bt2 - HCMUT – HCMNU Chapter1: First Order Differential...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: HCMUT – HCMNU Chapter1: First Order Differential Equations Faculty of Applied science 11/2/2009 Department of Math. Applied ________________________________________________________________________ Caâu 1 Tìm haøm u = u ( x, y ) thoaûphöôngtrìnhñaïo haømrieângcaáp1 vaøñieàukieänbieânsaubaèngphöôngphaùptaùchbieán: ∂u ∂u =M , u ( 0, y ) = Me −2 y + ( 2 M + 1) e 3 y ∂x ∂y Trình baøyvaéntaétcaùcböôùcgiaûi baøi toaùntruyeànnhieät sauvôùi phöôngphaùptaùchbieán(coùtheåsöûduïngñònhlyù nghieämduy nhaátcuûabaøi toaùnbieâncaáp2) ∂u ∂ 2u = 2M 2 , 0 < x < π , t > 0 ∂t ∂x u ( 0, t ) = u ( π , t ) = 0 , t > 0 & u ( x,0 ) = 2 M sin ( Mx ) + ( 3M + 1) sin ( 2 Mx ) , 0 < x < π Caâu 3 Trình baøyvaéntaétcaùcböôùcgiaûi baøi toaùntruyeànsoùng sauvôùi phöôngphaùptaùchbieán(coùtheåsöûduïngñònhlyù nghieämduy nhaátcuûabaøi toaùnbieâncaáp2) ∂ 2u M 2 ∂ 2u , 0< x <π , t >0 = ⋅ 4 ∂x 2 ∂t 2 & u ( 0, t ) = u ( π , t ) = 0 , 0< x <π t >0 Exercises No 2. Caâu 2 u ( x,0 ) = M sin ( Mx ) + ( 2 M + 1) sin ( 2 Mx ) , ∂u ( x,0) = M sin ( ( M − 1) x ) + ( M + 1) sin ( Mx ) , 0 < x < π ∂t 2 Với M=2. 1 ...
View Full Document

This note was uploaded on 11/02/2009 for the course ECE ece464 taught by Professor Abc during the Spring '09 term at Jacksonville College.

Ask a homework question - tutors are online