{"product_id":"2940148421436","title":"Ordinary and Partial Differential Equations","description":"\u003cbr\u003e 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. \u003cbr\u003e\u003cbr\u003e 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. \u003cbr\u003e\u003cbr\u003eThe following is a brief outline of the topics discussed in the book:\u003cbr\u003e \u003cbr\u003e \u003cbr\u003eSeparable exact o.d.e\u003cbr\u003eo Homogeneous first-order o.d.e.\u003cbr\u003eo Homogenizing first-order o.d.e. with quadratic polynomial\u003cbr\u003eo Condition for a total derivative\u003cbr\u003eo Solving first-order o.d.e. by integrating factor\u003cbr\u003eo Solving first-order o.d.e. by product of two arbitrary functions g(x)f(x)\u003cbr\u003eo Solving first-order o.d.e. of higher degree by reduction of degree followed by using product of two arbitrary functions g(x)f(x)\u003cbr\u003eo Solving first-order o.d.e. of 2nd-degree by means of quadratic roots.\u003cbr\u003eo Solving first-order o.d.e. of 2nd-degree by substitutive reduction to 1st-degree  \u003cbr\u003eo Parametric integration of first-order o.d.e. of 2nd-degree to express y in terms of powers in  y'.\u003cbr\u003eo General solution of Clairaut’s equation.\u003cbr\u003eo General solution of Lagrange’s equation.\u003cbr\u003eo Orthogonal curves of fluid flow.\u003cbr\u003eo Orthogonal projection of curves.\u003cbr\u003eo Isogonal projection of curves.\u003cbr\u003eo Solution of second-order o.d.e. by reducing it to first-order\u003cbr\u003eo Solution of second-order o.d.e. and higher degree by reducing it to first-order.\u003cbr\u003eo Conditions required for general solution of homogeneous o.d.e.\u003cbr\u003eo Reducing order of o.d.e. when a particular solution is know.\u003cbr\u003eo Characteristic equations and solution of 2nd-order o.d.e. by D-Operator.\u003cbr\u003eo Characteristic equations and solution of 2nd-order o.d.e. with complex roots.\u003cbr\u003eo General and particular solutions of the non-homogenous 2nd-order o.d.e.\u003cbr\u003eo Integrating 4th-order nonhomogeneous o.d.e. with sine function by using the Inverse D-Operator.\u003cbr\u003eo Simultaneous solution of 1st-order o.d.e.\u003cbr\u003eo Simultaneous solution of 2nd-order o.d.e.\u003cbr\u003eo Order reduction of 3rd-order nonhomogeneous o.d.e. by known particular solution\u003cbr\u003eo Solving 2nd-order o.d.e by product of two arbitrary functions g(x)f(x).\u003cbr\u003eo Solution of 2nd-order nonhomogenous o.d.e. by the method of variable parameters\u003cbr\u003eo Solution by the method of change of the independent variable x\u003cbr\u003eo Solution of 2nd-order o.d.e. by power series. \u003cbr\u003eo Solution of 2nd-order o.d.e. by power series by Frobenius’s method.\u003cbr\u003eo Airy-Lévy’s equation  \u003cbr\u003eo Elastic Vibration\u003cbr\u003eo Heat Equation\u003cbr\u003eo Laplace Equation\u003cbr\u003eo Wave Equation\u003cbr\u003eo Free oscillation or homogeneous o.d.e.\u003cbr\u003eo Forced oscillation or nonhomogeneous o.d.e.\u003cbr\u003eo Euler’s elastic bending problem.\u003cbr\u003eo Whirling of elastic rod. \u003cbr\u003eo Transverse wave transmission in a vertical elastic body.\u003cbr\u003eo Propagation of sound waves in gas medium.\u003cbr\u003eo Flow of electricity in wire.\u003cbr\u003eo Telegraph Equations:\u003cbr\u003eo Radio Equations\u003cbr\u003eo Heat conducting plate with rectangular cross-section.\u003cbr\u003eo One dimensional variable heat conduction\u003cbr\u003eo One dimensional variable heat conduction with nonvanishing final temperature.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003eKeywords\u003cbr\u003e\u003cbr\u003eOrdinary differential equations, partial differential equations, separation of variables, power series, reduction of order and degrees, homogenizing variables, engineering applications, physical applications.\u003cbr\u003e","brand":"Mohamed F. 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