Ross S.L. Introduction to Ordinary Differential Equations

4th Edition. — John Wiley & Sons, 1989. — 624 p. — ISBN: 0471098817The Fourth Edition of the best-selling text on the basic concepts, theory, methods, and applications of ordinary differential equations retains the clear, detailed style of the first three editions. Includes new material on matrix methods, numerical methods, the Laplace transform, and an appendix on polynomial equations. Stresses fundamental methods, and features traditional applications and brief introductions to the underlying theory.Differential Equations and Their Solutions.
Classification of Differential Equations; Their Origin and Application.
Solutions.
Initial-Value Problems, Boundary-Value Problems, and Existence of Solutions.
First-Order Equations for Which Exact Solutions Are Obtainable.
Exact Differential Equations and Integrating Factors.
Separable Equations and Equations Reducible to This Form.
Linear Equations and Bernoulli Equations.
Special Integrating Factors and Transformations.
Applications of First-Order Equations.
Orthogonal and Oblique Trajectories.
Problems in Mechanics.
Rate Problems.
Explicit Methods of Solving Higher-Order Linear Differential Equations.
Basic Theory of Linear Differential Equations.
The Homogeneous Linear Equation with Constant Coefficients.
The Method of Undetermined Coefficients.
Variation of Parameters.
The Cauchy-Euler Equation.
Statements and Proofs of Theorems on the Second-Order Homogeneous Linear Equation.
Applications of Second-Order Linear Differential Equations with Constant Coefficients.
The Differential Equation of the Vibrations of a Mass on a Spring.
Free, Undamped Motion.
Free, Damped Motion.
Forced Motion.
Resonance Phenomena.
Electric Circuit Problems.
Series Solutions of Linear Differential Equations.
Power Series Solutions About an Ordinary Point.
Solutions About Singular Points. The Method of Frobenius.
Bessel's Equation and Bessel Functions.
Systems of Linear Differential Equations.
Differential Operators and an Operator Method Applications.
Basic Theory of Linear Systems in Normal Form: Two Equations in Two Unknown Functions.
Homogeneous Linear Systems with Constant Coefficients: Two Equations in Two Unknown Functions.
Matrices and Vectors.
The Matrix Method for Homogeneous Linear Systems with Constant Coefficients: Two Equations in Two Unknown Functions.
The Matrix Method for Homogeneous Linear Systems with Constant Coefficients: n Equations in n Unknown Functions.
Statements and Proofs of Basic Theorems on Homogeneous Linear Systems.
Approximate Methods of Solving First-Order Equations.
Graphical Methods.
Power Series Methods
The Method of Successive Approximations.
Numerical Methods I: The Euler Method.
Numerical Methods II: The Improved Euler Method.
Numerical Methods III: The Runge-Kutta Method.
Numerical Methods IV: The Adams-Bashforth/Adams-Moulton (ABAM) Method.
Numerical Methods V: Higher-Order Equations; Systems.
The Laplace Transform.
Definition, Existence, and Basic Properties of the Laplace Transform.
The Inverse Transform and the Convolution.
Laplace Transform Solution of Linear Differential Equations with Constant Coefficients.
Laplace Transform Solution of Linear Differential Equations with Discontinuous Nonhomogeneous Terms.
Laplace Transform Solution of Linear Systems.
Appendix.
Suggested Reading.
Answers to Odd-Numbered Exercises.