1. 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 1 2 3 Canonical Form

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

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

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

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

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

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

8. 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 (4,0) (0,4) Steps 1)Find the parametric equations of C : 2) let 3) Replace

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

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

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