mathematical model: An abstract mathematical representation of a process, device or concept it uses a number of variables to represent inputs, outputs and internal states, and sets of equations and inequalities to describe their interaction.Ī mathematical model is a description of a system using mathematical concepts and language.exponential growth: The growth in the value of a quantity, in which the rate of growth is proportional to the instantaneous value of the quantity for example, when the value has doubled, the rate of increase will also have doubled.map projection: any systematic method of transforming the spherical representation of parallels, meridians and geographic features of the Earth’s surface to a nonspherical surface, usually a plane.Mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models.Mathematical models are used in the natural sciences, engineering disciplines, and in the social sciences.A mathematical model is a description of a system using mathematical concepts and language.One of the most important skills in algebra and calculus is being able to convert a function between these different forms, and this theme will recur in different forms throughout the text. These are not four different types of functions they are four different views of the same function. Examples include seismograph readings, electrocardiograms, and oscilloscope readings. Scientific data is often recorded in a visual format. Graphical: This involves modeling a function in a dimensional overlay. (You may recognize this as the (x,y) points used in graphing.) Numerical: This can be expressed as a list of value pairs, as in (4,14) - meaning that if a 4 goes in, a 14 comes out. Note that in an algebraic representation, the input number is represented as a variable (in this case, an x). For example, the expression 2x+6 can be represented as “Double x and add six” or “six added to two times x”.Īlgebraic: This is the most common, most concise, and most powerful representation: 2x+6. Verbal: When modeling a process mathematically, one often first develops a verbal description of the problem. Modern calculus texts emphasize that a function can be expressed in four different ways. The input variable (s) are sometimes referred to as the argument(s) of the function. In this example, if the input is -3, then the output is 9, and we may write f(-3)=9. The output of a function f corresponding to an input x is denoted by f(x) (read “ f of x“). An example is the function that relates each real number x to its square x^2. function: a relation in which each element of the domain is associated with exactly one element of the co-domainĪ function is a relation between a set of inputs and a set of permissible outputs, provided that each input is related to exactly one output.A function can be represented graphically.A function can be represented numerically.A function can be represented algebraically.For example, the circumference of a square is four times one of its sides. A function can be represented verbally.Developing Algebraic Thinking: Plotting and Growingĭeveloping Geometric Logic: Shapes and Pathsĭeveloping Measurement Benchmarks: Scales and Balancesĭeveloping Number Concepts: Ordering and Arranging, Module Aĭeveloping Number Concepts: Ordering and Arranging, Module BĮnVision MATH Common Core 2.0 Student Edition V1ĮnVision MATH Common Core 2.
0 kommentar(er)
