# Glossary

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Words |
Description |
---|---|

Absolute error |
The difference between an approximation and an exact answer. |

Abstraction |
The process of ignoring the details of how a function works in order to focus on a simpler model of what the function does. |

Accumulator |
A variable that is used to accumulate a result a little bit at a time. |

Analytic solution |
A way of solving an equation by performing algebraic operations and deriving an explicit way to compute a solution. |

Apply |
A way of processing a vector by performing some operation on each of the elements, producing a vector that contains the results. |

Argument |
An expression that appears in a function call to specify the value the function operates on. |

Assignment statement |
A command that creates a new variable (if necessary) and gives it a value. |

Body |
The statements inside a loop that are run repeatedly. |

Call (a function) |
To cause a function to execute and compute a result. |

Column vector |
A matrix that has only one column. |

Command |
A line of MATLAB code executed by the interpreter. |

Comment |
Part of a program that provides additional information about the program but does not affect its execution. |

Compound statement |
A statement, like if and `for` , that contains other statements in an indented body. |

Concatenation |
The operation of joining two vectors or matrices end-to-end to form a new vector or matrix. |

Cross product |
A product of two vectors with norm %proportional to the norms of the vectors and the sine of the angle %between them, and direction perpendicular to both. |

Differential equation (DE) |
An equation that relates the derivatives of an unknown function. |

Directly (compute) |
A way of computing an element in a sequence without using previous elements. |

dot product: |
A scalar product of two vectors, proportional to the %norms of the vectors and the cosine of the smallest angle between them. |

Element (of a matrix) |
One of the values in a vector or matrix. |

Element (of a sequence) |
One of the numbers in a mathematical sequence. |

Elementwise |
An operation that acts on the elements of a vector or matrix (unlike some linear algebra operations). |

Encapsulation |
The process of wrapping part of a program in a function in order to limit interactions (including name collisions) between the function and the rest of the program. |

Evaluate |
To compute the value of an expression. |

Existential quantification |
A logical condition that expresses the idea that ''there exists'' an element of a set with a certain property. |

Expression |
A sequence of operands and operators that specifies a mathematical computation and yields a value. |

First-order DE |
A differential equation that includes only first derivatives. |

Floating-point |
A way to represent numbers in a computer. |

Function |
A named computation; for example, log10 is the name of a function that computes logarithms in base 10. |

Function call |
A command that executes a function. |

Function handle |
A function handle is a way of referring to a function by name (and passing it as an argument) in MATLAB without calling it. |

Generalization |
Making a function more versatile by replacing specific values with input variables. |

Helper function |
A function in an M-file that is not the top-level function; it can only be called from another function in the same file. |

Incremental development |
A way of programming by making a series of small, testable changes. |

Index |
An integer value used to indicate one of the values in a vector or matrix (also called subscript in some MATLAB documentation). |

Input variable |
A variable in a function that gets its value, when the function is called, from one of the arguments. |

Interpreter |
The program that reads and executes MATLAB code. |

Linear DE |
A differential equation that includes no products or powers of the function and its derivatives. |

Logical function |
A function that returns a logical value (1 for ''true'' or 0 for ''false''). |

Logical vector |
A vector, often the result of applying a logical operator to a vector, that contains logical values 1 and 0. |

Loop |
A part of a program that runs repeatedly. |

Loop variable |
A variable, defined in a loop, that gets assigned a different value each time through the loop. |

M-file |
A file that contains a MATLAB program. |

Matrix |
A two-dimensional collection of values (also called ''array'' in some MATLAB documentation). |

Name collision |
The scenario where two scripts that use the same variable name interfere with each other. |

Nested function call |
An expression that uses the result from one function call as an argument for another. |

Nesting |
Putting one compound statement in the body of another. |

Norm |
The magnitude of a vector, sometimes called ''length,'' but not to be confused with the number of elements in a MATLAB vector. |

Numerical method |
A method (or algorithm) for generating a numerical solution. |

Numerical solution |
A way of solving an equation by finding a numerical value that satisfies the equation, often approximately. |

Operand |
A number or variable that appears in an expression along with operators. |

Operator |
One of the symbols, like * and `+` , that represent mathematical operations. |

Order of operations |
The rules that specify which operations in an expression are performed first. |

Ordinary DE (ODE) |
A differential equation in which all derivatives are taken with respect to the same variable. |

Output variable |
A variable in a function that is used to return a value from the function to the caller. |

Pack |
To copy values from a set of variables into a vector. |

Parameter |
A value that appears in a model to quantify some physical aspect of the scenario being modeled. |

Partial DE (PDE) |
A differential equation that includes derivatives with respect to more than one variable. |

Phase plot |
A plot that shows the state of a system as a point in the space of possible states. |

Postcondition |
Something that will be true when the script completes. |

Precondition |
Something that must be true when the script starts, in order for it to work correctly. |

Projection |
The component of one vector that is in the direction of the other. |

Prompt |
The symbols the interpreter prints to indicate that it's waiting for the user to type a command. |

Range |
A matrix of values specified with the colon operator, for example, `1:5` . |

Recurrently |
A way of computing the next element of a sequence based on previous elements. |

Reduce |
A way of processing the elements of a vector and generating a single value, for example, the sum of the elements. |

Relative error |
The difference between an approximation and an exact answer, expressed as a fraction or percentage of the exact answer. |

Row vector |
A matrix that has only one row. |

Scaffolding |
Code you write to help you program or debug, but which is not part of the finished program. |

Scalar |
A single value. |

Scientific notation |
A format for typing and displaying large and small numbers, e.g., `3.0e8` , which represents 3.0 x 10^{8} or 300,000,000. |

Script |
An M-file that contains a sequence of MATLAB commands. |

Search |
A way of processing a vector by examining the elements in order until one is found that has the desired property. |

Search path |
The list of folders where MATLAB looks for M-files. |

Sequence |
A set of numbers that correspond to the positive integers, in mathematics. |

Series |
The sum of the elements in a sequence, in mathematics. |

Shadow |
A kind of name collision in which a new definition causes an existing definition to become invisible. In MATLAB, variable names can shadow built-in functions (with hilarious results). |

Side effect |
An effect, like modifying the workspace, that is not the primary purpose of a function or script. |

Signature |
The first line of a function definition, which specifies the names of the function, the input variables, and the output variables. |

Silent function |
A function that doesn't display anything, generate a figure, or have any other side effects. |

Spatial vector |
A value that represents a multidimensional physical quantity like position, velocity, acceleration, or force. |

State |
If a system can be described by a set of variables, the values of those variables are called the state of the system. |

String |
A value that consists of a sequence of characters. |

System of equations |
A collection of equations written in terms of the same set of variables. |

Target |
The variable on the left side of an assignment statement. |

Time step |
The interval in time between successive estimates in the numerical solution of a differential equation. |

Top-level function |
The first function in an M-file; it's the only function that can be called from the Command Window or from another file. |

Trajectory |
A path in a phase plot that shows how the state of a system changes over time. |

Transpose |
An operation that transforms the rows of a matrix into columns (and the other way around). |

Unit vector |
A vector with norm 1, used to indicate direction. |

Universal quantification |
A logical condition that expresses the idea that all elements of a set have a certain property. |

Unpack |
To copy the elements of a vector into a set of variables. |

Value |
The result of a computation, most often a number, string, or matrix. |

Variable |
A named value. |

Vector |
A sequence of values. |

Workspace |
A set of variables and their values. |

Zero (of a function) |
An argument that makes the value of a function 0. |