A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). Mathematical models are also used in music, linguistics and philosophy (for example, intensively in analytic philosophy).
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Modeling (Dynamics)
This topic includes the following resources and journeys:
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17 items
DC Motor Speed: System Modeling
Beginner
Project
Theory
This examples walks through modeling a simple DC motor in MATLAB.
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What Are Dynamic Models? Chapter 1 from Dynamic Models in Biology
Beginner
Book
Theory
Throughout this book we use a wide-ranging set of case studies to illustrate different aspects of models and modeling. In this introductory chapter we describe and give examples of different...
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Modeling Physical Systems, An Overview
7 min
Beginner
Video
Theory
This video sets the stage for the topics that I want to cover over the next month or two. This is an overview of how you go from a physical system to a linear model where you can design a...
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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields...
Beginner
Book
Theory
From the reviews: "This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review...
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Autodesk Tinkercad
Beginner
App
Application
Tinkercad is a free, easy-to-use web app that equips the next generation of designers and engineers with the foundational skills for innovation: 3D design, electronics, and coding!
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Dynamic Modeling in Process Control
14 min
Beginner
Video
Theory
I'll show you how we can build the dynamic models necessary to derive process transfer functions as an introduction to process control.
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Building a Matlab/Simulink Model of an Aircraft: the Research Civil Aircraft...
51 min
Beginner
Video
Application
In this video we implement the RCAM model as a Matlab script that is called from a Simulink model. The result is a fully encapsulated Simulink model of a no...
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Second Order Dynamics Example
4 min
Beginner
Video
Theory
How will a second order process respond in the time domain when subjected to a unit step input? What other behaviors can we expect to see and why? Tune in to...
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Trimming a Model of a Dynamic System Using Numerical Optimization
60 min
Beginner
Video
Theory
In this video we show how to find a trim point of a dynamic system using numerical optimization techniques. We generate a cost function that corresponds to ...
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Second Order Dynamics
3 min
Beginner
Video
Theory
A crash course overview on second order dynamics in the frequency domain, what the key parameters are, and why they matter.
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Equations of Motion for a Planar Vehicle
43 min
Beginner
Video
Theory
In this video we outline equations of motion for a simple planar vehicle. This model is suitable for vehicles such as boats or hovercraft that that are rest...
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Second Order Dynamics in Process Control
17 min
Beginner
Video
Theory
How do we simulate two first order transfer functions in series, a inherently second order system, or two coupled differential equations? Tune in to find out!
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First Order Dynamics in Process Control
15 min
Beginner
Video
Theory
An overview on the identification and behavior of first order dynamics in process control.
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Manipulating Aerodynamic Coefficients
25 min
Beginner
Video
Theory
In this video we discuss some potential problems you may encounter when attempting to perform operations with dimensionless aerodynamic coefficients such as ...
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Dynamic Behavior and Input Types in Process Control
13 min
Beginner
Video
Theory
An introduction to the four types of dynamic behavior and five types of inputs (step, ramp, pulse, impulse, and sinusoidal), and why transfer functions are u...
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Predicting Second Order Transfer Function Behavior
4 min
Beginner
Video
Theory
Given a second order transfer function, I'll cover how we can predict the system behavior and derive the appropriate time constants and damping coefficient.
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A Nonlinear, 6 DOF Dynamic Model of an Aircraft: the Research Civil Aircraft...
103 min
Beginner
Video
Theory
In this video we develop a dynamic model of an aircraft by describing forces and moments generated by aerodynamic, propulsion, and gravity that act on the ai...
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