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# Engineering

• Non-linear deflection of a flexible cantilever pdf zip
• Batch chemical reactor pdf zip
• Lateral force developed by a tire, using an early Pacejka model. pdf zip
• NASA's Atmospheric Model (SI Units) pdf zip
• Using an electromagnetic shaker to drive a single degree of freedom system pdf zip
• Simple Estimates of a single prop, naturally aspirated, aircraft's performance pdf zip
• Ramp Design - testing for max allowable bending moment and deflection (US Customary Units) pdf zip
• Column Design - based on AISC Manual of Steel Construction (US Customary Units) pdf zip
• Engine Heat Rejection Calcs - good example of working with relative temperature differences (US Customary Units) pdf zip
• Calculate the Area Properties of Composite Rectangular Areas (US Customary Units) pdf zip
• Calculate the Area Properties of Composite Rectangular Areas (US Customary Units) pdf 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) pdf 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. pdf zip

# Numerical methods

• Newton-Raphson method for solving equations (G. Urroz) pdf zip
• Nonlinear system of algebraic equations, Broyden's method pdf zip
• Lagrange interpolation polynomials pdf zip
• Newton interpolation polynomials (forward finite difference) pdf zip
• Newton interpolation polynomials (backward finite difference) pdf zip
• Data fitting (single independent var., linear on parameters) pdf zip
• Data fitting (multiple, linear on parameters) pdf zip
• Simpson integration with Richardson extrapolation pdf zip
• Gauss-Legendre integration method pdf zip
• Second order linear ODE - finite difference method pdf zip
• Runge-Kutta 4th-order for single 1st-order ODE (G. Urroz) pdf zip
• Runge-Kutta 4th-order for systems of ODEs (G. Urroz) pdf zip
• Runge-Kutta 4th-order for single 2nd-order ODE (G. Urroz) pdf zip
• Runge-Kutta 5th-order adaptive - also "Batch chemical reactor" (see "Engineering", above) pdf zip
• Graphing implicit functions of 2 variables:  f(x,y)=K (where K is a constant) pdf zip

# Statistics

• Normal distribution pdf zip
• Student t-distribution pdf zip
• Chi-squared distribution pdf zip
• F-distribution pdf zip
• Examples of probability distributions (G. Urroz) pdf zip

# Data Manipulation

• Importing data from csv files pdf zip

# Civil Engineering Hydraulics/Fluid Mechanics

From college courses by G. Urroz
• CEE Fluid Mechanics Test 1: | Prob 1: pdf zip | Prob 2: pdf zip | Prob 3: pdf zip |
• CEE Fluid Mechanics Test 2: pdf zip | CEE Fluid Mechanics Test 3: pdf zip
• 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 Brett Towler
• Vertical Velocity Distribution in a Hydraulically Smooth Open Channel: pdf zip
• Hydraulic Geometry of Rivers: pdf zip
• Weir Flow using the Rehbock Equation: pdf zip
• Swamee-Jain Friction Factor Equation for Pipe Flow: pdf zip

# Structural Engineering

• Calculate the Area Properties of Composite Rectangular Areas (US Customary Units) pdf zip
• Non-linear deflection of a flexible cantilever pdf zip
• Ramp Design - testing for max allowable bending moment and deflection (US Customary Units) pdf zip
• Column Design - based on AISC Manual of Steel Construction (US Customary Units) pdf zip
• Design of Reinforced Concrete Beams according to NZS 3101-95 (SI Units) pdf zip
• Steel End-Plate Connection Design - adapted from Krishnamurthy 1978 (US Units) pdf zip
• Design of Reinforced Concrete Slab - Flexural Reinforcement (US Units) pdf zip
• Single span moment & shear envelopes for HL-93 loading using influence lines pdf zip

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