1° A. J. Clark School of Engineering °Department of Civil and Environmental EngineeringbyDr. Ibrahim A. AssakkafSpring 2001ENCE 203 - Computation Methods in Civil Engineering IIDepartment of Civil and Environmental EngineeringUniversity of Maryland, College ParkCHAPTER 8. DIFFERENTIAL EQUATIONS' AssakkafSlide No. 1° A. J. Clark School of Engineering ° Department of Civil and Environmental EngineeringENCE 203 ° CHAPTER 8. DIFFERENTIAL EQUATIONSIntroduction■Differential equations are used extensively in engineering and science to represent physical phenomena of a problem (problems).■A differential equation is any equation containing one or more derivative terms.■An ordinary differential equation is that involves a single independent variable.

2' AssakkafSlide No. 2° A. J. Clark School of Engineering ° Department of Civil and Environmental EngineeringENCE 203 ° CHAPTER 8. DIFFERENTIAL EQUATIONSIntroduction■Differential equations involving two or more independent variables are referred to as partial differential equations.■The analytical solutions of both ordinary and partial differential equations is called °closed-form solution°.■This solution requires the constant of integration be evaluated by using prescribed values of the independent variable(s).' AssakkafSlide No. 3° A. J. Clark School of Engineering ° Department of Civil and Environmental EngineeringENCE 203 ° CHAPTER 8. DIFFERENTIAL EQUATIONSIntroduction■Classification of Differential Equations± Ordinary Differential Equations² First-order² Higher-order² Linear² Nonlinear± Partial Differential Equations²These equations are usually classified according to their mathematical form.

3' AssakkafSlide No. 4° A. J. Clark School of Engineering ° Department of Civil and Environmental EngineeringENCE 203 ° CHAPTER 8. DIFFERENTIAL EQUATIONSIntroduction■Ordinary Differential Equations± The general forms of an ordinary differential equation is given by one of the following expression:( )( )( )( ))0(001010≠=+=+∑∑==mdxdx