lecture06

lecture06 - Section 2.4 Cont’d Feb 3 2009 Exact Equations...

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Unformatted text preview: Section 2.4, Cont’d Feb 3, 2009 Exact Equations Announcements WebAssign Assignment 2 is now online. The quiz this week will cover the integrating factor method Exact Equations Today’s session: Exact equations Solve dx = 0 Answer: x = C . The solution curves are a stream of parallel vertical lines (this means solution curves never cross). Solve dF = 0 Answer: F = C . The solution curves are a stream of parallel lines (in the appropriate frame; remember: solution curves never cross). dF = 0 is called an exact equation Fact: dF = ∂ F ∂ x dx + ∂ F ∂ y dy dF is also called a total differential Exact Equations Exact Equation Suppose we want to solve: dy dx =- M ( x , y ) N ( x , y ) Cross multiply: M ( x , y ) dx + N ( x , y ) dy = 0 Step 1. Try to compare it with something like: ∂ F ∂ x dx + ∂ F ∂ y dy = 0 Step 2. Identify the terms. This means: ∂ F ∂ x = M ( x , y ) and ∂ F ∂ y = N ( x , y ) Exact Equations Exact Equation, cont’d Step 3. Partial integrate one of the equation, then differentiate...
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This note was uploaded on 04/07/2009 for the course MATH taught by Professor Lotfi during the Spring '09 term at Arizona.

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lecture06 - Section 2.4 Cont’d Feb 3 2009 Exact Equations...

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