has direction as well as magnitude. Spherical Coordinates Spherical coordinates are a coordinate system in which points in three-dimensional space are given by two angles and a distance from the origin. Tangent Line A tangent line is a line that touches but does not cross a curve at a given point. Translation In geometry, a translation is a transformation consisting of a constant shift with no rotation or stretching.

### Complex Numbers

 Complex Conjugate: The complex conjugate of a complex number is the number obtained by flipping the sign of its imaginary part. Complex Number: A complex number is a number consisting of a real part and an imaginary part. A complex number is an element of the complex plane. Complex Plane: The complex plane is a term for the set of all complex numbers. Just as all real numbers can be imagined as lying on a line, all complex numbers can be thought of as points in a plane. i: i is the symbol used to denote the principal square root of -1, also called the imaginary unit. Imaginary Number: In mathematics, an imaginary number is multiple of the imaginary unit i (the square root of -1).

### Conic Sections

 Conic Section: The conic sections are the classes of nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone. A conic section can also be realized as the zero set of a quadratic equation in two variables. Ellipse: A conic section with eccentricity less than one. It resembles a squashed circle. Hyperbola: A hyperbola is a conic section with eccentricity greater than one and consists of two separate branches. Locus: A locus is the set of all points (usually forming a curve or surface) satisfying some condition. For example, the locus of points in a plane that are equidistant from a given point is a circle. Parabola: A parabola is a conic section with eccentricity equal to one. Parabolas appear as the graphs of quadratic equations and the trajectories of projectiles.

### Exponents and Logarithms

 e: The mathematical constant denoted e is the base of the natural logarithm which has value of approximately 2.718. Exponential Function: The exponential function is the function consisting of the base of the natural logarithm e taken to the power of a given variable. Logarithm: The logarithm is the power to which a number (called the base) must be raised to produce a given number. For example, the logarithm of 100 with respect to the base 10 is 2. Natural Logarithm: The natural logarithm is the logarithm having base e.

### Functions

 Domain: (1) In analysis, the domain of a function is the set of values for which a function is defined. (2) In topology, a domain is a connected, open set. Function: A function is a relation that uniquely associates members of one set with members of another set. The term "function" is sometimes implicitly understood to mean continuous function, linear function, or function into the complex numbers. Inverse Function: The inverse function f-1 of a function f is the function for which f(f-1(x)) = x for any x. Range: (1) In the theory of functions, the range is the set of all values that a function can take. (2) In data analysis, the range is the difference between the minimum and the maximum values of a data set.

### Vectors

 Cross Product: The cross product is a product of two vectors that results in a vector perpendicular to both. Dot Product: The dot product is particular product of two vectors which results in a scalar corresponding to the length of the projection of one vector onto the other. Normal Vector: A normal vector is a vector perpendicular to a surface. Vector: (1) In vector algebra, a vector mathematical entity that has both magnitude (which can be zero) and direction. (2) In topology, a vector is an element of a vector space.