Introduction
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I would say to many of friends and juniors working in engineering area "If you are good at two topics, Matrix and Differential Equations, you would be good at ANY of the engineering field." Of course, just being good at math would not automatically lead you to success in the field, but we cannot deny the fact that mathematical understanding is very crucial in most of engineering.
In this page, I would like to explain the basic concept of differential equation and it's applications as easy as I can do, but in some cases it is hard to avoid tackling the mathematical equations directly.
- What is Differential Equation ?
- Various ways of Representation
- Difference between Differential Equation and Algebraic Equation
- Terminology and Classification
- Why Differential Equation ?
- Modeling Overview
- How to get a Governing Equation ?
- Modeling Building Blocks
- Mechanical Building Block : Spring
- Mechanical Building Block : Damper
- Mechanical Building Block : Mass
- Mechanical Building Block : Spring-Mass
- Mechanical Building Block : Spring-Damper
- Mechanical Building Block : Spring-Mass-Damper
- Mechanical Building Block : Rotational Bar
- Mechanical Building Block : Rotational Damper
- Mechanical Building Block : Rotational Mass (Rotational Inertia)
- Modeling Examples :
- Mixing Problem(Single Tank)
- Mixing Problem(Two Tank)
- Mixing Problem (Three Tank)
- Physiologically Based Pharmacokinetic Model (Oxytetracycline Residues in Sheep)
- Velocity of Freefall Body
- Simple Pendulum - Newtonian
- Simple Pendulum - Lagrangian
- Single Spring
- Inverted Single Spring
- Inverted Spring-Mass with Damping
- Inverted Spring-Mass with Damping and Moving Base Line
- Inverted Spring-Mass with Damping and Moving Base Line and External Force
- Coupled Springs (Multi Spring)
- Electric Circuit Analysis
- Electro Mechanical System
- Differential Equation meeting Matrix
- Converting High Order Differential Equation into First Order Simultaneous Differential Equation
- Example : 2nd Order Homogeneous Lineare Differential Equation - System with No External Input
- Example : 2nd Order Non-Homogeneous Lineare Differential Equation - System with Single Input
- Example : Simultaneous Differential Equation (System Equation)
- Example from YouTube
- State Space Modeling
- Numerical Solution