Ordinary and Partial Differential Equations: Third Year College Course For Mathematicians, Physicists, and Engineers - Paperback

by Mohamed F. El-Hewie (Author)

This book comprises a course in differential equations, which students of engineering, physics, and mathematics complete as a requirement of bachelor in science degree. The reader must possess basic skills in calculus, since all elementary differentiations and integrations in this book assume that the student could visually spot the derivation from previous years in high school or college. The book is organized in the logical fashion as presented to college students. The ordinary differential equations (o.d.e.) are first studied in great details, since partial differential equations (p.d.e.) must be rendered ordinary by separation of variables so as yield meaningful solution. When separation of variables is untenable (such as in nonlinear partial differential equations), then referrals to numerical solutions are given. Within the scope of o.d.e., first- and second-order differential equations are discussed in details, also since equations of higher orders could be reduced in order by successive methods of substitutions, discussed in the book. Also, within the scope of o.d.e., equations with constant coefficients are dealt with greater details, since variable coefficients could be rendered constants by interim substitutions and reverse substations. Also, dealt with is the reduction of higher degrees of variables to lesser degrees. The following is a brief outline of the topics discussed in the book: Separable exact o.d.e oHomogeneous first-order o.d.e. oHomogenizing first-order o.d.e. with quadratic polynomial oCondition for a total derivative oSolving first-order o.d.e. by integrating factor oSolving first-order o.d.e. by product of two arbitrary functions g(x)f(x) oSolving first-order o.d.e. of higher degree by reduction of degree followed by using product of two arbitrary functions g(x)f(x) oSolving first-order o.d.e. of 2nd-degree by means of quadratic roots. oSolving first-order o.d.e. of 2nd-degree by substitutive reduction to 1st-degree oParametric integration of first-order o.d.e. of 2nd-degree to express y in terms of powers in y'. oGeneral solution of Clairaut's equation. oGeneral solution of Lagrange's equation. oOrthogonal curves of fluid flow. oOrthogonal projection of curves. oIsogonal projection of curves. oSolution of second-order o.d.e. by reducing it to first-order oSolution of second-order o.d.e. and higher degree by reducing it to first-order. oConditions required for general solution of homogeneous o.d.e. oReducing order of o.d.e. when a particular solution is know. oCharacteristic equations and solution of 2nd-order o.d.e. by D-Operator. oCharacteristic equations and solution of 2nd-order o.d.e. with complex roots. oGeneral and particular solutions of the non-homogenous 2nd-order o.d.e. oIntegrating 4th-order nonhomogeneous o.d.e. with sine function by using the Inverse D-Operator. oSimultaneous solution of 1st-order o.d.e. oSimultaneous solution of 2nd-order o.d.e. oOrder reduction of 3rd-order nonhomogeneous o.d.e. by known particular solution oSolving 2nd-order o.d.e by product of two arbitrary functions g(x)f(x). oSolution of 2nd-order nonhomogenous o.d.e. by the method of variable parameters oSolution by the method of change of the independent variable x oSolution of 2nd-order o.d.e. by power series. oSolution of 2nd-order o.d.e. by power series by Frobenius's method. oAiry-L vy's equation oElastic Vibration oHeat Equation oLaplace Equation oWave Equation oFree oscillation or homogeneous o.d.e. oForced oscillation or nonhomogeneous o.d.e. oEuler's elastic bending problem. oWhirling of elastic rod. oTransverse wave transmission in a vertical elastic body. oPropagation of sound waves in gas medium. oFlow of electricity in wire. oTelegraph Equations: oRadio Equations oHeat conducting plate with rectangular cross-section. oOne dimensional variable heat conduction oOne dimensional variable heat conduction with nonvanishing final tempe