常微分方程及其應用：理論與模型(英文)（簡體書）

《常微分方程及其應用：理論與模型》是常微分方程課程的英文教材，是作者結合多年的雙語教學經驗編寫而成。全書共5章，包括一階線性微分方程，高階線性微分方程，線性微分方程組。Laplace變換及其在微分方程求解中的應用，以及微分方程的穩定性理論。書中配有大量的應用實例和用Matlab軟件繪制的微分方程解的相圖，并介紹了繪制相圖的程序。 本書可作為高等院校理工科偏理或非數學專業的本科雙語教材，也可供相關專業的研究生、教師和廣大科技人員參考。

第1章 緒論

1．1 液壓控制系統概論

1．2 液壓控制系統的分類與適用場合

1．3 電液控制系統的基本組成及特點

1．4 電液控制技術的發展和應用概況

思考題及習題

第2章 電液控制基礎技術

2．1 信號檢測技術

2．2 電氣-機械轉換器

2．3 控制放大器

思考題及習題

第3章 液壓控制閥

3．1 概述

3．2 零開口四通圓柱滑閥的特性分析

3．3 正開口四通圓柱滑閥的特性分析

3．4 三通圓柱滑閥的特性分析

3．5 滑閥的功率輸出及效率

3．6 噴嘴擋板閥的特性分析

……

Chapter 1 First-order Differen-tial Equations
1.1 Introduction
Example 1.1.1 Dating of art works
On May 29， 1945， H.A.Van Meegeren， a third rate Dutch painter[3]， was arrested on the charge of collaborating with the enemy for [4] the sale to Goering of a painting of famed 17th century Dutch painter. Van Meegeren refused to accept the charge and an- nounced， in his prison cell [5]， that he had never sold painting to Goering. He stated that all the questioned paintings[6] were his own works. To settle the question an international panel of dis- tinguished chemists， physicists and art historians was appointed to investigate the matter. The panel took X-rays of the paint- ings to determine whether other paintings were underneath those paintings， analyzed the pigments[7] (coloring materials) used in the paintings， and examined the paintings for certain signs of old age[8].
The panel of experts found traces of the modern pigment cobalt blue[9] in some paintings. In addition， they also detected phenoformaldehyde[10]， which was not discovered until the turn of the 19th century[11]， in several paintings. On the basis of these evidences Van Meegeren was convicted， of forgery[12]， on October 12， 1947 and sentenced to one year in prison[13]. Two months later， he died of a heart attack.
However， many people refused to believe that the famed \Dis- ciples at Emmaus[14]" was a forgery[15]. In 1967， almost twenty years later， scientists at Carnegie Mellon University proved that the \Disciples at Emmaus" was indeed a forgery.
The key to the dating of materials lies in the phenomenon of radioactivity[16] discovered at the turn of the 20th century by the physicist Rutherford and his colleagues. They showed that the atoms of certain \radioactive" elements are unstable[17] and that within a given time period a fixed proportion of the atoms spontaneously disintegrates to form atoms of a new element[18]. Rutherford also showed that the radioactivity of a substance is directly proportional to[19] the number of atoms of the substance present. Let N(t) denotes the number of atoms present at time t， then dN/dt， the number of atoms that disintegrate per unit time， is proportional to N， thus we have the following equation
(1.1.1)
where[20] constant ， is positive and is known as the decay con- stant of the substance[21]. Usually， we use half-life[22]， the time required for half of a given quantity of radioactive atoms to decay， to measure the rate of disintegration of a substance. Assume that N(t0) = N0， then we have the mathematical model for computing half-life
(1.1.2)
By evaluating the present disintegration rates of the radioac- tive pigments in Van Meegeren's questioned paintings， the experts concluded that the paintings \Disciples at Emmaus"， \Woman Reading Music[23]" and \Woman Playing Mandolin[24]" must be modern forgeries.
Example 1.1.2 Detection of diabetes[25]
Diabetes mellitus[26] is a disease of metabolism which is charac- terized by too much sugar in the blood and urine[27]. Glucose tolerance test[28] (GTT) is a commonly used method to diagnose the disease. In this test， the patient is asked to take a large dose of glucose after an overnight fast[29]. During the next three to five hours， several measurements of the concentration of glu- cose are made in the patient's blood， and these measurements are used in the diagnosis of diabetes. Unfortunately， there is no universally accepted criterion[30] exist for interpreting the results of a GTT. Different physicians[31] interpreting the results of a GTT may come up with[32] different diagnoses. Here is a case. A Rhode Island physician， after reviewing the results of a GTT， came up with a diagnosis of diabetes. But another physician de- clared the patient to be normal after reviewing the results of the same GTT. To settle the question， the results of the GTT were sent to a specialist in Boston. After examining these results， the specialist concluded that the patient was suffering from a pituitary tumor[33].
In the mid-1960's， Drs. Rosevear and Molnar of the Mayo Clinic and Drs. Ackerman and Gatewood of the University of Min- nesota discovered a fairly reliable criterion for interpreting the re- sults of a GTT. They constructed a model which could accurately describe the blood glucose regulatory system[34] during a glucose tolerance test and in which one or two parameters[35] would yield criteria for distinguishing normal individuals from mild diabetics and prediabetics[36].
The basic model is described analytically[37] by following sys- tem of equations[38]
(1.1.3)
(1.1.4)
where G denotes the concentration of glucose in the blood and H denotes the concentration of the net hormonal[39] concentration. The function J(t) is the external rate at which the blood glucose concentration is being increased.
Definition 1.1.1 An equation relating an unknown function， its derivatives[40] and independent