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Computing the user-defined function of the matrix using Sylvester's formula. Example also shows how to get the coefficients of matrix characteristic polynomial with Leverrie-Faddeev method.

Expansion of the user-defined function to Maclaurin series with a custom degree.

Interaktive Einführung in die Grundfunktionen von SMath Studio (Zeitbedarf 2 Stunden)

Analysis of Beam with any number of supports and with any type of loadings.The worksheet requires that the associated Plugin (Structural Beam Analysis Utililty Functions by Redem Legaspi Jr.) be downloaded and enabled from SMath Studio Extension Manager tool.The worksheet does the following: 1.) Plots Beam Diagram, Shear Diagram, Moment Diagram, Deflection 2.) Calculates Support Reactions 3.) Calculates Shear, Moment, and Deflection at any given point.Refer to 'Beam Analysis Input Guide.sm' on how to use the plugin.

Analysis of Beam with any number of supports and with any type of loadings.The worksheet requires that the associated Plugin (Structural Beam Analysis Utililty Functions by Redem Legaspi Jr.) be downloaded and enabled from SMath Studio Extension Manager tool.The worksheet does the following: 1.) Plots Beam Diagram, Shear Diagram, Moment Diagram, Deflection 2.) Calculates Support Reactions 3.) Calculates Shear, Moment, and Deflection at any given point.Refer to 'Beam Analysis Input Guide.sm' on how to use the plugin.

Algorithm of Jacobi matrix generation and the definition of the Jacobian. The user specifies a function to construct Jacobian matrix in the loop using partial derivatives. The last step defines the functions to work with the result. All calculations are performs in symbols, with the possibility to get Symbolic and Numeric results of the algorithm.

Useful functions for working with sets.

Analysis of Beam with any number of supports and with any type of loadings.The worksheet requires that the associated Plugin (Structural Beam Analysis Utililty Functions by Redem Legaspi Jr.) be downloaded and enabled from SMath Studio Extension Manager tool.The worksheet does the following: 1.) Plots Beam Diagram, Shear Diagram, Moment Diagram, Deflection 2.) Calculates Support Reactions 3.) Calculates Shear, Moment, and Deflection at any given point.Refer to 'Beam Analysis Input Guide.sm' on how to use the plugin.

Calculation of the Beam load bearing with two supports to find stresses values of the supports. Worksheet requires to specify any number of the Point and/or Uniform Loads. Every input and output data supports values with Uniits.

Example for the solution of linear systems of equations with positiv definite coefficient matrix, via the Cholesky method

Oscillating cylinder steam engine

Example demonstrates a computation of gravitation acceleration on the Solar System astronomical object's surfaces. Computation performed for eight Solar System planets and for the Sun.

Game to compose colors of the rainbow in correct order.

Extracts the Geometric/Dimensional Properties of AISC (American Institute of Steel Construction) Shapes. The plugin eliminates the need of a look-up table or the use of the Shape Table from AISC Construction Manual.

Nonlinear equations solving with dichotomy method. User defines initial equation to proceed, calculation precision and the range. Program returns root of the initial equation, result accuracy and number of iterations.

Solving of Hermite polynomials. User specifies a power of the polinomial to get it's roots. Additionally represented graphs of first five Hermite functions.

The program of calculation of monolithic reinforced concrete foundations. Calculates the concrete foundation under static loading of an arbitrary number of columns. Creates a graphical representation with the preparation of specifications and steel sampling costs.

Efficient method for computing the greatest common divisor (GCD), also known as the greatest common factor (GCF) or highest common factor (HCF). The algorithm is also called Euclid's algorithm. User fills in two numbers to find out the GCD. This is a simple Numeric example, that uses While Loop inside.

Analysis of Beam with any number of supports and with any type of loadings.The worksheet requires that the associated Plugin (Structural Beam Analysis Utililty Functions by Redem Legaspi Jr.) be downloaded and enabled from SMath Studio Extension Manager tool.The worksheet does the following: 1.) Plots Beam Diagram, Shear Diagram, Moment Diagram, Deflection 2.) Calculates Support Reactions 3.) Calculates Shear, Moment, and Deflection at any given point.Refer to 'Beam Analysis Input Guide.sm' on how to use the plugin.

calculate properties of generic polygons:- perimeter- area- centroid- second moment of area- radii of gyration- elastic section modulus- plastic section modulus- orientation of principal axes of inertia- principal moments of inertia- radius of gyration about principal axes of inertia- shortcuts for easy plots- multilanguage[EN/IT]

Algorithm for conversion Arabic numerals to Roman numerals. User specifies a number using Arabic digits. Program shows a result of conversion in Roman numerals form.

Generates correlated random variables from uncorrelated random variables with normal distribution

Analysis of Beam with any number of supports and with any type of loadings.The worksheet requires that the associated Plugin (Structural Beam Analysis Utililty Functions by Redem Legaspi Jr.) be downloaded and enabled from SMath Studio Extension Manager tool.The worksheet does the following: 1.) Plots Beam Diagram, Shear Diagram, Moment Diagram, Deflection 2.) Calculates Support Reactions 3.) Calculates Shear, Moment, and Deflection at any given point.Refer to 'Beam Analysis Input Guide.sm' on how to use the plugin.

Dieses Beispiel demonstriert die Verwendung der Code-Bausteine hatch und fill in 2D-Diagrammen

Nonlinear equations solving with chord method. User defines initial equation to proceed, calculation precision and the range. Program returns root of the initial equation, result accuracy and number of iterations.

Simpson's rule is a method for numerical integration, the numerical approximation of definite integrals. User specifies function to integrate, interval and the number of iterations. At the end of calculation program controls the result with a built-in numerical integration function.

A collection of text regions with different font-families.

Newton's method of the nonlinear systems of equations solving. This algorithm can be used to solve standalone equation as well. User specifies system of the equations, first approximations of the roots and the result accuracy. While calculation Jacobi matrix is created. Number of steps (iterations) of the While loop also displayed for the analysis purposes.

Analysis of Beam with any number of supports and with any type of loadings.The worksheet requires that the associated Plugin (Structural Beam Analysis Utililty Functions by Redem Legaspi Jr.) be downloaded and enabled from SMath Studio Extension Manager tool.The worksheet does the following: 1.) Plots Beam Diagram, Shear Diagram, Moment Diagram, Deflection 2.) Calculates Support Reactions 3.) Calculates Shear, Moment, and Deflection at any given point.Refer to 'Beam Analysis Input Guide.sm' on how to use the plugin.

Analysis of Beam with any number of supports and with any type of loadings.The worksheet requires that the associated Plugin (Structural Beam Analysis Utililty Functions by Redem Legaspi Jr.) be downloaded and enabled from SMath Studio Extension Manager tool.The worksheet does the following: 1.) Plots Beam Diagram, Shear Diagram, Moment Diagram, Deflection 2.) Calculates Support Reactions 3.) Calculates Shear, Moment, and Deflection at any given point.Refer to 'Beam Analysis Input Guide.sm' on how to use the plugin.

Algorithm of Hesse matrix generation and the definition of the Hessian. The user specifies a function to construct Hessian matrix in the loop using partial derivatives. The last step defines the functions to work with the result. All calculations are performs in symbols, with the possibility to get Symbolic and Numeric results of the algorithm.

Solving of Legendre polynomials defined by Rodrigues' formula. User specifies a power of the polinomial to get it's roots. Additionally represented graphs of first five Legendre functions.

Animation in SMath Studio shown by the example of planetary gear with internal teeth.

Finite-Elemente-Programm für horizontale 2D-Balken mit exakter Darstellung linearer Streckenlasten. Grafische Systemdefinition, Querkraft-, Momenten- und Biegelinie.

Solution of ordinary differential equations using Fifth-order Runge–Kutta method with adaptive step. User defines initial equation coefficients, a Cauchy problem (initial value problem), segment limits and calculations precision. Program converts equation to the system of equations and starts evaluation with the Fifth-order Runge–Kutta method. Algorithm automatically choose the optimal step of the iterations in respect to the specified accuracy. After calculations program represents the graphs of numeric solution using cubic splines interpolation.

Analysis of Beam with any number of supports and with any type of loadings.The worksheet requires that the associated Plugin (Structural Beam Analysis Utililty Functions by Redem Legaspi Jr.) be downloaded and enabled from SMath Studio Extension Manager tool.The worksheet does the following: 1.) Plots Beam Diagram, Shear Diagram, Moment Diagram, Deflection 2.) Calculates Support Reactions 3.) Calculates Shear, Moment, and Deflection at any given point.Refer to 'Beam Analysis Input Guide.sm' on how to use the plugin.

Embedded Plate calculation program. Plate is calculated under static loading. Creates a graphical representation and prepares specifications.

The tridiagonal matrix algorithm (TDMA), also known as the Thomas algorithm, is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations. Example shows how to extract diagonals of the matrix and how to use it to calculate the result.

Solving of Laguerre polynomials. User specifies a power of the polinomial to get it's roots. Additionally represented graphs of first five Laguerre functions.