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# Calculus-level Languages, an introduction Calculus level computer languages are FortranCalculus (intro in 1991) and PROSE (intro in 1974). Both languages are based on "Automatic Differentiation" (AD). Calculus languages simplify computer coding to an absolute minimum; i.e., a mathematical model, constraints, and the objective function. Minimizing the amount of code allows the user to concentrate on the science or engineering problem at hand and not on the (numerical) process requirements to achieve an optimum solution.

Major benefits from Automatic Differentiation based software:

• Determines Optimal solutions
• Allows Rapid Model Prototyping
• Accelerates Problem "Understanding"
• Increases Engineering Output and Quality
• Reduces Time & Costly Problem / Solution Cycle

Fundamentals (R&D) FortranCalculus was designed to solve implicit problems. Implicit problems are abundant in every branch of science and technology. Simulation programs can be elevated to optimization programs by using the FIND statements. An example circuit simulation program was converted and showed a 90% reduction in development time. Simulation conversions seem to have the most to gain besides those problems that can only be solved with this tool. PDEs, ODEs, and Algebraic equations can be solved.

## Allows Rapid Prototyping for Adaptive Engineering

The following diagram attempts to show the 'normal' programming versus calculus-level programming activities/personnel. Many backgrounds are presently required to solve math problems. Calculus programming -only- requires one who can formulate a math model, constraints, and an objective function; the numerical solvers are built-in.

```
Basic, Fortran, MACSYMA, etc.  vs.   Calculus Programming
``` ```
Source Code:         Large             Small
Cost:                High              Low
Delay:               Long              Short```

For cost savings, optimum solutions, and increased engineering output, consider Calculus Programming.

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