IDE Chap1 Lec1 Basic Notion

IDE Chap1 Lec1 Basic Notion - HUT – DEPARTMENT OF MATH...

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Unformatted text preview: HUT – DEPARTMENT OF MATH. APPLIED ---------------------------------------------------------------------------------------------------------- INTRO DIFFERENTIAL EQUATIONS CHAPTER 1: First Order Differential Equations (2 weeks) LEC 1: BASIC NOTIONS OF FIRST ORDER DIFFERENTIAL EQUATION PhD. NGUYEÃN QUOÁC LAÂN (9/2007) CONTENTS----------------------------------------------------------------------------------------------------------------------------------- 1.2 GENERAL AND PARTICULAR SOLUTIONS 1.3 DIRECTION FIELD AND SOLUTION CURVES 1.1 DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELS 1.1 INTRODUCTION -------------------------------------------------------------------------------------------------------------- A differential equation is an equation involving an unknown function: y = y(x) (or y = y(t)) and its derivatives y’, y’’, y’’’ … Example: The following equations are DE with the unknown y ( ) 1 3 5 ' + = x y ( ) ( ) ( ) 2 = − + + dy y x dx y x ( ) 3 sin 2 ' 3 ' ' x y y y = + − ( ) ( ) t x y y t y x y , unknown : 4 2 = ∂ ∂ = ∂ ∂ 1.1 MATHEMATICAL MODELS --------------------------------------------------------------------------------------------------------------...
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IDE Chap1 Lec1 Basic Notion - HUT – DEPARTMENT OF MATH...

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