f11week02

f11week02 - Week 2 2 Homework 2 Chapter 1 Section 7(mixing...

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Unformatted text preview: Week 2: 2. Homework 2: Chapter 1, Section 7 (mixing problems only) Chapter 2, Sections 1, 2, 3 Due Monday, Jan 31st 2 Chapter 1: 1.7 Mixing problems (Monday ) Chapter 2: 2.1, 2.2 Matrices, Matrix Algebra (Wednesday ) 2.2 Matrix Algebra (continued), 2.3 Linear Systems (Friday ) 3 Linear DE, Main Step: to solve linear DE dy dx + p ( x ) y = q ( x ) multiply by the integral factor f = e integraltext p dx and use d dx ( fy ) = f ( y ′ + py ) on the left to get d dx ( fy ) = fq. 4 Problem: Inflamable substance, temp T = 50 (F), placed in hot oven, temp T m = 450 (F). After 20 min substance temp T = 150 . Find temp at 40 min. If substance ignites at 350, find time of combustion. Solution: Newton’s Law of cooling: T = T ( t ) temp at time t, dT dt = − k ( T − T m ) , T m = 450 , t in min. ————– dT dt = − k ( T − T m ) , T m = 450 , T (0) = 50 , T (20) = 150 , find T (40) and t c so T ( t c ) = 350 . Method: separation....
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This note was uploaded on 11/24/2011 for the course MATH 205 taught by Professor Zhang during the Spring '08 term at Lehigh University .

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f11week02 - Week 2 2 Homework 2 Chapter 1 Section 7(mixing...

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