Jacobi elliptic functionsIn mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum (see also pendulum (mathematics)), as well as in the design of electronic elliptic filters. While trigonometric functions are defined with reference to a circle, the Jacobi elliptic functions are a generalization which refer to other conic sections, the ellipse in particular. The relation to trigonometric functions is contained in the notation, for example, by the matching notation for .
Theta functionIn mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. As Grassmann algebras, they appear in quantum field theory. The most common form of theta function is that occurring in the theory of elliptic functions. With respect to one of the complex variables (conventionally called z), a theta function has a property expressing its behavior with respect to the addition of a period of the associated elliptic functions, making it a quasiperiodic function.
MATLABMATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities.
Lemniscate elliptic functionsIn mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied by Giulio Fagnano in 1718 and later by Leonhard Euler and Carl Friedrich Gauss, among others. The lemniscate sine and lemniscate cosine functions, usually written with the symbols sl and cl (sometimes the symbols sinlem and coslem or sin lemn and cos lemn are used instead), are analogous to the trigonometric functions sine and cosine.
Hyperbolic functionsIn mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the unit hyperbola. Also, similarly to how the derivatives of sin(t) and cos(t) are cos(t) and –sin(t) respectively, the derivatives of sinh(t) and cosh(t) are cosh(t) and +sinh(t) respectively. Hyperbolic functions occur in the calculations of angles and distances in hyperbolic geometry.
DebuggingIn computer programming and software development, debugging is the process of finding and resolving bugs (defects or problems that prevent correct operation) within computer programs, software, or systems. Debugging tactics can involve interactive debugging, control flow analysis, unit testing, integration testing, , monitoring at the application or system level, memory dumps, and profiling. Many programming languages and software development tools also offer programs to aid in debugging, known as debuggers.
Inverse trigonometric functionsIn mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains). Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry.
Rate of returnIn finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows (or securities, or other investments) which the investor receives from that investment over a specified time period, such as interest payments, coupons, cash dividends and stock dividends. It may be measured either in absolute terms (e.g., dollars) or as a percentage of the amount invested. The latter is also called the holding period return.
DebuggerA debugger or debugging tool is a computer program used to test and debug other programs (the "target" program). The main use of a debugger is to run the target program under controlled conditions that permit the programmer to track its execution and monitor changes in computer resources that may indicate malfunctioning code. Typical debugging facilities include the ability to run or halt the target program at specific points, display the contents of memory, CPU registers or storage devices (such as disk drives), and modify memory or register contents in order to enter selected test data that might be a cause of faulty program execution.
Transcendental functionIn mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function. In other words, a transcendental function "transcends" algebra in that it cannot be expressed algebraically. Examples of transcendental functions include the exponential function, the logarithm, and the trigonometric functions. Formally, an analytic function f (z) of one real or complex variable z is transcendental if it is algebraically independent of that variable.
Return on investmentReturn on investment (ROI) or return on costs (ROC) is a ratio between net income (over a period) and investment (costs resulting from an investment of some resources at a point in time). A high ROI means the investment's gains compare favourably to its cost. As a performance measure, ROI is used to evaluate the efficiency of an investment or to compare the efficiencies of several different investments. In economic terms, it is one way of relating profits to capital invested.
Trigonometric functionsIn mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.
Time value of moneyThe time value of money is the widely accepted conjecture that there is greater benefit to receiving a sum of money now rather than an identical sum later. It may be seen as an implication of the later-developed concept of time preference. The time value of money is among the factors considered when weighing the opportunity costs of spending rather than saving or investing money. As such, it is among the reasons why interest is paid or earned: interest, whether it is on a bank deposit or debt, compensates the depositor or lender for the loss of their use of their money.
Return on capitalReturn on capital (ROC), or return on invested capital (ROIC), is a ratio used in finance, valuation and accounting, as a measure of the profitability and value-creating potential of companies relative to the amount of capital invested by shareholders and other debtholders. It indicates how effective a company is at turning capital into profits. The ratio is calculated by dividing the after tax operating income (NOPAT) by the average book-value of the invested capital (IC).
Indentation (typesetting)FORCETOC In the written form of many languages, an indentation or indent is an empty space at the beginning of a line to signal the start of a new paragraph. Many computer languages have adopted this technique to designate "paragraphs" or other logical blocks in the program. For example, the following lines are indented, using between one and six spaces: This paragraph is indented by 1 space. This paragraph is indented by 3 spaces. This paragraph is indented by 6 spaces.
Indentation styleIn computer programming, an indentation style is a convention governing the indentation of blocks of code to convey program structure. This article largely addresses the free-form languages, such as C and its descendants, but can be (and often is) applied to most other programming languages (especially those in the curly bracket family), where whitespace is otherwise insignificant. Indentation style is only one aspect of programming style. Indentation is not a requirement of most programming languages, where it is used as secondary notation.
Debug symbolA debug symbol is a special kind of symbol that attaches additional information to the symbol table of an , such as a shared library or an executable. This information allows a symbolic debugger to gain access to information from the source code of the binary, such as the names of identifiers, including variables and routines. The symbolic information may be compiled together with the module's , or distributed in a separate file, or simply discarded during the compilation and/or linking.
Even and odd functionsIn mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses. They are important in many areas of mathematical analysis, especially the theory of power series and Fourier series. They are named for the parity of the powers of the power functions which satisfy each condition: the function is an even function if n is an even integer, and it is an odd function if n is an odd integer.
Stepping (debugging)Program animation or stepping refers to the debugging method of executing code one instruction or line at a time. The programmer may examine the state of the program, machine, and related data before and after execution of a particular line of code. This allows the programmer to evaluate the effects of each statement or instruction in isolation, and thereby gain insight into the behavior (or misbehavior) of the executing program. Nearly all modern IDEs and debuggers support this mode of execution.
Accounting rate of returnThe accounting rate of return, also known as average rate of return, or ARR is a financial ratio used in capital budgeting. The ratio does not take into account the concept of time value of money. ARR calculates the return, generated from net income of the proposed capital investment. The ARR is a percentage return. Say, if ARR = 7%, then it means that the project is expected to earn seven cents out of each dollar invested (yearly). If the ARR is equal to or greater than the required rate of return, the project is acceptable.
