Chapter 1 First order Partial Differential Equations Sec
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Chapter 1: First order Partial Differential Equations Sec 1. 2: The Linear Equation Consider the linear first order partial differential equation in two independent variables: We assume that a, b, c, and f are functions in (x, y). They are continuous in some region of the plane. a(x, y) and b(x, y) are not both zero for the same (x, y) (? ? ? ) We will show to solve this equation. The key is to determine a change of variable
Chapter 1: First order Partial Differential Equations Sec 1. 2: The Linear Equation PDE ODE Consider the ODE: 1 st order linear ODE Method: Find integrating factor = K Multiply equation by K LHS = Integrate both sides
Chapter 1: First order Partial Differential Equations Sec 1. 2: The Linear Equation Characteristic equation Consider the linear 1 st PDE Find the general solution of the. PDE solution
Chapter 1: First order Partial Differential Equations Sec 1. 2: The Linear Equation Consider the linear first order partial differential equation in two independent variables: 1. Find the characteristic equation: 2. Find the general solution of the characteristic equation and put it in the form: 3. Use the transformation: 4. To change PDE into this form:
Chapter 1: First order Partial Differential Equations Sec 1. 2: The Linear Equation Consider the linear 1 st PDE 1 2 3 4 characteristic equation: Solution: transformation:
Chapter 1: First order Partial Differential Equations Sec 1. 2: The Linear Equation Consider the linear 1 st PDE characteristic curves: 1 2 3 4 characteristic equation: C=4 Solution: C=1 transformation: C=-4
