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Ordinary and Partial Differential Equations - Third Year College Course For Mathematicians, Physicists, and Engineers (Paperback)
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Ordinary and Partial Differential Equations - Third Year College Course For Mathematicians, Physicists, and Engineers (Paperback)
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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-Levy'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 temperature
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