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The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations.
A USAF 1951 resolution chart in PDF format is provided by Yoshihiko Takinami. This chart should be printed such that the side of the square of the 1st element of the group -2 should be 10 mm long. USAF 1951 Resolution Target Further explanations and examples; Koren 2003: Norman Koren's updated resolution chart better suited for computer analysis
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.
It provides a rich Excel-like user interface and its built-in vector programming language FPScript has a syntax similar to MATLAB. FreeMat, an open-source MATLAB-like environment with a GPL license. GNU Octave is a high-level language, primarily intended for numerical computations. It provides a convenient command-line interface for solving ...
It was a free tool for academics. Jack Little, who would eventually set up the company, came across the tool while he was a graduate student in electrical engineering at Stanford University. [3] [4] Little and Steve Bangert rewrote the code for MATLAB in C while they were colleagues at an engineering firm.
The table of month offsets show a divergence in February due to the leap year. A common technique (later used by Zeller) is to shift the month to start with March, so that the leap day is at the tail of the counting. In addition, as later shown by Zeller, the table can be replaced with an arithmetic expression.
Similarly, a differential equation is said to be linear if it can be written with linear differential operators, but it can still have nonlinear expressions in it. In a mathematical programming model, if the objective functions and constraints are represented entirely by linear equations , then the model is regarded as a linear model.
The MacCormack method is well suited for nonlinear equations (Inviscid Burgers equation, Euler equations, etc.) The order of differencing can be reversed for the time step (i.e., forward/backward followed by backward/forward). For nonlinear equations, this procedure provides the best results.