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FortranCalculus Class

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FC-Compiler™ is a (free) Calculus-level Compiler that simplifies Tweaking parameters in ones math model. The FortranCalculus (FC) language is for math modeling, simulation, and optimization. FC is based on Automatic Differentiation that simplifies computer code to an absolute minimum; i.e., a mathematical model, constraints, and the objective (function) definition. 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. Download at http://goal-driven.net/apps/fc-compiler.html

FC-Compiler™ App has many (50+) example problems with output (see 'Demos' on main menu) for viewing and getting ideas on solving your own problems. These are improved productivity examples do to using Calculus-level Problem-Solving. Please share this Calculus Problem-Solving tool with your friends. Thanks!

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FortranCalculus Class

  1. 1. Improve Math Models &Improve Math Models & Increase ProductivityIncrease Productivity By Phil BrubakerBy Phil Brubaker forfor Scientists,Scientists, Engineers & ManagementEngineers & Management Optimal Designs EnterpriseOptimal Designs Enterprise goal-driven.netgoal-driven.net
  2. 2. Improve Models &Improve Models & Increase ProductivityIncrease Productivity AgendaAgenda Design ObjectivesDesign Objectives Language BackgroundLanguage Background Example CodeExample Code Optimization of OptimizationsOptimization of Optimizations
  3. 3. Code DefinitionCode Definition OptimizationOptimization == SimulationSimulation ++ Objective (Function)Objective (Function)
  4. 4. Why OptimizationWhy Optimization over Simulation?over Simulation? Maximize Parameter Tolerance for Mfg.Maximize Parameter Tolerance for Mfg. Solutions are at min./max. locations whereSolutions are at min./max. locations where their partial derivatives = 0 & thus allow largesttheir partial derivatives = 0 & thus allow largest delta errors.delta errors. Minimize # of Executions for a solutionMinimize # of Executions for a solution
  5. 5. IntroductionIntroduction toto FortranCalculusFortranCalculus a Calculus-level Computer Languagea Calculus-level Computer Language 1974 First Commercial Release (PROSE)1974 First Commercial Release (PROSE) I taught PROSE in 1975-79.I taught PROSE in 1975-79. Solved problems within 4 hours (each)Solved problems within 4 hours (each) Present version is FortranCalculusPresent version is FortranCalculus Main obstacle: no design objectiveMain obstacle: no design objective
  6. 6. Objective-Driven EngineeringObjective-Driven Engineering What are yourWhat are your Goals/ObjectivesGoals/Objectives forfor a given Project?a given Project?
  7. 7. What are you building?What are you building? Mr. Arithmetic Mr. Algebra Mr. CalculusMr. Arithmetic Mr. Algebra Mr. Calculus ------------------- --------------- ----------------------------------- --------------- ---------------- Slide Rule Simulate OptimizeSlide Rule Simulate Optimize
  8. 8. Objective-Driven CutsObjective-Driven Cuts Sawmill's operation Objective for cutting log?Objective for cutting log?
  9. 9. Objective-Driven CutsObjective-Driven Cuts Sawmill's operation Objective for cutting log?Objective for cutting log? Maximize company's profitsMaximize company's profits Minimize pollutionMinimize pollution Minimize 'waste'Minimize 'waste' Maximize 2" x 4"sMaximize 2" x 4"s
  10. 10. Sawmill's operation Parameters to consider:Parameters to consider: Log-to-lumber Processing:Log-to-lumber Processing: Size of logSize of log: diameter, length, taper, knots, etc.: diameter, length, taper, knots, etc. Time requiredTime required to: cut log, sharpen blades, lubricateto: cut log, sharpen blades, lubricate machinery, etc.machinery, etc. Strength or flexibilityStrength or flexibility desired of various sizes.desired of various sizes. InventoryInventory Market trendsMarket trends Objective-Driven CutsObjective-Driven Cuts
  11. 11. Chaotic Design ProcessChaotic Design Process Control BoxControl Box Bingo, a design!Bingo, a design!
  12. 12. Objective-Driven DesignObjective-Driven Design Surveillance Design Objective:Surveillance Design Objective: Maximize surveillance coverageMaximize surveillance coverage Minimize number of satellitesMinimize number of satellites Solution? (Not realistic; Objective needs work.)Solution? (Not realistic; Objective needs work.)
  13. 13. Objective-Driven DesignObjective-Driven Design Thin-Film-Head (TFH) for Magnetic Recording TFH with coilTFH with coil Disc platter cross-sectionDisc platter cross-section Typical Readback PulseTypical Readback Pulse Optimum pulse shapeOptimum pulse shape versusversus
  14. 14. Objective-Driven DesignObjective-Driven Design Thin-Film-Head (TFH) for Magnetic RecordingThin-Film-Head (TFH) for Magnetic Recording Design Objective?Design Objective? Maximize ProfitMaximize Profit Maximize Pulse SymmetryMaximize Pulse Symmetry Minimize Pulse WidthMinimize Pulse Width Minimize PollutionMinimize Pollution Maximize User SatisfactionMaximize User Satisfaction ?????? Solution: Determine TFH geometrySolution: Determine TFH geometry parameters A, B, C, etc. to achieve objective.parameters A, B, C, etc. to achieve objective.
  15. 15. Objective-Driven DesignObjective-Driven Design Matched Filter for Magnetic RecordingMatched Filter for Magnetic Recording Electrical FilterElectrical Filter Yin(t) ==>Yin(t) ==> TransferTransfer FunctionFunction -------------------------- H(s)H(s) ==> Yout(t)==> Yout(t) versusversus Typical Input Pulse, Yin(t)Typical Input Pulse, Yin(t) Desired Output Pulse, Yout(t)Desired Output Pulse, Yout(t)
  16. 16. Objective-Driven DesignObjective-Driven Design Matched Filter for Magnetic RecordingMatched Filter for Magnetic Recording Results:Results: Textbook problem solved in 4 hoursTextbook problem solved in 4 hours Design required 2 years to acquire a true practicalDesign required 2 years to acquire a true practical objective functionobjective function Development time droppedDevelopment time dropped from 12 to 1 weekfrom 12 to 1 week Design was mathematically optimalDesign was mathematically optimal
  17. 17. "One Step from First Principles to Solutions""One Step from First Principles to Solutions" EnhancingEnhancing Scientific & EngineeringScientific & Engineering ProductivityProductivity FortranCalculus BackgroundFortranCalculus Background Optimal Designs EnterpriseOptimal Designs Enterprise goal-driven.netgoal-driven.net
  18. 18. Industry IssueIndustry Issue A Proven ApproachA Proven Approach SummSummaryary Fortran CalculusFortran Calculus LanguageLanguage AgendaAgenda
  19. 19. Scientific & EngineeringScientific & Engineering ProductivityProductivity Industry IssueIndustry Issue Costly Problem/Solution Cycle ...Costly Problem/Solution Cycle ... Model Married to AlgorithmModel Married to Algorithm Validation DelayedValidation Delayed Long Problem/Solution CycleLong Problem/Solution Cycle Problem "Understanding" DelayedProblem "Understanding" Delayed
  20. 20. Basic, Fortran, MACSYMA, etc. LanguagesBasic, Fortran, MACSYMA, etc. Languages FormulateFormulate ProblemProblem Approximations,Approximations, Methods, etc.Methods, etc. Programming ofProgramming of Reduced ProblemReduced Problem Debug Problem,Debug Problem, Math, & ProgramMath, & Program EngineerEngineer MathematicianMathematician ProgrammerProgrammer AllAll Rapid Prototyping for AdaptiveRapid Prototyping for Adaptive EngineeringEngineering
  21. 21. Rapid PrototypingRapid Prototyping for Adaptive Engineeringfor Adaptive Engineering Basic, Fortran, MACSYMA, etc. Languages (Cont.)Basic, Fortran, MACSYMA, etc. Languages (Cont.) Engineering:Engineering: Quickly FrozenQuickly Frozen Commitment:Commitment: LargeLarge Cost:Cost: HighHigh Delay:Delay: LongLong Algebra Level SummaryAlgebra Level Summary
  22. 22. FC Technology HistoryFC Technology History Late 1960's - Pioneered - TRW / NASALate 1960's - Pioneered - TRW / NASA Mid 1970's - Validated - PROSE, Inc.Mid 1970's - Validated - PROSE, Inc. Late 1980's - Migrated - Du PontLate 1980's - Migrated - Du Pont Today -Today - FortranCalculusFortranCalculus PioneeredPioneered ValidatedValidated MigratedMigrated OperationalOperational
  23. 23. Scientific & EngineeringScientific & Engineering ProductivityProductivity FortranCalculusFortranCalculus A Proven ApproachA Proven Approach ...... Allows Rapid PrototypingAllows Rapid Prototyping Decouples Models from AlgorithmsDecouples Models from Algorithms Allows Interchangeable AlgorithmsAllows Interchangeable Algorithms Accelerates Problem "Understanding"Accelerates Problem "Understanding" Enabled by "Automatic Differentiation"Enabled by "Automatic Differentiation"
  24. 24. Rapid Prototyping for AdaptiveRapid Prototyping for Adaptive EngineeringEngineering Calculus-level Languages: Prose & fortranCalculusCalculus-level Languages: Prose & fortranCalculus FormulateFormulate ProblemProblem Debug ProblemDebug Problem EngineerEngineer EngineerEngineer
  25. 25. Rapid PrototypingRapid Prototyping for Adaptive Engineeringfor Adaptive Engineering FortranCalculus Language (Cont.)FortranCalculus Language (Cont.) Engineering:Engineering: AdaptiveAdaptive Commitment:Commitment: SmallSmall Cost:Cost: LowLow Delay:Delay: ShortShort Calculus Level SummaryCalculus Level Summary
  26. 26. Enabling TechnologyEnabling Technology FortranCalculusFortranCalculus Symbolic Differentiation Evaluated at a PointSymbolic Differentiation Evaluated at a Point GeneratesGenerates Gradient VectorsGradient Vectors Jacobian MatricesJacobian Matrices Hessian MatricesHessian Matrices ... of Any Programmed Model... of Any Programmed Model Automatic DifferentiationAutomatic Differentiation
  27. 27. Enabling TechnologyEnabling Technology FortranCalculusFortranCalculus EnablesEnables Inverse Problem SolvingInverse Problem Solving Nonlinear OptimizationNonlinear Optimization Optimization of Differential EquationsOptimization of Differential Equations Structured Nesting of Optimization AlgorithmStructured Nesting of Optimization Algorithmss Automatic Differentiation (Cont.)Automatic Differentiation (Cont.)
  28. 28. FortranCalculusFortranCalculus,, a calculus level languagea calculus level language Increases Science/Engineering ProductivityIncreases Science/Engineering Productivity Allows Rapid Model PrototypingAllows Rapid Model Prototyping Reduces Costly Problem/Solution CycleReduces Costly Problem/Solution Cycle Accelerates Problem "Understanding"Accelerates Problem "Understanding" Proven Concept Since 1968Proven Concept Since 1968 Provides a Competitive Technical EdgeProvides a Competitive Technical Edge SummarySummary
  29. 29. Explicit & Implicit EquationsExplicit & Implicit Equations Inverse & Optimization ProblemsInverse & Optimization Problems Differential EquationsDifferential Equations IVP & BVP ProblemsIVP & BVP Problems Limits & ConstraintsLimits & Constraints FortranCalculusFortranCalculus LanguageLanguage Example CodeExample Code AgendaAgenda
  30. 30. Complete Example CodeComplete Example Code global allglobal all problem rocket ! three stage rocket design optimizationproblem rocket ! three stage rocket design optimization dimension spi(3),spivac(3),tburn(3),thrust(3),xip(3),wprop(3),dimension spi(3),spivac(3),tburn(3),thrust(3),xip(3),wprop(3), & ratio(3),wstage(3),strfac(3),delv(3),g(2)& ratio(3),wstage(3),strfac(3),delv(3),g(2) thrust(1)=350 : thrust(2)=1500 : thrust(3)=4100thrust(1)=350 : thrust(2)=1500 : thrust(3)=4100 tburn(1)=110 : tburn(2)=100 : tburn(3)=180tburn(1)=110 : tburn(2)=100 : tburn(3)=180 xip(1)=5d-3 : xip(2)=0 : xip(3)=0xip(1)=5d-3 : xip(2)=0 : xip(3)=0 spivac(1)=315 : spivac(2)=315 : spivac(3)=315spivac(1)=315 : spivac(2)=315 : spivac(3)=315 FINDFIND thrust(1),thrust(2),tburn(2),tburn(3); in stages;thrust(1),thrust(2),tburn(2),tburn(3); in stages; * by Hera; reporting dlvtot,tbtot; to minimize weight* by Hera; reporting dlvtot,tbtot; to minimize weight endend model stagesmodel stages FindFind thrust(3),tburn(1); in eqns; by Ajax; to match gthrust(3),tburn(1); in eqns; by Ajax; to match g endend model eqnsmodel eqns data gc,wpayld,delvip,tbip/32.174,50,2.8e4,400/data gc,wpayld,delvip,tbip/32.174,50,2.8e4,400/ dlvtot=0 : tbtot=0dlvtot=0 : tbtot=0 weight=wpayldweight=wpayld do 10 i=1,3do 10 i=1,3 spi(i)=spivac(i)*(1-xip(i))spi(i)=spivac(i)*(1-xip(i)) wprop(i)=thrust(i)*tburn(i)/spi(i)wprop(i)=thrust(i)*tburn(i)/spi(i) wstage(i)=0.0234*thrust(i)+wprop(i)+1.255*wprop(i)**0.704+4wstage(i)=0.0234*thrust(i)+wprop(i)+1.255*wprop(i)**0.704+4 strfac(i)=wprop(i)/wstage(i)strfac(i)=wprop(i)/wstage(i) weight=weight+wstage(i)weight=weight+wstage(i) ratio(i)=weight/(weight-wprop(i))ratio(i)=weight/(weight-wprop(i)) delv(i)=gc*spi(i)*log(ratio(i))delv(i)=gc*spi(i)*log(ratio(i)) dlvtot=dlvtot+delv(i)dlvtot=dlvtot+delv(i) tbtot=tbtot+tburn(i)tbtot=tbtot+tburn(i) 10 continue10 continue g(1)=dlvtot-delvip ! total delta v constraintg(1)=dlvtot-delvip ! total delta v constraint g(2)=tbtot-tbipg(2)=tbtot-tbip ! total burn time constraint! total burn time constraint endend Math Model
  31. 31. Example Convergence ReportExample Convergence Report o o oo o o LOOP NUMBER .... [INITIAL] 5 6LOOP NUMBER .... [INITIAL] 5 6 UNKNOWNSUNKNOWNS A ( 1) 1.000000E+00 4.432149E-01 3.737358E-01A ( 1) 1.000000E+00 4.432149E-01 3.737358E-01 B ( 1) 1.000000E+00 4.040783E+00 4.284183E+00B ( 1) 1.000000E+00 4.040783E+00 4.284183E+00 C ( 1) 1.230000E+02 4.305000E+02 4.920000E+02C ( 1) 1.230000E+02 4.305000E+02 4.920000E+02 OBJECTIVEOBJECTIVE ERRSUM 8.189812E+00ERRSUM 8.189812E+00 4.870502E-02 3.879211E-024.870502E-02 3.879211E-02 o o oo o o
  32. 32. Explicit EquationExplicit Equation o o oo o o FindFind A,B,CA,B,C; In; In EngineEngine; to ...; to ... o o oo o o ModelModel EngineEngine Y = Function( X;Y = Function( X; A,B,CA,B,C)) End ModelEnd Model Math Model
  33. 33. Implicit EquationImplicit Equation o o oo o o FindFind A,B,CA,B,C; In; In EngineEngine; to; to MatchMatch GG o o oo o o ModelModel EngineEngine GG = Y - Function( X, Y;= Y - Function( X, Y; A,B,CA,B,C)) End ModelEnd Model
  34. 34. Inverse ProblemInverse Problem o o oo o o Ydesired = 123.456 ! target valueYdesired = 123.456 ! target value FindFind A,B,CA,B,C; In; In EngineEngine; to; to MatchMatch GG o o oo o o ModelModel EngineEngine Y = Function( X;Y = Function( X; A,B,CA,B,C)) GG = Ydesired - Y= Ydesired - Y End ModelEnd Model
  35. 35. Optimization ProblemOptimization Problem o o oo o o FindFind A,B,CA,B,C; In; In EngineEngine; to; to MinimizeMinimize GG o o oo o o ModelModel EngineEngine GG = Y - Function( X;= Y - Function( X; A,B,CA,B,C)) End ModelEnd Model
  36. 36. Explicit Differental EquationsExplicit Differental Equations o o oo o o InitiateInitiate ISISISIS; For; For EngineEngine;; Equations Y2Dot/YDot, YDot/Y; ...Equations Y2Dot/YDot, YDot/Y; ... o o oo o o IntegrateIntegrate EngineEngine; By; By ISISISIS o o oo o o ModelModel EngineEngine Y2DotY2Dot = Function( YDot, Y= Function( YDot, Y)) End ModelEnd Model
  37. 37. Implicit Differental EquationsImplicit Differental Equations Initiate ...Initiate ... o o oo o o IntegrateIntegrate EngineEngine; By; By ISISISIS o o oo o o ModelModel EngineEngine FindFind Y2DotY2Dot; In IDE; To Match; In IDE; To Match GG End ModelEnd Model Model IDEModel IDE GG == Y2DotY2Dot -- Fun(Fun(Y2DotY2Dot,, YDot, YYDot, Y)) End ModelEnd Model
  38. 38. Initial Value ProblemsInitial Value Problems Explicit EquationsExplicit Equations InitiateInitiate YDot = 123.456 : Y2Dot = 234.567 : Y3Dot = ...YDot = 123.456 : Y2Dot = 234.567 : Y3Dot = ... ! Initial Values! Initial Values o o oo o o IntegrateIntegrate ...... o o oo o o Model ...Model ... YnDotYnDot = Function( Yn= Function( Yn11Dot, ... , YDot, YDot, ... , YDot, Y)) End ModelEnd Model
  39. 39. Initial Value ProblemsInitial Value Problems Implicit EquationsImplicit Equations o o oo o o Integrate ...Integrate ... o o oo o o FindFind YnDot; ...; To MatchYnDot; ...; To Match GG o o oo o o Model ...Model ... GG = YnDot - Function( YnDot, ... , YDot, Y= YnDot - Function( YnDot, ... , YDot, Y)) End ModelEnd Model
  40. 40. Boundary Value ProblemsBoundary Value Problems Explicit EquationsExplicit Equations o o oo o o FindFind YDot0, ... To MatchYDot0, ... To Match HH o o oo o o IntegrateIntegrate ...... o o oo o o HH = (Y0 - Y0_desired)**2 += (Y0 - Y0_desired)**2 + (Ylast - Ylast_desired)**2 ! boundary values(Ylast - Ylast_desired)**2 ! boundary values
  41. 41. Boundary Value ProblemsBoundary Value Problems Implicit EquationsImplicit Equations o o oo o o FindFind YDot0, ...; To MatchYDot0, ...; To Match HH o o oo o o IntegrateIntegrate ...... o o oo o o FindFind YnDot; ...; To MatchYnDot; ...; To Match GG o o oo o o Model ...Model ... GG = YnDot - Function( YnDot, ... , YDot, Y= YnDot - Function( YnDot, ... , YDot, Y)) End ModelEnd Model
  42. 42. Limits & Inequality ConstraintsLimits & Inequality Constraints o o oo o o FindFind ... With Lowers ... And Uppers ... Holding ...... With Lowers ... And Uppers ... Holding ... o o oo o o
  43. 43. TweakTweak TweakTweak TweakTweak o o oo o o FindFind E,F,GE,F,G ...... ! Add to any problem! Add to any problem o o oo o o ! in order to tweak! in order to tweak E,F,GE,F,G ......
  44. 44. Nested Calculus ProcessesNested Calculus Processes o o oo o o FindFind ...... o o oo o o IntegrateIntegrate ...... o o oo o o IntegrateIntegrate ...... o o oo o o FindFind ......
  45. 45. How are problems solved?How are problems solved? o o oo o o FindFind ...... byby 'Solver''Solver' o o oo o o 'Solver' is a numerical method using'Solver' is a numerical method using Automatic Differention to calculateAutomatic Differention to calculate necessary derivatives. Thenecessary derivatives. The available solvers are in a MCavailable solvers are in a MC library; e.g. Ajax, Mars, Neptune,library; e.g. Ajax, Mars, Neptune, etc.etc.
  46. 46. Objective-Driven EngineeringObjective-Driven Engineering OptimizationsOptimizations withinwithin OptimizationOptimization A nesting example Optimal Designs EnterpriseOptimal Designs Enterprise goal-driven.netgoal-driven.net
  47. 47. Automotive Mfg. CompanyAutomotive Mfg. Company Optimization LevelsOptimization Levels Optimal Designs EnterpriseOptimal Designs Enterprise Level 1 Company Company Design Dept. Mfg. Dept. Engine Mfg. Power Train Engine Design Power Train Level 2 Dept.s Level 3 Groups
  48. 48. Design Department'sDesign Department's Engine Design CodeEngine Design Code (Get Iron, Rubber, etc values from Co. database)(Get Iron, Rubber, etc values from Co. database) FindFind EngineSizeEngineSize, etc; In, etc; In EngineEngine; to Minimize; to Minimize PollutionPollution; and Maximize; and Maximize GasEfficiencyGasEfficiency...... o o oo o o ModelModel EngineEngine HorsePower = ... Iron ...HorsePower = ... Iron ... EngineSizeEngineSize ...... GasEfficiencyGasEfficiency = ... TerrainType ... HorsePower= ... TerrainType ... HorsePower PollutionPollution = ... CarWeight ... HorsePower ...= ... CarWeight ... HorsePower ... GasInEfficiency ... RubberGasInEfficiency ... Rubber End ModelEnd Model Level 3
  49. 49. Design Department's CodeDesign Department's Code (Get Iron, Rubber, etc values from Co. database)(Get Iron, Rubber, etc values from Co. database) FindFind CarWeightCarWeight, etc; In, etc; In CarDesignCarDesign; to Minimize; to Minimize CarPollutionCarPollution; and Maximize; and Maximize CarSafetyCarSafety ...... o o oo o o ModelModel CarDesignCarDesign Call EngineDesignCall EngineDesign !! Another OptimizationAnother Optimization Call PowerTrainCall PowerTrain !! Another OptimizationAnother Optimization CarPollutionCarPollution = ...= ... CarWeightCarWeight ... HorsePower ...... HorsePower ... GasInEfficiency ... Rubber ... CoalGasInEfficiency ... Rubber ... Coal CarSafetyCarSafety = ... Iron ... CarWeight ...= ... Iron ... CarWeight ... End ModelEnd Model Level 2
  50. 50. Company's CodeCompany's Code (Get present Iron, Rubber, etc values from Co. database)(Get present Iron, Rubber, etc values from Co. database) FindFind IronIron,, RubberRubber, etc; In, etc; In CompanyCompany; to Minimize; to Minimize Time2MarketTime2Market; and Maximize; and Maximize ProfitProfit ...... o o oo o o ModelModel CompanyCompany Call DesignCall Design !! Another OptimizationAnother Optimization Call ManufacturingCall Manufacturing !! Another OptimizationAnother Optimization Call SalesCall Sales !! Another OptimizationAnother Optimization Time2MarketTime2Market = ...= ... IronIron ...... ProfitProfit = ...= ... IronIron ...... RubberRubber ... Coal ...... Coal ... End ModelEnd Model Level 1
  51. 51. Code for OptimizationsCode for Optimizations Level 3 Code ... GroupsLevel 3 Code ... Groups Most Important ... fundamental equationsMost Important ... fundamental equations Can Run IndependentlyCan Run Independently Contains Math Models to Simulate Design/Mfg.Contains Math Models to Simulate Design/Mfg. Level 2 Code ... Dept.sLevel 2 Code ... Dept.s Runs Latest Level 3 code tooRuns Latest Level 3 code too Level 1 Code ... CompanyLevel 1 Code ... Company Runs Latest of All LevRuns Latest of All Levelsels All L 3s All L 2s L 1 Some L 3s l L 2 1 L 3 Easy to UpdateEasy to Update
  52. 52. Objective-Driven EmployeesObjective-Driven Employees forfor Entire CompanyEntire Company OptimizationOptimization ofof OptimizationsOptimizations
  53. 53. What are you building?What are you building? Mr. Arithmetic Mr. Algebra Mr. CalculusMr. Arithmetic Mr. Algebra Mr. Calculus ------------------- --------------- ----------------------------------- --------------- ---------------- Slide Rule Simulate OptimizeSlide Rule Simulate Optimize
  54. 54. ConclusionConclusion UseUse FortranCalculusFortranCalculus to improveto improve Math ModelsMath Models Design ProductivityDesign Productivity Manufacturing TolerancesManufacturing Tolerances Optimal Designs EnterpriseOptimal Designs Enterprise goal-driven.netgoal-driven.net

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