Differential Equations
DIFFERENTIAL EQUATIONS: A SIMPLIFIED APPROACH, 2nd Edition
DIFFERENTIAL EQUATIONS PRIMER By: AUSTRIA, Gian Paulo A. ECE / 3, Mapúa Institute of Technology NOTE: THIS PRIMER IS SUBJECT TO COPYRIGHT. IT CANNOT BE REPRODUCED WITHOUT PRIOR PERMISSION FROM THE AUTHOR. DEFINITIONS / TERMINOLOGIES A differential equation is an equation which involves derivatives and is mathematical models which can be used to approximate real-world problems. It is a specialized area of differential calculus but it involves a lot of integral calculus as well, so in general, differential equations straddle the specific parts of basic calculus or it can be considered part of advanced calculus. There are two general types of differential equations. An ordinary differential equation involves only two variables, whereas a partial differential equation involves more than two. A differential equation can have many variables. The independent variable is the variable of concern from which the terms are derived on, whereas if the same variable appears in its derivative, then it is a dependent variable. Variables are different from parameters, which are constants with no derivatives.
The given equation is the general differential equation for calorimetry. The variable q is dependent, t is dependent, and c and m are the parameters.
( (
) )
( (
) )
The equation shows that y is the dependent variable while x is the independent variable. Note that in the first term, y appeared in both the function and the derivative.
The order of a differential equation is the cardinality of the highest order derivative, while the degree is the exponential factor of the highest order in the equation.
The order of the equation is 3, because the highest order is y’’’ or y(3).
The order of the equation is 5, and its degree is 2. (Note: Do not be tempted to use the highest degree present as the degree of the equation.)
The linearity of the equation is determined by some factors: 1. The
DIFFERENTIAL EQUATIONS PRIMER By: AUSTRIA, Gian Paulo A. ECE / 3, Mapúa Institute of Technology NOTE: THIS PRIMER IS SUBJECT TO COPYRIGHT. IT CANNOT BE REPRODUCED WITHOUT PRIOR PERMISSION FROM THE AUTHOR. DEFINITIONS / TERMINOLOGIES A differential equation is an equation which involves derivatives and is mathematical models which can be used to approximate real-world problems. It is a specialized area of differential calculus but it involves a lot of integral calculus as well, so in general, differential equations straddle the specific parts of basic calculus or it can be considered part of advanced calculus. There are two general types of differential equations. An ordinary differential equation involves only two variables, whereas a partial differential equation involves more than two. A differential equation can have many variables. The independent variable is the variable of concern from which the terms are derived on, whereas if the same variable appears in its derivative, then it is a dependent variable. Variables are different from parameters, which are constants with no derivatives.
The given equation is the general differential equation for calorimetry. The variable q is dependent, t is dependent, and c and m are the parameters.
( (
) )
( (
) )
The equation shows that y is the dependent variable while x is the independent variable. Note that in the first term, y appeared in both the function and the derivative.
The order of a differential equation is the cardinality of the highest order derivative, while the degree is the exponential factor of the highest order in the equation.
The order of the equation is 3, because the highest order is y’’’ or y(3).
The order of the equation is 5, and its degree is 2. (Note: Do not be tempted to use the highest degree present as the degree of the equation.)
The linearity of the equation is determined by some factors: 1. The
References: Rainville, E. D., Bedient, P. E. (1989). Elementary Differential Equations, 7th Edition. New York City: Macmillan Publishing Company. Rainville, E. D., Bedient, P. E. (2005). Elementary Differential Equations, 8th Edition. New York City: Macmillan Publishing Company. 35 DIFFERENTIAL EQUATIONS: A SIMPLIFIED APPROACH, 2nd Edition For comments, reactions, and further suggestions, contact me at (0916) 356 5680 or (0908) 735 0633. You can also e-mail me at musashirhatakeyama674@gmail.com. Thank you for reading through this and I hope your adventure on MATH24 would be memorable. God bless you. 36