Examples
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Engineering
Non-linear deflection of a flexible cantilever
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Batch chemical reactor
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Lateral force developed by a tire, using an early Pacejka model.
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NASA's Atmospheric Model (SI Units)
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Using an electromagnetic shaker to drive a single degree of freedom system
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Simple Estimates of a single prop, naturally aspirated, aircraft's performance
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Ramp Design - testing for max allowable bending moment and deflection (US Customary Units)
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Column Design - based on AISC Manual of Steel Construction (US Customary Units)
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Engine Heat Rejection Calcs - good example of working with relative temperature differences (US Customary Units)
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Calculate the Area Properties of Composite Rectangular Areas (US Customary Units)
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Calculate the Area Properties of Composite Rectangular Areas (US Customary Units)
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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)
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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.
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Financial
Financial Equations
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Numerical methods
Newton-Raphson method for solving equations (G. Urroz)
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Nonlinear system of algebraic equations, Broyden's method
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Lagrange interpolation polynomials
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Newton interpolation polynomials (forward finite difference)
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Newton interpolation polynomials (backward finite difference)
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Data fitting (single independent var., linear on parameters)
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Data fitting (multiple, linear on parameters)
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Simpson integration with Richardson extrapolation
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Gauss-Legendre integration method
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Second order linear ODE - finite difference method
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Runge-Kutta 4th-order for single 1st-order ODE (G. Urroz)
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Runge-Kutta 4th-order for systems of ODEs (G. Urroz)
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Runge-Kutta 4th-order for single 2nd-order ODE (G. Urroz)
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Runge-Kutta 5th-order adaptive - also "Batch chemical reactor" (see "Engineering", above)
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Graphing implicit functions of 2 variables: f(x,y)=K (where K is a constant)
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Statistics
Normal distribution
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Student t-distribution
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Chi-squared distribution
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F-distribution
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Examples of probability distributions (G. Urroz)
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Data Manipulation and Interpolation
Importing data from csv files (author:
B. Towler
)
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Bi-linear Interpolation (author:
B. Towler
)
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Civil Engineering Hydraulics/Fluid Mechanics
From college courses by
G. Urroz
CEE Fluid Mechanics Test 1: | Prob 1:
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| Prob 2:
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| Prob 3:
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|
CEE Fluid Mechanics Test 2:
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| CEE Fluid Mechanics Test 3:
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Video examples of calculations with units for hydraulics:
See Part 2 SMath Studio
\
CEE 3510 HYDRAULICS :
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
B. Towler
Vertical Velocity Distribution in a Hydraulically Smooth Open Channel:
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Hydraulic Geometry of Rivers:
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Weir Flow using the Rehbock Equation:
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Swamee-Jain Friction Factor Equation for Pipe Flow:
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Structural Engineering
Calculate the Area Properties of Composite Rectangular Areas (US Customary Units)
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Non-linear deflection of a flexible cantilever
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zip
Ramp Design - testing for max allowable bending moment and deflection (US Customary Units)
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zip
Column Design - based on AISC Manual of Steel Construction (US Customary Units)
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Design of Reinforced Concrete Beams according to NZS 3101-95 (SI Units)
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Steel End-Plate Connection Design - adapted from Krishnamurthy 1978 (US Units)
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Design of Reinforced Concrete Slab - Flexural Reinforcement (US Units)
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Single span moment & shear envelopes for HL-93 loading using influence lines
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Design of a single span simply supported timber beam according to EN 1995-Eurocode 5 (SI units)
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