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School: Capitol College
Course: Laplace And Fourier Analysis
MA360 Sp2006 Kallfelz Handout 6b (week of Feb 20 ) This cursory review of linear ODEs (first and second order) is entirely example-driven. First-order & Any garden variety first order linear ODE is of the form: a 0 (t )x(t ) + a1 (t )x(t ) = f (t ) , d &
School: Capitol College
Course: Laplace And Fourier Analysis
MA360 Sp2006 Kallfelz Handout 6a (week of Feb 20 ) Assignment: page 80 Sheng (Exercise 7) Problems 1,3,5,7 Example (#2, Sheng p 68) ( s 2 )(2 s 1)( s +1) 11s 2 2 s + 5 F (s ) = = (s2) A + (2 sB1) + ( s +1) C s=2 A= 112 2 22 + 5 ( 22 1)(2 +1) = 45 9 =5 27
School: Capitol College
Course: Laplace And Fourier Analysis
MA360 Sp2006 Kallfelz The Unit Impulse Function1 Handout 4b (week of Jan 30 ) Consider square wave of width a and height 1/a, anchored at t0, i.e.: a (t 0 ) = 1 a (u (t t 0 ) u (t (t 0 + a) ) = u (t t 0 ) u (t t 0 a ) a 1 a t0 t0 + a Then by definition:
School: Capitol College
Course: Laplace And Fourier Analysis
MA 360 ASSIGNMENT I Due: February 8, 2006 (during class (preferred due date.) Absolute due date: no later than 5:30 pm Monday, Feb. 20th (you can leave it in my faculty mailbox in faculty lounge) DIRECTIONS 1. In accordance with syllabus policy (page 2, s
School: Capitol College
Course: Laplace And Fourier Analysis
MA360 Handout 4a (week of Jan 30 ) Sp2006 Kallfelz Note: New (absolute) due date for Assignment I (See posted assignment sheet for details) Assignment: pp. 52-55 Sheng: 2a), b), e), 3b), c), 4a), d) Summary of Theorems (Ch 1, Sheng) Theorems 1. Lcfw_af(t)
School: Capitol College
Course: Laplace And Fourier Analysis
MA360 Sp2006 Kallfelz Handout 3b (week of Jan 23) Assignment: P 41 Sheng: 1,2,4,5( a), b), c),6( b), c), 7a) Second session of Class: Remaining Material in Ch I, Sheng Lemma 3b.1: limsL[f(t)] = limsF(s) = 0, for any continuous1 f. Proof: L[ f (t )] = f
School: Capitol College
Course: Laplace And Fourier Analysis
MA 360 ASSIGNMENT I Due: February 8, 2006 (during class (preferred due date.) Absolute due date: no later than 5:30 pm Monday, Feb. 20th (you can leave it in my faculty mailbox in faculty lounge) DIRECTIONS 1. In accordance with syllabus policy (page 2, s
School: Capitol College
Course: Laplace And Fourier Analysis
MA360 Sp2006 Kallfelz Handout 6b (week of Feb 20 ) This cursory review of linear ODEs (first and second order) is entirely example-driven. First-order & Any garden variety first order linear ODE is of the form: a 0 (t )x(t ) + a1 (t )x(t ) = f (t ) , d &
School: Capitol College
Course: Laplace And Fourier Analysis
MA360 Sp2006 Kallfelz Handout 6a (week of Feb 20 ) Assignment: page 80 Sheng (Exercise 7) Problems 1,3,5,7 Example (#2, Sheng p 68) ( s 2 )(2 s 1)( s +1) 11s 2 2 s + 5 F (s ) = = (s2) A + (2 sB1) + ( s +1) C s=2 A= 112 2 22 + 5 ( 22 1)(2 +1) = 45 9 =5 27
School: Capitol College
Course: Laplace And Fourier Analysis
MA360 Sp2006 Kallfelz The Unit Impulse Function1 Handout 4b (week of Jan 30 ) Consider square wave of width a and height 1/a, anchored at t0, i.e.: a (t 0 ) = 1 a (u (t t 0 ) u (t (t 0 + a) ) = u (t t 0 ) u (t t 0 a ) a 1 a t0 t0 + a Then by definition:
School: Capitol College
Course: Laplace And Fourier Analysis
MA 360 ASSIGNMENT I Due: February 8, 2006 (during class (preferred due date.) Absolute due date: no later than 5:30 pm Monday, Feb. 20th (you can leave it in my faculty mailbox in faculty lounge) DIRECTIONS 1. In accordance with syllabus policy (page 2, s
School: Capitol College
Course: Laplace And Fourier Analysis
MA360 Handout 4a (week of Jan 30 ) Sp2006 Kallfelz Note: New (absolute) due date for Assignment I (See posted assignment sheet for details) Assignment: pp. 52-55 Sheng: 2a), b), e), 3b), c), 4a), d) Summary of Theorems (Ch 1, Sheng) Theorems 1. Lcfw_af(t)
School: Capitol College
Course: Laplace And Fourier Analysis
MA360 Sp2006 Kallfelz Handout 3b (week of Jan 23) Assignment: P 41 Sheng: 1,2,4,5( a), b), c),6( b), c), 7a) Second session of Class: Remaining Material in Ch I, Sheng Lemma 3b.1: limsL[f(t)] = limsF(s) = 0, for any continuous1 f. Proof: L[ f (t )] = f
School: Capitol College
Course: Laplace And Fourier Analysis
MA360 Sp2006 Kallfelz Handout 3a (week of Jan 23) Assignment: P 41 Sheng: 1,2,4,5( a), b), c),6( b), c), 7a) First session of Class: Remaining problems from list of student questions that I didnt get to discussing Exercise 10, page 4 (Sheng) 0 t < 1 0 Fro
School: Capitol College
Course: Laplace And Fourier Analysis
MA360 Handout 1b (week of Jan 9) Sp2006 Kallfelz Assignment: 1,4,6,7,10 (pg5-Sheng) /2.(a),(c),(f),(h) (pg 17) [Read pp1-16, Sheng, and Review techniques and examples in Handouts1a, Handouts 1b] I.) The Laplace Transform Underlying Motivation(s) Consider
School: Capitol College
Course: Laplace And Fourier Analysis
MA 360 ASSIGNMENT I Due: February 8, 2006 (during class (preferred due date.) Absolute due date: no later than 5:30 pm Monday, Feb. 20th (you can leave it in my faculty mailbox in faculty lounge) DIRECTIONS 1. In accordance with syllabus policy (page 2, s