Ordinary differential equations 常微分方程
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内容提要：
Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines general solution of a differential equation. Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.
目录：
PREFACE FOR THE TEACHER
PREFACE FOR THE STUDENT 1 BASIC CONCEPTS Lisson 1 How Differential Equations Originate Lisson 2 The Meaning of the Terms Set and Function.Im-plicit Function.Elementary Functions. Lisson 3 The Differential Equation Lisson 4 The General Solution of a Differential Equation Lisson 5 Direction Field. 2 SPECIAL TYPES OF DIFFERENTIAL EQUATIONS OF THE FIRST ORDER Lisson 6 Meaning of the Differential of a Function.Separable Differential Differential Equations. Lisson 7 First Order Differential Equation with Homogeneous Coefficients Lisson 8 Differential Equations with Linear Coefficients. Lisson 9 Exact Differential Equations Lisson 10 Recognizable Exact Differential Equations.Integrating Factors. Lisson 11 The Linear Differential Equation of the Firat Order.Bernoulli Equation Lisson 12 Miscellaneous Methods of Solving a First Order Differential Equation. 3 PROBLEMS LEADING TO DIFFERENTIAL EQUATIONS OF THE FIRST ORDER Lisson 13 Geometric Problems. Lisson 14 Trajectories …… 4 LINEAR DIFFERENTIAL EQUATIONS OF ORDER GREATER THAN ONE 5 OPERATORS AND LAPLACE TRANSFORMS 6 PROBLEMS LEADING TO LINEAR DIFFERENTIAL EQUATIONS OF ORDER TWO 7 SYSTEMS OF DIFFERENTIAL EQUATIONS.LINEARIZATION OF FIRST ORDER SYSTEMS 8 PROBLEMS GIVING RISE TO SYSTEMS OF EQUATIONS.SPECIAL TYPES OF SECOND ORDER LINEAR AND NON-LINEAR EQUATIONS SOLVABLE BY REDUCING TO SYSTEMS 9 SERIES METHODS 10 NUMERICAL METHODS 11 EXISTENCE AND UNIQUENESS THEOREM FOR THE FIRSST ORDER DIFFERENTIAL EQUATION y'=f（x,y）.PICARD'S METHOD.ENVELOPES.CLAIRAUT EQUATION. 12 EXISTENCE AND UNIQUENESS THEOREMS FOR A SYSTEM OF FIRST ORDER DIFFERENTIAL EQUATIONS AND FOR LINEAR AND NONLINEAR DIFFERENTIAL EQUATIONS OF ORDER GREATER THAN ONE.WRONSKIANS. Bibliography Index |