Examples

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==Engineering==

* Non-linear deflection of a flexible cantilever [{UP}Examples/finger4.pdf|pdf] [{UP}Examples/finger4.zip|zip]
* Batch chemical reactor [{UP}Examples/batchreactor.pdf|pdf] [{UP}Examples/batchreactor.zip|zip]
* Lateral force developed by a tire, using an early Pacejka model. [{UP}Examples/pacejka2.pdf|pdf] [{UP}Examples/pacejka2.zip|zip]
* NASA's Atmospheric Model (SI Units) [{UP}Examples/NASA_atmosphere.pdf|pdf] [{UP}Examples/NASA_atmosphere.zip|zip]
* Using an electromagnetic shaker to drive a single degree of freedom system [{UP}Examples/lingV456.pdf|pdf] [{UP}Examples/ling.zip|zip]
* Simple Estimates of a single prop, naturally aspirated, aircraft's performance [{UP}Examples/aircraftperformance_sm3.pdf|pdf] [{UP}Examples/ap.zip|zip]
* Ramp Design - testing for max allowable bending moment and deflection (US Customary Units) [{UP}Examples/Engineering Calculations - Ramp Design.pdf|pdf] [{UP}Examples/Engineering Calculations - Ramp Design.zip|zip]
* Column Design - based on AISC Manual of Steel Construction (US Customary Units) [{UP}Examples/Engineering Calculations - Column Design.pdf|pdf] [{UP}Examples/Engineering Calculations - Column Design.zip|zip]
* Engine Heat Rejection Calcs - good example of working with relative temperature differences (US Customary Units) [{UP}Examples/Engine Heat Rejection Calcs.pdf|pdf] [{UP}Examples/Engine Heat Rejection Calcs.zip|zip]
* Calculate the Area Properties of Composite Rectangular Areas (US Customary Units) [{UP}Examples/Calc Area Properties of Composite Rectangular Areas.pdf|pdf] [{UP}Examples/Calc Area Properties of Composite Rectangular Areas.zip|zip]
* Calculate the Area Properties of Composite Rectangular Areas (US Customary Units) [{UP}Examples/Calc Area Properties of Composite Rectangular Areas.pdf|pdf] [{UP}Examples/Calc Area Properties of Composite Rectangular Areas.zip|zip]
* Calculate properties of generic polygons (perimeter, area, centroid, second moment of area, radius of gyration, elastic section modulus, plastic section modulus, orientation of principal axes of inertia, principal moments of inertia, radii of gyration about principal axes of inertia); multilanguage (ENG/ITA) [{UP}Examples%2fPolyProperties.pdf|pdf] [{UP}Examples%2fPolyProperties_2013.02.01.sm.zip|zip]
* Electrical engineering - calculate current, voltage, real, reactive and apparent power in an AC circuit using the complex domain and using custom units for AC power quantities. [{UP}Examples/ElecEngExample.pdf|pdf] [{UP}Examples/ElecEngExample.zip|zip]

==Financial==

* Financial Equations [{UP}Examples/financial.pdf|pdf] [{UP}Examples/financial.zip|zip] 

==Numerical methods==

* Newton-Raphson method for solving equations (G. Urroz) [{UP}Examples/NewtonRaphsonApplications.pdf|pdf] [{UP}Examples/NewtonRaphsonApplications.zip|zip]
* Nonlinear system of algebraic equations, Broyden's method [{UP}Examples/broyden-method.pdf|pdf] [{UP}Examples/broyden-method.zip|zip]
* Lagrange interpolation polynomials [{UP}Examples/lagrange.pdf|pdf] [{UP}Examples/lagrange.zip|zip]
* Newton interpolation polynomials (forward finite difference) [{UP}Examples/newtoninterp.pdf|pdf] [{UP}Examples/newtoninterp.zip|zip]
* Newton interpolation polynomials (backward finite difference) [{UP}Examples/newtoninterpb.pdf|pdf] [{UP}Examples/newtoninterpb.zip|zip]
* Data fitting (single independent var., linear on parameters) [{UP}Examples/linfit.pdf|pdf] [{UP}Examples/linfit.zip|zip]
* Data fitting (multiple, linear on parameters) [{UP}Examples/linfit_multiple.pdf|pdf] [{UP}Examples/linfit_multiple.zip|zip]
* Simpson integration with Richardson extrapolation [{UP}Examples/simpsonrichardson.pdf|pdf] [{UP}Examples/simpsonrichardson.zip|zip]
* Gauss-Legendre integration method [{UP}Examples/gauss-legendre.pdf|pdf] [{UP}Examples/gauss-legendre.zip|zip]
* Second order linear ODE - finite difference method [{UP}Examples/finitedifferences.pdf|pdf] [{UP}Examples/finitedifferences.zip|zip]
* Runge-Kutta 4th-order for single 1st-order ODE (G. Urroz) [{UP}Examples/RK4SingleEquation.pdf|pdf] [{UP}Examples/RK4SingleEquation.zip|zip]
* Runge-Kutta 4th-order for systems of ODEs (G. Urroz) [{UP}Examples/RK4SystemEquations.pdf|pdf] [{UP}Examples/RK4SystemEquations.zip|zip]
* Runge-Kutta 4th-order for single 2nd-order ODE (G. Urroz) [{UP}Examples/RK4-2ndOrderODE.pdf|pdf] [{UP}Examples/RK4-2ndOrderODE.zip|zip]
* Runge-Kutta 5th-order adaptive - also "Batch chemical reactor" (see "Engineering", above) [{UP}Examples/batchreactor.pdf|pdf] [{UP}Examples/batchreactor.zip|zip]
* Graphing implicit functions of 2 variables: <esc>&nbsp;</esc>f(x,y)=K (where K is a constant) [{UP}Examples/ImplicitFunctionGrapher.pdf|pdf] [{UP}Examples/ImplicitFunctionGrapher.zip|zip]

==Statistics==

* Normal distribution [{UP}Examples/normaldist.pdf|pdf] [{UP}Examples/normaldist.zip|zip] 
* Student t-distribution [{UP}Examples/studentdist.pdf|pdf] [{UP}Examples/studentdist.zip|zip] 
* Chi-squared distribution [{UP}Examples/chisquareddist.pdf|pdf] [{UP}Examples/chisquareddist.zip|zip] 
* F-distribution [{UP}Examples/fdist.pdf|pdf] [{UP}Examples/fdist.zip|zip] 
* Examples of probability distributions (G. Urroz) [{UP}Examples/CEE3030Fall2009Test02Solution.pdf|pdf] [{UP}Examples/CEE3030Fall2009Test02Solution.zip|zip]

==Data Manipulation and Interpolation==

* Importing data from csv files (author:'''[http://works.bepress.com/brett_towler/|B. Towler]''') [{UP}Examples/importDataCSV.pdf|pdf] [{UP}Examples/importDataCSV.zip|zip] 
* Bi-linear Interpolation (author:'''[http://works.bepress.com/brett_towler/|B. Towler]''') [{UP}Examples/BilinearInterpolation.pdf|pdf] [{UP}Examples/BilinearInterpolation.zip|zip]

==Civil Engineering Hydraulics/Fluid Mechanics==
From college courses by '''[http://www.neng.usu.edu/cee/faculty/gurro/Classes/Classes_Main.htm|G. Urroz]'''
* CEE Fluid Mechanics Test 1: | Prob 1: [{UP}Examples/CEE3500Test01Problem01.pdf|pdf] [{UP}Examples/CEE3500Test01Problem01.zip|zip] | Prob 2: [{UP}Examples/CEE3500Test01Problem02.pdf|pdf] [{UP}Examples/CEE3500Test01Problem02.zip|zip] | Prob 3: [{UP}Examples/CEE3500Test01Problem03.pdf|pdf] [{UP}Examples/CEE3500Test01Problem03.zip|zip] |
* CEE Fluid Mechanics Test 2: [{UP}Examples/CEE3500Test02Solutions.pdf|pdf] [{UP}Examples/CEE3500Test02Solutions.zip|zip] | CEE Fluid Mechanics Test 3: [{UP}Examples/CEE3500Test03Solutions.pdf|pdf] [{UP}Examples/CEE3500Test03Solutions.zip|zip]
* Video examples of calculations with units for hydraulics: [http://www.neng.usu.edu/cee/faculty/gurro/Classes/ClassNotesAllClasses/CEE3510/LabFiles/CL01_ComputationalTools01.htm | See Part 2 SMath Studio]\
* CEE 3510 HYDRAULICS : [http://www.neng.usu.edu/cee/faculty/gurro/Classes/Classes_Spring2012/CEE3510_Spring2012/CEE3510_Schedule.htm|Spring 2012 Schedule] - Each link in the Schedule contains links to examples with SMath Studio solutions for pipe flow, pump-pipeline systems, pipe networks, pumps, and open-channel flow (some examples include solutions using EPANET and HEC-RAS)

Developed by '''[http://works.bepress.com/brett_towler/|B. Towler]'''
* Vertical Velocity Distribution in a Hydraulically Smooth Open Channel: [{UP}Examples/Vertical Velocity Distribution in a Hydraulically Smooth OCF 120704.pdf|pdf] [{UP}Examples/Vertical Velocity Distribution in a Hydraulically Smooth OCF 120704.zip|zip]
* Hydraulic Geometry of Rivers: [{UP}Examples/Hydraulic Geometry of Rivers 120704.pdf|pdf] [{UP}Examples/Hydraulic Geometry of Rivers 120704.zip|zip]
* Weir Flow using the Rehbock Equation: [{UP}Examples/Weir Flow using the Rehbock Equation 120704.pdf|pdf] [{UP}Examples/Weir Flow using the Rehbock Equation 120704.zip|zip]
* Swamee-Jain Friction Factor Equation for Pipe Flow: [{UP}Examples/Swamee-Jain friction factor for pipe flow 121231.pdf|pdf] [{UP}Examples/Swamee-Jain friction factor for pipe flow 121231.zip|zip]
==Structural Engineering==
* Calculate the Area Properties of Composite Rectangular Areas (US Customary Units) [{UP}Examples/Calc Area Properties of Composite Rectangular Areas.pdf|pdf] [{UP}Examples/Calc Area Properties of Composite Rectangular Areas.zip|zip]
* Non-linear deflection of a flexible cantilever [{UP}Examples/finger4.pdf|pdf] [{UP}Examples/finger4.zip|zip]
* Ramp Design - testing for max allowable bending moment and deflection (US Customary Units) [{UP}Examples/Engineering Calculations - Ramp Design.pdf|pdf] [{UP}Examples/Engineering Calculations - Ramp Design.zip|zip]
* Column Design - based on AISC Manual of Steel Construction (US Customary Units) [{UP}Examples/Engineering Calculations - Column Design.pdf|pdf] [{UP}Examples/Engineering Calculations - Column Design.zip|zip]
* Design of Reinforced Concrete Beams according to NZS 3101-95 (SI Units) [{UP}Examples%2fRCBeamDesignNZS3101.pdf|pdf] [{UP}Examples%2fRCBeamDesignNZS3101.zip|zip]
* Steel End-Plate Connection Design - adapted from Krishnamurthy 1978 (US Units) [{UP}EndPlateConnectionKrishnamurthy1978.pdf|pdf] [{UP}EndPlateConnectionKrishnamurthy1978.zip|zip]
* Design of Reinforced Concrete Slab - Flexural Reinforcement (US Units) [{UP}DesignReinforcedConcreteSlabACI318.pdf|pdf] [{UP}DesignReinforcedConcreteSlabACI318.zip|zip]
* Single span moment & shear envelopes for HL-93 loading using influence lines [{UP}HL-93.pdf|pdf] [{UP}HL-93.zip|zip]
* Design of a single span simply supported timber beam according to EN 1995-Eurocode 5 (SI units) [{UP}Examples/SimplySupportedTimberBeam_Eurocode5_v1.0_all.pdf|pdf] [{UP}Examples/SimplySupportedTimberBeam_Eurocode5_v1.0.zip|zip]