Do students really understand what an ordinary differential equation is?
From an analysis of the students’ answers, it was concluded that the students who were quite successful in algebraic solutions, indeed did not fully understand the related concepts, and they had serious difficulties in relation to these concepts.
What do you mean by ordinary differential equation?
In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions.
Why are odes important in describing biological systems?
Among the different modeling approaches, ordinary differential equations (ODE) are particularly important and have led to significant advances. Ordinary differential equations are used to model biological processes on various levels ranging from DNA molecules or biosynthesis phospholipids on the cellular level.
What is differential equations used for in engineering?
Differential equations are mathematical tools to model engineering systems such as hydraulic flow, heat transfer, level controller of a tank, vibration isolation, electrical circuits, etc.
What is the Order of the ordinary differential equations?
The order of ordinary differential equations is defined to be the order of the highest derivative that occurs in the equation. The general form of n-th order ODE is given as; F (x, y,y’,….,yn ) = 0. Note that, y’ can be either dy/dx or dy/dt and yn can be either dny/dxn or dny/dtn. An n-th order ordinary differential equations is linear
Why is it important to study differential equations?
Since one of the fundamental laws of nature is a differential equation, it makes sense that you should study differential equations if you want to understand nature. I don’t know who said it first but I’ve always liked the quote “The laws of nature are expressed as differential equations”
What are differentdifferential equations?
Differential equations are equations that contains one or more terms involving derivatives of one variable (dependent variable) with respect to another variable (independent variable) or we can say that these are equations involving derivatives of a function or functions. They have a remarkable ability to predict the world around us.
Why do people use maple for differential equations?
There are several reasons. Perhaps most important is Maple’s ability to draw graphs of solutions, which often makes their important features much more apparent. Maple also has a powerful symbolic differential equations solver that produces expressions for solutions in most cases where such expressions are known to exist.