Lecture on INFINITE SERIES AND DIFFERENTIAL EQUATIONS

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Lecture on INFINITE SERIES AND DIFFERENTIAL EQUATIONS

HANOI UNIVERSITY OF TECHNOLOGYFACULTY’ OF APPLIED MATHEMATICS AND INFORMATICS ADVANCED TRAINING PROGRAMLecture onINFINITE SERIES AND DIFFERENTIAL EQUA

Lecture on INFINITE SERIES AND DIFFERENTIAL EQUATIONS ATIONSDr. Nguyen Thieu HuyHa hoi-2009Wjwn Thev Hự/PrefaceThe Lecture OU infinite series and differential equations is written for students of Advanced

Training Programs of Mechatronics (from California State University-CSU Cliico) and Material Science (from University of Illinois- UIƯC). To prepare Lecture on INFINITE SERIES AND DIFFERENTIAL EQUATIONS

for the manuscript of this lecture, we have to combine not only the two syllabuses of two courses on Differential Equations (Math 260 of CSƯ Glico and

Lecture on INFINITE SERIES AND DIFFERENTIAL EQUATIONS

Math 385 of ƯIƯC). but also the part of infinke series that should have been given in Calculus I and II according to the syllabuses of rhe csu and UI

HANOI UNIVERSITY OF TECHNOLOGYFACULTY’ OF APPLIED MATHEMATICS AND INFORMATICS ADVANCED TRAINING PROGRAMLecture onINFINITE SERIES AND DIFFERENTIAL EQUA

Lecture on INFINITE SERIES AND DIFFERENTIAL EQUATIONS the same syllabus). Therefore, this lecture provides the most important modules of knowledge which are given in all syllabuses.Ulis lecture is intend

ed for engineering students and others who require a working knowledge of differential equations and series: included are technique and applications o Lecture on INFINITE SERIES AND DIFFERENTIAL EQUATIONS

f differential equations and infinite series. Since many physical laws and relations appear mathematically in the form of differential equations, such

Lecture on INFINITE SERIES AND DIFFERENTIAL EQUATIONS

equations are of fundamental importance in engineering mathematics. Therefore, the main objective of this course is to help students to be familiar w

HANOI UNIVERSITY OF TECHNOLOGYFACULTY’ OF APPLIED MATHEMATICS AND INFORMATICS ADVANCED TRAINING PROGRAMLecture onINFINITE SERIES AND DIFFERENTIAL EQUA

Lecture on INFINITE SERIES AND DIFFERENTIAL EQUATIONS solving such equations.Iwould like to thank Dr. Tran Xuan Tiep for his reading and reviewing of the manuscript. I would like to express my love and g

ratefulness to my wife Dr. Vu Thi Ngoc Ha for her constant support and inspừation during the preparation of the lecture.Hanoi. April 4. 2009Dr. Nguyen Lecture on INFINITE SERIES AND DIFFERENTIAL EQUATIONS

Thieu Huy1LèOưe on hlbtẽ Senes arc unerenoai tquanonsContentCHAPTER 1: INFINITE SERIES...........................................31.Definitions of In

Lecture on INFINITE SERIES AND DIFFERENTIAL EQUATIONS

finite Series and Fundamental Facts............32.Tests for Convergence and Divergence of Series of Constants.....43.Theorem on Absolutely Convergent

HANOI UNIVERSITY OF TECHNOLOGYFACULTY’ OF APPLIED MATHEMATICS AND INFORMATICS ADVANCED TRAINING PROGRAMLecture onINFINITE SERIES AND DIFFERENTIAL EQUA

Lecture on INFINITE SERIES AND DIFFERENTIAL EQUATIONS tions............102.Theorems on uniformly convergent series........................123.Power Series..................................................

.134.Fourier Series.................................................17Problems............................................................22CHAPTER 3: Lecture on INFINITE SERIES AND DIFFERENTIAL EQUATIONS

BASIC CONCEPT OF DIFFERENTIAL EQUATIONS..................281.Examples of Differential Equations.............................282.Definitions and Relat

Lecture on INFINITE SERIES AND DIFFERENTIAL EQUATIONS

ed Concepts...............................30CHAPTER 4: SOLUTIONS OF FIRST-ORDER DIFFERENTIAL EQUATIONS..........321.Separable Equations...............

HANOI UNIVERSITY OF TECHNOLOGYFACULTY’ OF APPLIED MATHEMATICS AND INFORMATICS ADVANCED TRAINING PROGRAMLecture onINFINITE SERIES AND DIFFERENTIAL EQUA

Lecture on INFINITE SERIES AND DIFFERENTIAL EQUATIONS .............334.Linear Equations...............................................355.Bernoulli Equations............................................366

.Modelling: Electric Circuits...................................37 Lecture on INFINITE SERIES AND DIFFERENTIAL EQUATIONS

HANOI UNIVERSITY OF TECHNOLOGYFACULTY’ OF APPLIED MATHEMATICS AND INFORMATICS ADVANCED TRAINING PROGRAMLecture onINFINITE SERIES AND DIFFERENTIAL EQUA