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The general linear 2ed order PDE in two variables x, y.

Chapter 2:Linear Second-Order Equations. Sec 2.2,2.3,2.4:Canonical Form. The general linear 2ed order PDE in two variables x, y. 1. 2. Canonical Form. 3. Chapter 2:Linear Second-Order Equations. Sec 2.2,2.3,2.4:Canonical Form. The general linear 2ed order PDE in two variables x, y. 1.

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The general linear 2ed order PDE in two variables x, y.

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  1. Chapter 2:Linear Second-Order Equations Sec 2.2,2.3,2.4:Canonical Form The general linear 2ed order PDE in two variables x, y. 1 2 Canonical Form 3

  2. Chapter 2:Linear Second-Order Equations Sec 2.2,2.3,2.4:Canonical Form The general linear 2ed order PDE in two variables x, y. 1 Use the transformation:

  3. Chapter 2:Linear Second-Order Equations Sec 2.2,2.3,2.4:Canonical Form

  4. Chapter 2:Linear Second-Order Equations Sec 2.2,2.3,2.4:Canonical Form The general linear 2ed order PDE in two variables x, y. 1 Step 1 Form characterestic equation: Solve these equations Step 2

  5. Chapter 2:Linear Second-Order Equations Sec 2.2,2.3,2.4:Canonical Form The general linear 2ed order PDE in two variables x, y. 2 Step 1 Form characterestic equation: Solve this equation Step 2 Choose any cont func with cont 1st 2ed partial derivatives with

  6. Chapter 2:Linear Second-Order Equations Sec 2.2,2.3,2.4:Canonical Form The general linear 2ed order PDE in two variables x, y. 3

  7. Chapter 2:Linear Second-Order Equations Sec 2.2,2.3,2.4:Canonical Form linear 2ed order PDE in two variables x, y. 3 In which k is a constant and (x0,y0) some chosen point. Such function will satisfy (*) exactly when the line integral is independent of path.

  8. (0,4) (4,0) Line integrals Integration of a function defined over an interval [a,b] Integration of a function defined along a curve C Example 1: Evaluation of the Line Integral Evaluate .along the the quarter-circle C • Steps • Find the parametric equations of C : • let • 3) Replace

  9. Under what condition the integral is independent of the path is independent of the path is an exact differential

  10. Chapter 2:Linear Second-Order Equations Sec 2.2,2.3,2.4:Canonical Form linear 2ed order PDE in two variables x, y. 3 Step 1 Solve for : Step 2 Write:

  11. Chapter 2:Linear Second-Order Equations Sec 2.2,2.3,2.4:Canonical Form Problems for section 2.1 through 2.4 (page 36-37) In each problem (a) classify (b) sketch the characteristics (c) find canonical MATLAB >> ezplot('y-2*x+1') >> hold on >> ezplot('y-2*x+4') >> ezplot('y-2*x-6') >>

  12. Chapter 2:Linear Second-Order Equations Sec 2.2,2.3,2.4:Canonical Form The general linear 2ed order PDE in two variables x, y. 1 2 Choose 3 Solve for :

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