The MATH and the Vernier System at Faculty of Aeronautics Štefan Berežný, Kristína Budajová, Eva Komová, Henrich Glaser-Opitz TECHNICAL UNIVERSITY IN KOŠICE.

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Presentation transcript:

The MATH and the Vernier System at Faculty of Aeronautics Štefan Berežný, Kristína Budajová, Eva Komová, Henrich Glaser-Opitz TECHNICAL UNIVERSITY IN KOŠICE Faculty of Aeronautics

What is the MATH? Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz The MATH is the software application Open-source For Numerical calculations

Architecture and design Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz Nonlinear equation 2.Definite integration 3.Double definite integration 4.Numerical differentiation 5.System of linear equations 6.Matrix calculation 7.The least mean square approximation

Supported methods Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz 20164

The MATH Graph Dialog Window Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz 20165

Example (two graphs) Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz 20166

Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz Nonlinear equation  Bisection method  Regula Falsi method  Secant method  Newton method  Iteration method

Main window for bisection method Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz 20168

Main window for Regula Falsi method Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz 20169

Main window for Newton method Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz

Main window for Secant method Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz

Main window for Iteration method Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz

Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz Definite integration  Rectangular method  Trapezoid method  Simpson’s method  Monte Carlo Hit of Miss method  Monte Carlo Average method

Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz Main window for Rectangular method

Visualization of definite integration Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz

Main window for Trapezoid method Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz

Main window for Simpson’s method Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz

Definite integration using Monte Carlo Hit or Miss method Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz

Graphical visualization of definite integration using Monte Carlo Hit or Miss method Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz

The least square approximation Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz

Main window for the least square approximation Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz

To summarize, the MATH application is designed to achieve several goals: Provide all calculation steps for each numerical method with easy to use graphical interface; Enable graphical visualization of calculated data as well as the option of exporting acquired data and graphs in suitable formats. Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz

Vernier system Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz Vernier Software & Technology was founded in Portland, Oregon in 1981 in the home of David Vernier, a high- school physics teacher, and Christine Vernier, a local business manager.

Set of measurments Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz Interface LabQuest and software,

Set of measurments Sensors (magnetics field sensor) Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz

Experiments Determination of kinematic viscosity Determination of gravitational acceleration Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz

Determination of kinematic viscosity Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz

Gravitational acceleration Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz

List of instructions for students Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz

To summarize, the main benefits to use of Vernier system are: It improves student understanding of science concepts. It supports engagement in higher order thinking skills, such as analysis, synthesis, and evaluation. It enables students to perform many new experiments and measurements not only in the laboratory. Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz

THANK YOU FOR YOUR ATTENTION Š. Berežný, K. Budajová, E. Komová, H. Glaser-Opitz